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Topology control in wireless sensor networks

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Topology control in wireless sensor networks
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Wightman Rojas, Pedro
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Network Topology
Topology Construction
Topology Maintenance
Connectivity
Sensing Coverage
Connected Dominating Set
Dissertations, Academic -- Computer Science and Engineering -- Doctoral -- USF   ( lcsh )
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Abstract:
ABSTRACT: Wireless Sensor Networks (WSN) offer a flexible low-cost solution to the problem of event monitoring, especially in places with limited accessibility or that represent danger to humans. WSNs are made of resource-constrained wireless devices, which require energy efficient mechanisms, algorithms and protocols. One of these mechanisms is Topology Control (TC) composed of two mechanisms, Topology Construction and Topology Maintenance. This dissertation expands the knowledge of TC in many ways. First, it introduces a comprehensive taxonomy for topology construction and maintenance algorithms for the first time. Second, it includes four new topology construction protocols: A3, A3Lite, A3Cov and A3LiteCov. These protocols reduce the number of active nodes by building a Connected Dominating Set (CDS) and then turning off unnecessary nodes. The A3 and A3-Lite protocols guarantee a connected reduced structure in a very energy efficient manner. The A3Cov and A3LiteCov protocols are extensions of their predecessors that increase the sensing coverage of the network. All these protocols are distributed -they do not require localization information, and present low message and computational complexity. Third, this dissertation also includes and evaluates the performance of four topology maintenance protocols: Recreation (DGTRec), Rotation (SGTRot), Rotation and Recreation (HGTRotRec), and Dynamic Local-DSR (DLDSR). Finally, an event-driven simulation tool named Atarraya was developed for teaching, researching and evaluating topology control protocols, which fills a need in the area of topology control that other simulators cannot. Atarraya was used to implement all the topology construction and maintenance cited, and to evaluate their performance. The results show that A3Lite produces a similar number of active nodes when compared to A3, while spending less energy due to its lower message complexity. A3Cov and A3CovLite show better or similar coverage than the other distributed protocols discussed here, while preserving the connectivity and energy efficiency from A3 and A3Lite. In terms of network lifetime, depending on the scenarios, it is shown that there can be a substantial increase in the network lifetime of 450% when a topology construction method is applied, and of 3200% when both topology construction and maintenance are applied, compared to the case where no topology control is used.
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Dissertation (Ph.D.)--University of South Florida, 2010.
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by Pedro Wightman Rojas.
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TopologyControlinWirelessSensorNetworks by PedroMarioWightmanRojas Adissertationsubmittedinpartialfulllment oftherequirementsforthedegreeof DoctorofPhilosophy DepartmentofComputerScience&Engineering CollegeofEngineering UniversityofSouthFlorida MajorProfessor:MiguelA.Labrador,Ph.D. RafaelPerez,Ph.D. KennethChristensen,Ph.D. WilfridoMoreno,Ph.D. WilliamR.Stark,Ph.D. DateofApproval: February12,2010 Keywords:NetworkTopology,TopologyConstruction,TopologyMaintenance, Connectivity,SensingCoverage,ConnectedDominatingSet c 2010,PedroMarioWightmanRojas

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TomythreemusesAstrid,HillaryandSophiabecauseallofyouinspiremetobealittle bitbettereveryday,andtoMotherNaturefortheawesomejobshedoeswithhertrees whichIhumblytrytoreplicate

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Acknowledgements ThelastveyearshavebeenpartofanexperienceinwhichIhavegratefullyhadthe opportunitytogrownotonlyasaprofessionalbutasahumanbeing. IwillstartbythankingmymentorandadviserDr.MiguelLabrador,whohasguidedand supportedmethroughouttheseyearswithadmirablepatience,andwhoalsohasbecome agoodfriend.ThanksalsotoallthestaffattheDepartmentofComputerScienceand EngineeringatUSFandUniversidaddelNortewhichhavebeenalwaysthereforme. ThankstomycommitteeDr.Christensen,Dr.Moreno,Dr.PerezandDr.Starkforacceptingmyinvitationtobepartofthisexperienceandfortheirvaluablecommentsand suggestions. MydeepestgratitudetomywifeHillaryandmybeloveddaughterSophia,whoselove, patienceandsupporthavehelpedtokeepmeontherighttrack.Iextendthisgratitude especiallytomymotherforherunconditionallove,andtomyparents-in-lawwithout whosehelpIwouldnothavehadtheopportunitytonishthisdissertation. ThankstoallmyfriendswhoInolongerconsiderjustfriends,becausewehavebecome morelikeafamily:thankstoDala,Migue,andallthepeoplefromtheInformationSystemsLabfortheirsupportandthegoodlaughs.SpecialthankstoAldowhosehelpwas criticalinthesenalmonthsandtoAlcidesforthenameofthesimulator,amongother excellentsuggestions. Finally,andmostimportantly,IthankGodforgivingmetheopportunitytogrowand improvemyselfinordertobeabletoservebetter.

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TableofContents ListofTablesvii ListofFiguresviii Abstractxiii Chapter1Introduction1 1.1WirelessSensorNetworks2 1.2TopologyControl5 1.2.1NetworkTopology5 1.2.2DenitionofTopologyControl8 1.3ProblemStatement11 1.4Contributions15 1.5StructureoftheDissertation17 Chapter2LiteratureReview19 2.1TopologyControlTaxonomy20 2.1.1TopologyConstructionTaxonomy21 2.1.2TopologyMaintenanceTaxonomy22 2.2Connectivity-orientedTopologyConstruction23 i

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2.2.1ControllingtheTransmissionPower24 2.2.1.1CentralizedApproaches24 2.2.1.2DistributedApproaches29 2.2.1.3HeterogeneousDevices32 2.2.2HierarchicalTechniques33 2.2.2.1Backbone-basedTechniques34 2.2.2.2Cluster-basedTechniques43 2.2.2.3AdaptiveTechniques44 2.2.3HybridApproaches44 2.3Coverage-orientedTopologyConstruction45 2.3.1ClassicationFactors46 2.3.1.1DenitionoftheAreaofInterest47 2.3.1.2Redundancy48 2.3.2OtherConsiderationsinCoverage-orientedTopology ConstructionProtocols49 2.3.3ExamplesofCoverage-orientedTopologyConstruction Protocols50 2.4TopologyMaintenance61 2.4.1ClassicationFactors62 2.4.1.1SelectionPolicy:Static,DynamicandHybrid62 2.4.1.2LevelofInvolvement:GlobalandLocal65 2.4.1.3TriggeringMechanisms66 ii

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2.4.2ExamplesofTopologyMaintenanceAlgorithms68 Chapter3Methodology72 3.1AnAnalyticalSolutiontotheMCDSProblem72 3.2TheMIPApproachfortheMinimumConnectedDominating SetProblem77 3.3PerformanceEvaluation:Assumptions,Metrics,Factorsand Levels82 3.3.1Assumptions82 3.3.2PerformanceMetrics83 3.3.3FactorsandLevels84 3.3.4EnergyModel86 Chapter4TheA3andA3LiteTopologyConstructionProtocolsforConnectivity88 4.1Introduction89 4.2TheA3Algorithm90 4.2.1TheNeighborhoodDiscoveryProcess91 4.2.2ChildrenSelectionProcess92 4.2.3SecondOpportunityProcess94 4.2.3.1TheSelectionMetric96 4.3TheA3LiteAlgorithm98 4.3.1TheNeighborhoodDiscoveryProcess98 4.3.2ChildrenSelectionProcess99 4.4PerformanceEvaluation100 iii

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4.4.1Experiment1:ChangingtheNodeDegree102 4.4.2Experiment2:ChangingtheNodeDensity105 4.4.3Experiment3:IdealGridTopologies108 Chapter5TheA3CovandA3CovLiteTopologyConstructionProtocolsfor Coverage111 5.1TheA3CovAlgorithm112 5.2TheA3CovLiteAlgorithm116 5.3The a -CoverageSensingCoverageDenition116 5.4PerformanceEvaluation119 5.4.1ComparisonwithTheoreticalDeployments120 5.4.1.1Experiment1:SameRadii123 5.4.1.2Experiment2:DifferentRadii128 5.4.1.3Experiment3:Different a -coverage132 5.4.2ComparisonwithDistributedProtocols138 5.4.2.1ComparisonWithACOS138 5.4.2.2ComparisonWithStanGA143 Chapter6TopologyMaintenanceProtocols146 6.1Introduction146 6.2StaticGlobalTopologyRotation147 6.3DynamicGlobalTopologyRecreation148 6.4DynamicLocal-DSR149 6.5HybridGlobalTopologyRecreationandRotation152 iv

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6.6PerformanceEvaluation153 6.6.1PerformanceEvaluationofStaticGlobalTopology MaintenanceTechniques155 6.6.1.1SparseNetworks156 6.6.1.2DenseNetworks160 6.6.2PerformanceEvaluationofDynamicGlobalTopology MaintenanceTechniques161 6.6.2.1SparseNetworks163 6.6.2.2DenseNetworks164 6.6.3PerformanceEvaluationofDynamicLocalTopology MaintenanceTechniques168 6.6.3.1SparseNetworks169 6.6.3.2DenseNetworks169 6.6.4PerformanceEvaluationofHybridGlobalTopology MaintenanceTechniques171 6.6.4.1SparseNetworks174 6.6.4.2DenseNetworks174 6.7ComparisonofTopologyMaintenanceTechniques176 6.8SensitivityAnalysis181 6.8.1Time-basedAnalysis182 6.8.2Energy-basedAnalysis184 6.8.3Density-basedAnalysis186 Chapter7ConclusionsandFutureWork191 v

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7.1Conclusions191 7.2SummaryofContributions193 7.3FutureWork195 ListofReferences197 Appendices210 AppendixA:ABriefOverviewofAtarraya211 AbouttheAuthorEndPage vi

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ListofTables Table3.1Parametersfortheenergymodel.87 Table4.1Simulationparametersforconnectivity-orientedprotocols.101 Table5.1Simulationparametersforcoverage-orientedprotocols.121 Table5.2Radiiandtopologysizesforcoverage-orientedprotocols.123 Table6.1Simulationparametersfortopologymaintenanceprotocols.154 vii

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ListofFigures Figure1.1Diagramofcomponentsofawirelesssensordevice.2 Figure1.2Exampleofanetworkarchitecturethatincludesawirelesssensor network.3 Figure1.3Comparisonoftopologies:theMaxPowerGraphversusthereduced topology.7 Figure1.4Diagramthatmodelstheiterativeexecutionofatopologycontrol algorithm.11 Figure2.1Generaltaxonomyfortopologycontrolprotocols.21 Figure2.2Taxonomyofconnectivity-orientedtopologyconstructionprotocols.24 Figure2.3Topologycontrolbyreducingthenumberofactivenodesandthe creationofanetworkbackbone.35 Figure2.4Growingatreewith1-hopneighborinformation.37 Figure2.5Classicationofcoverage-orientedtopologyconstructionprotocols.46 Figure2.6Differentdeploymentgeometriesforconnectedcoveragetopologies with R S = R C .52 Figure2.7Exampleoforiginalandmodiedsolutionsofthecirclepacking problem.56 Figure2.8Theoreticalcomparisonbetweenthepackingproblemandtheoptimal deployments.57 Figure2.9Multiplenode-disjointCDStreesoverthesamenetwork.64 viii

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Figure2.10Classicationoftopologymaintenance.68 Figure3.1ExamplesofMDSsolutions.73 Figure3.2Exampleoftheowoftokenstechnique.79 Figure4.1TheA3algorithm.91 Figure4.2TheA3protocolnitestatemachine.92 Figure4.3TheA3Liteprotocolnitestatemachine.98 Figure4.4Resultsofexperiment1:changingthenodedegree.103 Figure4.5Resultsofexperiment2:changingthenodedensity.106 Figure4.6Squaregridsdeployment.108 Figure4.7Resultsofexperiment3:idealgridtopologies.110 Figure5.1TheA3Covprotocolnitestatemachine.113 Figure5.2TheA3CovLiteprotocolnitestatemachine.115 Figure5.3Exampleof a -coverage.117 Figure5.4Performanceinsparsenetworkswhen R Comm = R Sense .125 Figure5.5Performanceindensenetworkswhen R Comm = R Sense .126 Figure5.6Performanceinsparsenetworkswhen R Comm > R Sense .129 Figure5.7Performanceindensenetworkswhen R Comm > R Sense .130 Figure5.8Performanceinsparsenetworkswhen R Comm > R Sense and a > 1.133 Figure5.9Performanceindensenetworkswhen R Comm > R Sense and a > 1.134 Figure5.10Performanceinsparsenetworkswhen R Comm > R Sense and a < 1.136 Figure5.11Performanceindensenetworkswhen R Comm > R Sense and a < 1.137 ix

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Figure5.12PerformanceoftheA3CovandA3CovLiteprotocolsinsparsenetworkswithdifferentradiiand a -coverageparameter.139 Figure5.13PerformanceoftheA3CovandA3CovLiteprotocolsindensenetworkswithdifferentradiiand a -coverageparameter.140 Figure5.14ComparisonofperformanceoftheA3Cov,A3CovLiteprotocolsand theACOSprotocolfor800nodes.142 Figure5.15ComparisonofperformanceoftheA3Cov,A3CovLiteprotocolsand theStanGAprotocolfordifferentcoveragecongurations.144 Figure6.1PhaseoneoftheDSR-baseddynamiclocaltopologymaintenance technique.151 Figure6.2Networklifetimewithandwithoutstaticglobaltopologymaintenance usingtheA3,EECDS,andCDS-Rule-Ktopologyconstructionmechanismsinsparsenetworks.158 Figure6.3Bestperformingstaticglobaltopologymaintenancetechniquesin sparsenetworks.159 Figure6.4Networklifetimewithandwithoutstaticglobaltopologymaintenance usingtheA3,EECDS,andCDS-Rule-Ktopologyconstructionmechanismsindensenetworks.162 Figure6.5Bestperformingstaticglobaltopologymaintenancetechniquesin densenetworks.163 Figure6.6NetworklifetimewithandwithoutdynamicglobaltopologymaintenanceusingtheA3,EECDS,andCDS-Rule-Ktopologyconstruction mechanismsinsparsenetworks.165 Figure6.7Bestperformingdynamicglobaltopologymaintenancetechniquesin sparsenetworks.166 Figure6.8NetworklifetimewithandwithoutdynamicglobaltopologymaintenanceusingtheA3,EECDS,andCDS-Rule-Ktopologyconstruction mechanismsindensenetworks.167 Figure6.9Bestperformingdynamicglobaltopologymaintenancetechniquesin densenetworks.168 x

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Figure6.10NetworklifetimewithandwithoutdynamiclocaltopologymaintenanceusingtheA3,EECDS,andCDS-Rule-Ktopologyconstruction mechanismsinsparsenetworks.170 Figure6.11Bestperformingdynamiclocaltopologymaintenancetechniquesin sparsenetworks.171 Figure6.12NetworklifetimewithandwithoutdynamiclocaltopologymaintenanceusingtheA3,EECDS,andCDS-Rule-Ktopologyconstruction mechanismsindensenetworks.172 Figure6.13Bestperformingdynamiclocaltopologymaintenancetechniquesin densenetworks.173 Figure6.14NetworklifetimewithandwithouthybridglobaltopologymaintenancetechniquesusingtheA3,EECDS,andCDS-Rule-Ktopology constructionmechanismsinsparsenetworks.175 Figure6.15Bestperforminghybridglobaltopologymaintenancetechniquesin sparsenetworks.176 Figure6.16NetworklifetimewithandwithouthybridglobaltopologymaintenancetechniquesusingtheA3,EECDS,andCDS-Rule-Ktopology constructionmechanismsindensenetworks.177 Figure6.17Bestperforminghybridglobaltopologymaintenancetechniquesin densenetworks.178 Figure6.18Bestperformingtopologymaintenancetechniquesinsparseand densenetworks.179 Figure6.19Time-basedsensitivityanalysisofnetworklifetimeforstatic,dynamic,andhybridtopologymaintenancetechniques.183 Figure6.20Bestperformingtechniquesoutoftimesensitivitytests.184 Figure6.21Energy-basedsensitivityanalysisofnetworklifetimeforstatic,dynamic,andhybridtopologymaintenancetechniques.185 Figure6.22Bestperformingtechniquesoutofenergysensitivitytests.186 xi

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Figure6.23Nodedensity-basedsensitivityanalysisofnetworklifetimeforstatic, dynamic,andhybridtopologymaintenancetechniques.187 Figure6.24Bestperformingtechniquesoutofthedensitysensitivitytests.189 Figure6.25Comparisonofnetworklifetimewhenusingtopologyconstruction andmaintenance,topologyconstructiononlyandnotopologycontrol.190 FigureA.1Atarraya'sfunctionalcomponents.213 FigureA.2Usefuldiagramstodesignacommunicationprotocol.243 FigureA.3Simulationcontrolpanel.247 FigureA.4Otherprotocolsforeducationalpurposes.249 FigureA.5DifferenttopologydesignsgeneratedbyAtarraya.256 FigureA.6Deploymentdenitionpanel.257 FigureA.7Otherparametersfordeploymentdenition.261 FigureA.8ExampleofstatisticsgeneratedbyAtarraya.264 FigureA.9Reportpanel.265 FigureA.10Nodestatisticspanel.266 FigureA.11Mainwindowdescription.267 FigureA.12Visualizationcontrolpanel.268 xii

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TopologyControlinWirelessSensorNetworks PedroMarioWightmanRojas ABSTRACT WirelessSensorNetworksWSNofferaexiblelow-costsolutiontotheproblemof eventmonitoring,especiallyinplaceswithlimitedaccessibilityorthatrepresentdanger tohumans.WSNsaremadeofresource-constrainedwirelessdevices,whichrequireenergyefcientmechanisms,algorithmsandprotocols.OneofthesemechanismsisTopologyControlTCcomposedoftwomechanisms,TopologyConstructionandTopology Maintenance. ThisdissertationexpandstheknowledgeofTCinmanyways.First,itintroducesacomprehensivetaxonomyfortopologyconstructionandmaintenancealgorithmsfortherst time.Second,itincludesfournewtopologyconstructionprotocols:A3,A3Lite,A3Cov andA3LiteCov.TheseprotocolsreducethenumberofactivenodesbybuildingaConnectedDominatingSetCDSandthenturningoffunnecessarynodes.TheA3andA3Liteprotocolsguaranteeaconnectedreducedstructureinaveryenergyefcientmanner. TheA3CovandA3LiteCovprotocolsareextensionsoftheirpredecessorsthatincrease thesensingcoverageofthenetwork.Alltheseprotocolsaredistributedtheydonot requirelocalizationinformation,andpresentlowmessageandcomputationalcomplexity. Third,thisdissertationalsoincludesandevaluatestheperformanceoffourtopology maintenanceprotocols:RecreationDGTRec,RotationSGTRot,RotationandRecreationHGTRotRec,andDynamicLocal-DSRDLDSR. xiii

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Finally,anevent-drivensimulationtoolnamedAtarrayawasdevelopedforteaching, researchingandevaluatingtopologycontrolprotocols,whichllsaneedintheareaof topologycontrolthatothersimulatorscannot.Atarrayawasusedtoimplementallthe topologyconstructionandmaintenancecited,andtoevaluatetheirperformance.TheresultsshowthatA3LiteproducesasimilarnumberofactivenodeswhencomparedtoA3, whilespendinglessenergyduetoitslowermessagecomplexity.A3CovandA3CovLite showbetterorsimilarcoveragethantheotherdistributedprotocolsdiscussedhere,while preservingtheconnectivityandenergyefciencyfromA3andA3Lite.Intermsofnetworklifetime,dependingonthescenarios,itisshownthattherecanbeasubstantialincreaseinthenetworklifetimeof450%whenatopologyconstructionmethodisapplied, andof3200%whenbothtopologyconstructionandmaintenanceareapplied,compared tothecasewherenotopologycontrolisused. xiv

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Chapter1:Introduction Dataistoday'sgold:ndingnewsources,newwaystogatheritandnewkindsofconclusionstodrawfromitarebecomingveryattractiveresearchareaswithcountlessapplicationsintheworld.Inthetimeyouspentreadingthisdissertation,billionsofbitswillbe generatedwiththeonlypurposeofgatheringdataaboutvirtuallyeverything:howmany carsarecrossingtheSkywaybridgeinSt.Petersburg,FL,thetemperatureoneachoor oftheEmpireStatebuildinginNewYorkcity,orthecurrentlocationofagroupofzebras inthesavannasofCentralAfrica,andthisisjustthebeginning.However,gatheringthis datafromplacesthatarenoteasilyaccessibleorthataredangeroustohumansrequires therighttechnology. Onetechnologythattstherequirementsneededforalow-costandexiblewaytoobtain datafromvirtuallyanylocation,fromurbanenvironments,topersonalnetworksandalso scenarioswithlimitedaccesstocommunicationandpowerinfrastructuresis Wireless SensorNetworksWSNs .Asitwillbeseenlateronthischapter,thesenetworksaremade ofdevicesveryconstrainedinresources,whichmakesitimperativeforthemtoworkin averyefcientmanner,especiallyintermsofenergyconsumption.Oneofthewaysa WSNcanbecomemoreenergy-efcientisbyusing TopologyControlTC ,whichisthe mainfocusofthisdissertation. ThischapterformallyintroducestheconceptofWirelessSensorNetworksandTopology Control.Furthermore,thischapterexplainsindetailthemotivationsbehindtheuseof 1

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Figure1.1:Diagramofcomponentsofawirelesssensordevice. WSNsandhowTopologyControlalgorithmscanimprovetheirperformance.Subsequently,theproblemstatementwillbeintroduced,accompaniedbysomediscussionon thekeystudyvariablesandproceduresusedinthiswork.Aftertheproblemstatement, thechapterincludesthedetailedlistofcontributionspresentedinthisdissertation,and nalizeswiththestructureofthedissertation. 1.1WirelessSensorNetworks Advancesinsensorandwirelesscommunicationtechnologiesinconjunctionwithdevelopmentsinmicroelectronicshavemadeavailableanewtypeofcommunicationnetwork madeofbattery-poweredintegratedwirelessdeviceswithsensingcapabilities.Wireless SensorNetworks,astheyarenamed,areself-conguredandinfrastructurelesswireless networksmadeofsmalldevicesequippedwithspecializedsensors,wirelesstransceivers, aprocessingunit,asmallmemoryunit,andapowersource,whichcanbeassmallasa pairofAAbatteries.Ageneraldiagramofthestructureofoneofthesedevicescanbe seeninFigure1.1,takenfrom[1]. 2

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Figure1.2:Exampleofanetworkarchitecturethatincludesawirelesssensornetwork. ThemaingoalofaWSNistocollectdatafromtheenvironmentandsendittoareporting sitewherethedatacanbestored,observedandanalyzed.Wirelesssensordevicesalso respondtoqueriessentfromacontrolsitetoperformspecicinstructionsorprovideondemandsensingsamples.Finally,wirelesssensordevicescanbeequippedwithactuators toperformactionsuponcertainconditions.ThesenetworksaresometimesmorespecicallyreferredasWirelessSensorandActuatorNetworks. SomeoftheapplicationsinwhichtheuseofaWSNhasbeenidealincludethemonitoringandactinguponeventsindangerousorunaccessibleplacesforhumans.Assuch, WSNshavebeeninstalledinplacessuchaschemicalplants,tomonitorpoisonousgases; waterplants,rivers,lakesandthelike,toassessthelevelandqualityofthewater;areas withendangeredspecies,tomonitortheirtravelpatternsandbehaviors;buildings,to monitorthequalityoftheairandmakethemmoreenergy-efcient;usedbythemilitary, todetectintruders;orusedinothersimilarapplications. Figure1.2presentsanexampleofacompletesolutionthatintegratesWSNswithother currenttechnologies,likethecellularnetwork,theInternet,andotherwirelessadhoc 3

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technologies[1].Asitcanbeseen,atypicalstructureofaWSNincludestwotypesof wirelessdevices: sinknodes and regularnodes ThesinknodesarethegatewaysoftheWSN:alldatageneratedfromthesensornetwork willbegatheredatthesinknodeandtransmittedtothecontrolsiteusingasecondary communicationinterface,likeEthernet,cellular,satelliteoranotherwirelessnetwork. Furthermore,thesinknodesalsoallowinformationfromoutsideintotheWSN,likecommands,updatesorqueries.Insomecases,thesinknodesalsoplaytheroleoforganizers ofthenetwork,keepingtrackofthestateofthenodesandaddressassignation,orby beingtheinitiatorsofthemaintenanceprocedures. Theregularnodesarethegrossmajorityinthenetwork;theyareinchargeofcollecting allthedataaboutthevariablesbeingmonitoredandofreportingittothesinknode.In addition,ifthenetworkislargeenoughthatsomedevicescannotreachthesinknode directly,theregularnodesmustprovidemulti-hopforwardingofthedata,sothateventhe farthestnodescansendtheirdatatothesinknode.Duetothecriticalresponsibilitiesof thesinknodes,theyoftenhaveabettercongurationintermsofprocessing,memoryand, mainly,energy,whencomparedtotheregularnodes;inotherwords,wheneveryregular nodecanfail,thesinknodesareexpectednotto. EventhoughtheapplicationdomainofWSNshasbeenrestrictedtosimpledata-oriented monitoringandreportingapplications,especiallybecauseoftheenergyconstrainedcharacteristicsofthecurrenttechnology,newnetworkarchitectureswithheterogeneousdevicesandexpectedadvancesintechnologyareeliminatingsomeofthecurrentlimitations andexpandingthespectrumofpossibleapplicationsforWSNsconsiderably,including moreadvancedfunctionslikehandlingmultimediadata. However,atthepresenttime,ofalltheconstraintsconsideredinmostavailablewireless sensordevices,energyconsumptionisofparamountimportance.Thisassertioncanbe 4

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explainedwiththefollowingtworeasons:rst,asinglewirelessdevicepossessesasmall energysource,whichisexpectedtolastseveralmonths;andsecond,ifthenetworkisdeployedinaninaccessiblearea,changingdepletedbatteriesisnotfeasible,sothewireless devicesmustusetheiralreadysmallenergysourceinaveryefcientway.Thesearethe mainreasonwhymostoftheresearchonWSNshasbeenconcentratedonthedesign ofenergy-andcomputationally-efcientalgorithmsandprotocols;thisinterestcanbe measuredbythelargenumberofalgorithms,techniques,andprotocolsthathavebeen developedtosaveenergy,andtherebyextendthelifetimeofthenetwork.Oneofthemost importanttechniquesutilizedtoreduceenergyconsumptioninwirelesssensornetworks isTopologyControl. 1.2TopologyControl 1.2.1NetworkTopology BeforetheconceptofTopologyControlisintroduced,aswellasallitsbenetsforthe network'soperations,itisimportanttostartbydedicatingsometimetotheconceptof NetworkTopology ,whichisabsolutelynecessarytounderstandthefoundationsandmotivationsbehindTC.Asimpledenitionofnetworktopologycanbethefollowing: NetworkTopology isthesetofallactivenodesandactivelinksinthenetwork alongwhichdirectcommunicationcanoccur[2]. Thisdenitioncanbeextendedbasedontheconceptof GeometricRandomGraphs .Let G = V ; E ; r beaGeometricRandomGraphsGRG,inwhich V isthesetofvertices, E isthesetofedges,and r istheradiusofthetransmissionrangeofthenodes.Everyvertex on V representsawirelesssensordevice,andhasageometriccoordinateassociatedtoit 5

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andanopenballwithradius r .Thisopenballisasetthatcontainsalltheverticeswith distancelessthan r respectivetothenode,whichrepresentsthecommunicationareaof thenodes.Thenodesintheopenballaretheonlyneighborsthatthenodecancommunicatewithdirectly.TheformaldenitionoftheopenballispresentedinEquation1.1[3] asfollows: B r x = f y : d x ; y < r g .1 where x ; y 2 V and d ; istheEuclideandistancebetweentwonodes.Thesetofedges E aretheunionofallpairscreatedbyeachvertexandalltheadjacentverticescontainedin itsopenball.Providingthatcommunicationisnotalwaysbidirectional,linksaremodeled asunidirectionaledges.Giventhattheopenballsoftheverticesareindependent,the existenceoftheedge x ; y doesnotimplytheexistenceoftheedge y ; x .Inaddition, ifanymetriccanbecalculatedbetweenapairofadjacentnodes,i.e.,distance,angle, remainingenergy,etc.,itcanbeusedastheweightoftheedge, w .Thismetric,aswell astheedges,isnotalwayssymmetric,soweightscouldbedifferentfromonedirectionto theother.TheformaldenitionofthesetofedgesispresentedinEquation1.2.However, itisassumedthatallnetworksusedinthisdissertationcanbemodeledasbidirectional graphs. E = f x ; y ; w : y 2 B r x ^ w 2 g ; x ; y 2 V .2 Theresultantgraphwhenallthesensorsaresettotransmitattheirmaximumpoweris calledthe MaximumPowerGraph ,or MaxPower graph.Thisisnormallythecasewhen thenodeshavejustbeendeployedandtheyareexploringtheirneighborhood.Thisgraph representsthemaximumtopologyofthenetworkintermsofactivenodesandactive 6

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aTheMaximumPowerGraph. bThereducedtopologyafterthe topologyconstructionmechanism. Figure1.3:Comparisonoftopologies:theMaxPowerGraphversusthereducedtopology. links.OneexampleofthisgraphisshowninFigure1.3a,inwhich500nodesareuniformlydeployedinanareaof500 m 500 m withtransmissionrangesof80 m Intermsoftheorganizationoftheanetworktopology,itcanbepredesignedbytheuser inthecaseswheremanualallocationofthenodesispossible,oritcanbetotallyrandom inthecaseswherethedeploymentismadebyothermeans,i.e.,thenodesaredropped fromahelicopter. Intherstcase,theuserhastotalcontroloverthetopology:theusercancalculatethe minimumamountofrequirednodesandtheirexactpositionsontheareainordertoperformthetaskinanoptimalmanner.Thistechniqueisnotfeasibleforapplicationsin whichaccessibilityisnotpossibleorinadangerousscenariowherethelivesofthepeople performingthedeploymentareatrisk.Inaddition,thissolutionmanynotbefeasiblefor largenetworksorwhenimmediateavailabilityofthenetworkisrequired. Inthesecondcase,whenthetopologyisrandomlydeployedonaninaccessiblearea,the userlacksthepowertoassignexactlocationstothenodesandneedsahighernumberof nodesinordertoguaranteecoverageofthearea.Theseissuescreateanotherproblems, 7

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namelyarandomtopologycongurationthatisnotaptforoptimalperformance,which canshowcharacteristicssuchas: Therecanbeverydenseareasinwhichmanynodesaretransmittingpacketsvery often,generatingagreatamountofcollisionsanddelays. Thenodesmaybetransmittingatfullpower,whichisnotnecessarytoreachthe nextnodeintheirpathtowardsthesink. Therearemanynodesthat,duetoproximity,aresensingthesameeventsandthus, sendingredundantdatatothesink. Inallofthesecases,thenetworkiswastingenergyinunnecessaryactions.Thesearethe problemsthatTopologyControlcanhelptoprevent. 1.2.2DenitionofTopologyControl Themaingoaloftopologycontrolistomodifytheinitialmaximumpowertopologyand avoidtheoccurrenceofthepreviouslymentionedproblemsandtheirimpactontheenergyconsumptionbyalteringtheinitialtopology,whilekeepingimportantcharacteristics likeconnectivityandcoverage. Iftheuserwantstopre-designatopologytoguaranteeoptimality,theneedoftopology controlisnotcriticalandthesolutionoftheoptimaltopologycanbecalculatedoff-line andreplicatedinreality.However,asolutionofthisnatureshouldtakeintoaccountthe characteristicsoftheterrain,theradiospectrumandothervariablesthatmayaffectthe actualcommunicationbetweennodesoncetheyhavebeendeployed,butsometimesthat informationisdifculttoobtainandthepermanenttesting,themanualdeploymentand 8

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thelargenumberofpossiblecombinationsnecessarytogenerateasuccessfuloutputmay delaythewholedeploymentprocess. Thesecondcaseiswhenthedeploymentsarerandomtopologiesandthelocationofthe nodescannotbechangedorsometimesnotevendetermined.Inthisscenariosthereare stilltwovariablesthattheusercanusetoreorganizethetopology:thestateofactivityof thenodesactive,inactiveandtheradiotransmissionpower.Therstvariableallowthe usertoreducethenumberofactivenodes,whichhasanimpactonthedensityincertain areas,reducinginterferenceandthegenerationofredundantdata.Inactivenodesturnoff theirtransceiversandgointoaverylowenergyconsumptionmode,fromwhichtheycan beturnedonagaintobepartoftheactivenetworkiftheyareneededinthefuture.The secondvariablehasadirectimpactonenergyconsumptionandonthelevelofinterference,giventhatradiotransmissionisthemostexpensiveoperationintermsofenergyand oneofthemostcommonlydone;inotherwords,reducingtheenergyrequiredtotransmit amessagewillrepresentimportantsavings. Theadvantageofarandomtopologyisthatthedeploymentcanbedonerelativelyquickly,andthenetworkmaybecomeavailablealmostimmediately.Inaddition,atopology controlalgorithmshouldberobustenoughtotakecareofthecharacteristicsofthedeploymentarea.Themaindisadvantageofthiskindofdeploymentisthatahigheramount ofnodesisrequiredinordertoincreasetheprobabilityofhavingnodesineveryregionof themonitoredarea,whichhasadirectimpactonthecostofthenetwork. OneexampleoftheapplicationoftopologycontrolcanbeseeninFigure1.3b,which showshowtheMaxPowernetworkshowninFigure1.3acanbereducedafterapplyinga TCalgorithmtodecreasethenumberofactivenodes.Amoreformaldenitionoftopologycontrolcanbethefollowing: 9

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TopologyControl isthereorganizationandmanagementfromtimetotime ofcertainnodeparametersandmodesofoperationtomodifythetopology ofthenetwork,withthegoalofextendingitslifetimewhilealsopreserving importantcharacteristics,suchasnetworkconnectivityandsensingcoverage.[1]. Ingeneral,TCcanbeseenasaniterativeprocess,asshowninFigure1.4,extractedfrom [1].First,thereisaninitializationphasecommontoallwirelesssensornetworkdeployments.Inthisphase,nodesdiscoverthemselvesandusetheirmaximumtransmission powertobuildtheinitialtopology.Afterthisinitializationphase,thesecondphasebuilds anewreducedtopology.Thisphaseiscalled TopologyConstruction .Thenewreduced topologywillrunforcertainamountoftime,astheparticipatingsensorswillconsume theirenergyovertime.Therefore,assoonasthetopologyconstructionphaseestablishes thereducednetwork,the TopologyMaintenance phasemuststartworking. Duringthisphase,anewalgorithmmustbeinplacetomonitorthestatusofthereduced topologyandtriggeratopologyrestorationprocesswhenappropriate,thatmaybeaprocessentirelydenedbythemaintenanceprotocolitselforthatmayincludetheinvocation ofthetopologyconstructionalgorithm.Overthelifetimeofthenetwork,itisexpected thatthiscyclewillberepeatedmanytimesuntiltheenergyofthenetworkisdepleted. Therearemanydifferentalgorithmsthatcanbeusedinthetopologyconstructionand maintenancephases.Inthisdissertation,newtopologyconstructionandtopologymaintenanceprotocolswillbeintroduced. 10

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Figure1.4:Diagramthatmodelstheiterativeexecutionofatopologycontrolalgorithm. 1.3ProblemStatement TheoutcomeseeninFigure1.3blooksverysimple: Yes,it'satreethatcoverseveryone.So,isthatall? ,well,letthefollowingexplanationshowwhytheproblemof topologycontrolisnotassimpleasitlooks. Firstofall,thealgorithmsandprotocolsshouldruninadistributedmanner,sotheycan beimplementedinlargenetworks.Second,topologyconstructionalgorithmsandprotocolsmusthavealowcomputationalandmessagecomplexity,sotheycanbeefciently runincomputationallyweakdevicesandnotdrainthenodes'batteries.Third,itisdesirablethatthealgorithmsareabletorunwithoutthehelpofadditionalhardwarelike GPSdevicesorlocalizationmechanisms,solowcostismaintainedandnoadditional energyisspent.Finally,thetopologyconstructionalgorithmmustproduceaconnected networkthatwillcovertheareaofinterestwithaminimumnumberofnodes,whilethe topologymaintenancealgorithmsmustguaranteethattheresourcesofthenetworkare usedeffectivelyinordertokeepthenetworkactivethelongestpossibletime.Allthese constraintscombinedmakethedesignandimplementationofsimpledistributedtopology controlalgorithmsaverychallengingproblem. 11

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Inorderfortheseprocessestobeeffectiveandprovidetheexpectedresultsintermsof extendingthelifetimeofthenetwork,bothtopologyconstructionandmaintenancemechanismsmustbedesignedwithcarefulconsiderationofthefollowingrequirementaspects: Distributedalgorithm: Centralizedtopologycontrolmechanismsneedglobalinformationandthereforeareveryexpensivewhenimplemented. Localinformation: Nodesshouldbeabletomaketopologycontroldecisionslocally.Thisreducestheenergycostsandmakesthemechanismscalable. Locationinformation: Theneedofextrahardware,likeGPSdevices,orsupport mechanismslikelocalizationprotocolsaddtothecostintermsofdollarsandenergyconsumption. Connectivity: Thereducednetworkmustbeconnected,soallactivenodescan exchangemessagesamongthemselvesaswellaswiththesinknode. Coverage: Thereducetopologymustcovertheareaofinterestdespitethenumber ofactivenodes. Smallnodedegree: Asmallnodedegreemeansasmallnumberofneighbors,which mayproducealowernumberofcollisionsandretransmissions,savingenergy. Linkbidirectionality: Bi-directionallinksfacilitatetheproperoperationofsome MediumAccessControlMAClayerprotocols,suchastheoneutilizedbythe IEEE802.11standard,whichsendsRequest-To-SendRTSandClear-To-Send CTSsignalsandalsoacknowledgmentsinthereturnpath. Simplicity: Topologycontrolalgorithmsmusthavealowcomputationalcomplexity, sotheycanberuninwirelesssensordevices. 12

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Lowmessagecomplexity: Topologycontrolmechanismsmustworkwithverylow messageoverhead,sotheyareenergy-efcientandcanberunmanytimesaspartof thetopologycontrolcycle. Energy-efciency: Allthefactorsconsideredthusfarandthosediscussedinthelast sectionconvergeintheissueofenergy-efciency,whichisessentialfortopology controlmechanismsandwirelesssensornetworksingeneral. Energyawareness: Thedecisionmakingprocessintheselectionofthereduced topologymustbeawareofthenodes'sremainingenergyinordertoavoidgiving responsibilitiestoweaknodesthatcanjeopardizetheactivityofthenetwork. Spanner: ThereducedtopologyshouldbeaspanneroftheUnitDiskGraphin termsofbothlengthandnumberofhops.Asubgraph G 0 isaspannerofagraph G forlengthnumberofhopsifthereisapositiverealconstant x suchthatforany twonodes,thelengthnumberofhopsoftheshortestpathin G 0 isatmost x times ofthelengthnumberofhopsoftheshortestpathin G .Theconstant x iscalledthe lengthnumberofhopsstretchfactor Convergencetime: Thetopologyconstructionandmaintenanceprocessesshould takeplaceasfastaspossibleandconvergeafteralimitednumberofsteps. Memoryconsumption: Wirelesssensordevicesoftenhaveasmallamountofmemory.Sometopologycontroltechniquesmayrequireconsiderableamountsofmemory,suchasthosethatstorepre-calculatedtopologies. Evenenergydistribution: Topologycontroltechniquesshouldsomehowtryto distributetheenergyconsumptioninanevenmanneramongallthenodesinthe 13

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network.Thetopologiesshouldbechangedsothatallnodeshaveasimilarparticipationinthenetwork. Thisdissertationpresentsnewtopologycontrolmechanismsthatworkconsideringthese aspects.Allthetopologyconstructionprotocolsproposedinthisdocumentworkbyndingaminimumsetofactivenodes,thatprovidesaconnectednetworkthatisabletoperformallthetasksrequiredbytheuser,whetherconnectivityorcoverage,whileturningall therestofthenodesofftosavetheirenergyforfuturemaintenanceoftheactivetopology. ThecalculationofthissetofspecialnodesismodeledusingtheMinimumConnected DominatingSetMCDSproblemforcommunicationtasks,andtheMinimumConnected SensingCoverageMCSCproblemforconnectivityandcoverage,whichwillbeexplainedindetailinthenextchapter. Themainreasonwhythismethodologywasselectedisthat,nexttoradiotransmission, idlelisteningisthemostcostlyoperationofanode.Thismeansthat,ifallthenodes arekeptawakeandtheonlychangeismadetothetransmissionpower,theidlelistening timefromtheentirenetworkwillstilldecreasetheamountofsavedenergy;plusthefact thattheproblemofredundantsensingisstillpresent,whichwillincreasetheloadofthe networkwithnoneed. Intheproposedsolutionsofthiswork,allredundantnodeshavetheirtransceiversturned off,sonoenergyiswastedinidlemodeandunnecessaryredundancyisreduced.The hypothesisisthatthealgorithmsproposedinthisdissertation,whilecreatingminimal messageoverheadcomparedtotheircounterparts,canreduceandmaintainanactive topology,extendingthelifetimeofthenetwork,whilekeepingradioconnectivityand sensingcoverageofthedeploymentarea. 14

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1.4Contributions Thecontributionspresentedinthisdissertationarethefollowing: Newtaxonomiesfortopologycontrol,topologyconstructionandtopologymaintenancealgorithms. Basedonthenewdenitionoftopologycontrol,whichdifferentiatestheconstructionandmaintenanceprocesses,anewtaxonomyfortopologycontrolalgorithmswasproposedinordertointegrateandextendthecurrent algorithmspresentedin[2,4,5]whichfocusonlyontherstprocess.Themain contributioninthisareaisthedenitionofataxonomyfortopologymaintenance algorithmsforthersttime,whichnoneofthecitedworksinclude.Inaddition, somemodicationswereperformedontheexistingtaxonomies,inordertoinclude specialbranchestotopologyconstructionprotocolsforheterogeneousnetworksand coverage-orientedprotocols. TheA3familyofsimpletopologyconstructionalgorithms. Inthisdissertation,four newtopologyconstructionalgorithmsareintroduced:A3,A3Lite,A3Covand A3CovLite.Theseprotocolscalculatea ConnectedDominatingSetCDS onthe initialMaxPowertopology,leavinginactivestateonlythedominatingnodeswhich provideconnectivityandcoverageinthenetwork,andturningoffalldominated redundantnodes,whichareconsideredunnecessaryforthecorrectactivityof thenetworkatthetimeofexecution.A3istherstversionofthealgorithmand providesabackboneforconnectivitypurposesonly.Theinitialprotocolwaseventuallymodiedintotwonewbranches:the Lite versionsandthe Cov versions.The Lite versionsprovideaverylowcomputationalandmessagecomplexity,compared tothe Non-Lite counterparts.The Cov versionsproduceareducedtopologythat providesahigherdegreeofareacoveragecomparedtothe Non-Cov versions.The 15

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evaluationoftheseprotocolsisbasedonthecomparisonofaveragebehaviorin randomtopologiesagainstotheralgorithmsintheliterature,andagainsttheoretical optimaldeployments. Asetoftopologymaintenancealgorithms. Fourtopologymaintenancealgorithms arepresentedinthisdocument: DynamicGlobalTopologyRecreationDGTRec StaticGlobalTopologyRotationSGTRot HybridGlobalTopologyRecreationand RotationHGTRecRot and DynamicLocalDSR,DLDSR .Thersttwoprotocols havebeenproposedbeforeintheliterature,buthavenotbeenimplementedindetail.Thelasttwoarecompletelynewalgorithms.Thesealgorithmsweredesigned basedontheproposedtaxonomyfortopologymaintenancealgorithms.Theperformanceevaluationofthesealgorithmsisbasedonthecomparisonoftheaverage resultsinrandomtopologies,andworkingjointlywiththreedifferenttopology constructionprotocols.Itisveryimportanttomentionthat,totheknowledgeof theauthor,thisisthersttimethatamodularizationofthetopologyconstructions andmaintenanceprotocolshasbeenimplementedforjointtestingperformance. Atarraya:anewsimulationtoolforteachingandresearchingtopologycontrol algorithms. Asatoolwasneededtodesignandtesttheproposedtopologycontrolalgorithms,thetopologycontrolsimulator Atarraya wascreated.Atarraya isadiscrete-eventsimulatorforevaluatingtopologycontrolalgorithms.Itwas developedinJava,whichallowsAtarrayatobeaveryportableapplicationamong differentoperatingsystems.Inaddition,thesimulatorisbeingofferedforfree tothescienticcommunityasanopensourceproject,basedontheGNUlicense model.Thissimulatorprovidesafriendlyenvironmentfordesigningbothtopology constructionandmaintenancealgorithms,allowingthemodularitytocombinethose protocols,whichhasnotbeenseeninanyothersimulatorofitskind.Inaddition, 16

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itcanbeextendedtosupportschemesfordataaggregation,routing,nodemobility anddifferentenergymodels. Anewbookontopologycontrol. Mostoftheworkpresentedinthisdissertationhas beenincludedinthebook TopologyControlinWirelessSensorNetworks-witha companionsimulationtoolforteachingandresearch ,writtenbyMiguelLabrador andPedroWightman,andpublishedin2009bySpringerScience[1].Thisbook presentsanintegraldenitionoftopologycontrol,basedonthedecouplingofthe constructionandmaintenanceprocesses,andalsoprovidesthesimulatorAtarraya asatoolnotonlyforresearchinganddesigningofnewTCprotocols,butalsoasa usefultoolforteachingcommunicationprotocolsinanuser-friendlyenvironment. Anewmixedintegerprogrammingdenitionoftheminimalconnecteddominating setproblem. EventhoughtherehasbeenpreviousdenitionsoftheMCDSproblem intheliterature,mostofthemdependontheseparatesolutionoftheproblems ofconnectivityanddomination,whichmaynotnecessarilyguaranteeanoptimal jointsolution,orinextensivepreprocessing.Thisdissertationprovidesandefinitionoftheproblembasedonaverysimpleinsightoftheproblemthatsolves bothconnectivityanddominanceinasingleformulation,anddoesnotrequireany preprocessing.Theresultsofthisnewmodelarecomparedwiththeresultsfromthe approximationprotocolspresentedinChapter3. 1.5StructureoftheDissertation Thestructureofthedissertationwillcontinueasfollows.Chapter2willbededicatedto theliteraturereviewoftheproblemoftopologycontrol,includingtheintroductiontothe proposedtaxonomy,andreferencestothemostimportantalgorithmsinbothtopology 17

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constructionandtopologymaintenanceinthecategoriesofthetaxonomy.Inaddition,a sectionofthechapterwillbededicatedtotheConnectedDominatingSet-basedprotocols fortopologyconstructionforbothconnectivityandcoverage.Chapter3describesthe methodologyusedfortheperformanceevaluationofthedifferenttopologyconstruction andmaintenanceprotocolsintroducedinthisdissertation,includingboththeanalytical andsimulation-basedapproaches.Chapter4willintroducethetopologyconstruction algorithmsA3andA3Lite,whicharefocusedonlyonproducingaconnectedtopology withaminimumnumberofactivenodes,andwillshowtheirperformanceevaluation againsttwoverywellknownCDS-basedtopologyconstructionalgorithms.TheA3Cov andA3CovLitetopologyconstructionalgorithmswillbeintroducedinChapter5,which providenotonlyaconnectedtopologybutatopologythatcoversahighdegreeofthedeploymentarea,andwillshowtheirperformanceevaluationagainstsomeoptimaltheoreticaldeployments,their Non-Cov versionsandtwoothercoverage-orientedtopologyconstructionprotocols.Chapter6willpresentthetopologymaintenancealgorithmsproposed inthisdissertation,includingtheirjointperformancetestingwithsomeofthetopology constructionalgorithmspresentedinChapter4.Theconclusionsofthisworkandsome nalremarkswillbepresentedinChapter7.Inaddition,adetaileddescriptionofthe internalstructureanduseofthesimulatorAtarrayawillbeincludedintheAppendixA. 18

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Chapter2:LiteratureReview Thestudyoftopologycontrolhasgainedimportancesincetheendofthepreviousdecade, especiallyinwirelessadhocandsensornetworks,becauseofallthepotentialbenets inenergyconsumptionthatcomewithtransformingtheMaxPowergraphintoamore manageableandefcientnetwork.Researchersinthisareatookadvantageofthesimilaritiesofthesenetworkswiththerandomgraphsontheoreticalelds,inordertoadopt theexistingbasttheoryingraphsandapplyitintothisnewkindofnetwork. Thisfactdeterminedthattherstattemptstoperformtopologycontrolwerebasedmainly inclassicalgraphalgorithms,liketheminimalspanningtree,thesetcoverandcoloring problem,justtomentionsome,becausethewerealreadycapableofalteringtheoriginal structureofagraphinordertoreducethetopology. However,mostofthesealgorithmsrequireglobalinformationandworkinacentralized manner,whichbecameanaturalinitialassumptiontomakeinordertoallowtheuseof thesesolutions.Theseassumptionsstoppedbeingvalidveryquicklyforscenariosin whichthesizeofthenetworkmadeitinfeasibletouseacentralizedsolutionorwhen globalinformationwastoexpensivetoobtain.Thisopenedthehorizonforthedevelopmentofdistributedprotocolsthatrequiredlocalinformation,whichcorrespondedmore withsomeoftherealcharacteristicsofthesenetworks:theycanreachhighlevelsof scalability,randomnessinlocalizationofthenodesandtheircommunicationlinks,and globalinformationistoocostlytocollectanddistribute. 19

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Theamountofworkintheareahasbeenverybroadandvaried.Aspartofthiswork,a newtaxonomyforclassifyingtopologycontrolprotocolsispresented.Thenewproposed taxonomyisanextensionofthreeprevioustaxonomies,introducedin[2,4,5].Thenew taxonomy,whichisoneofthemaincontributionofthiswork,providesaroadmapforthe restofthischapter. 2.1TopologyControlTaxonomy AsmentionedinChapter1,topologycontrolalgorithmsweretraditionallyconsideredas amonolithicprocess:reductionandmaintenancewereimplementedasasingleprotocol. Themainproblemwiththisapproachisthatusuallythemaintenanceprocesswasnot assumedcriticalinthedesignofthealgorithm,sonotestswereperformedinordertodeterminethebestmaintenancepolicyforthereducedtopologyproducedbythealgorithm. Inaddition,thisconceptionalsoaffectedtheclassicationoftopologycontrolalgorithms, restrictingitonlytohowthenetworktopologywasreduced.Thetwopreviouslydened taxonomiesfortopologycontrolalgorithmscoveredthefollowingareas: Thetaxonomypresentedin[4]isfocusedonlyontopologyconstructionalgorithms thatchangethetransmissionrangetoreducethenetworktopology. Thetaxonomypresentedin[2]hasabroaderdenitionoftopologyconstruction algorithms,consideringalsohierarchicalandhybridalgorithms. Thetaxonomypresentedin[5]isfocusedonlyinthecoverage-orientedtopology constructionprotocols. 20

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Figure2.1:Generaltaxonomyfortopologycontrolprotocols. Theunionofthesethreetaxonomiesproducesafairlycompletetaxonomyfortopology constructionalgorithmsonly.However,sometopologyconstructionareaswerenotexplicitlyclassiedinthoseworks,suchasnetworkswithheterogeneousdevices. Theproposedtaxonomynotonlyextendstheareaoftopologyconstructionintheaforementionedarea,butalsoincludesanewtaxonomyfortopologymaintenanceprotocols, whichwascompletelyignoredinprevioustaxonomies.Theinclusionofthisnewbranch ismotivatedbythefactthattheselectionofatopologymaintenanceprotocolhasserious implicationsonthelifetimeofthenetwork,soinordertostudytheimpactofmaintenanceontopologyconstructionprotocols,aclearclassicationofthedifferentmethods toperformmaintenanceisanecessity.Figure2.1depictstheclassicationoftopology controlmechanismsintotwomainbranches:TopologyConstructionandTopologyMaintenance. 2.1.1TopologyConstructionTaxonomy Therstbranchofthetaxonomydenesthetopologyconstructiontechniquesanddivides itintotwobranches:topologyconstructionforconnectivityandtopologyconstructionfor 21

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coverage.Thealgorithmsintherstbrancharefocusedonlyinproducingaconnected reducedtopology,butdonotguaranteethecorrectlevelofcoverageofthedeployment area.Theprotocolsinthesecondbrancharemoreorientedinprovidingcoverageinthe area,evenif,insomecases,connectivityisnotguaranteed. Thefollowinglistillustratesageneraldescriptionofthedifferenttechniquesusedby mostofthetheconnectivity-orientedtopologyconstructionprotocols: Somesolutionsbuildareducedtopologybycontrollingthetransmissionpower,for bothhomogeneousandheterogeneousnetworks.Bothcentralizedanddistributed techniquesarepresented. Someprotocolsbuildhierarchicaltopologiesbymeansofbackbonesandclusters. Otherprotocolsusehybridschemes,mixingdifferenttechniquesinordertoreduce thetopology. Incontrast,thefollowinglistenumeratessomeofthedifferenttechniquesusedbycoverage-orientedtopologyconstructionprotocols: Someprotocolsaredesignedtoprovidecoverageofasetofpredenedtargets distributedinthedeploymentarea,andnottheentirearea Somesolutionscanofferdifferentlevelsofredundancyinthecoverage 2.1.2TopologyMaintenanceTaxonomy Thesecondmainbranchintheproposedtaxonomyisdedicatedtotopologymaintenance protocols.Theclassicationdimensionsofthetechniquesinthiscategoryarebasedon thefollowingparameters: 22

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Selectionofthenodesforthemaintenanceproblem:pre-calculatedstatictopology selection,ontheydynamicselectionorahybridselectionscheme. Levelofinvolvementofthenodesinthemaintenanceprocess:globalinvolvement, whenallthenodesinthenetworkparticipateonthealgorithms,orlocalinvolvementwhenjustasmallsubsetofthemperformthemaintenance. Triggeringmechanismofthemaintenancealgorithm:time,energy,nodedensity, randomselection,nodefailure,etc. Thefollowingsectionwillillustratesomeofthecharacteristictechniquesineachofthe categoriesofthetaxonomy,givingahigherprioritytothehierarchicalprotocolsinthe topologyconstructionbranch,giventhatthetopologyconstructionprotocolspresentedin thisdissertationbelongtothatcategory. 2.2Connectivity-orientedTopologyConstruction Topologyconstruction,asexplainedinChapter1,istherstprocessthatisexecutedover thenetworkoncethenetworkhasbeendeployed.Themaingoalofthesealgorithmsisto reducethetopologyofthenetwork,whilekeepingthenetworkconnected.Thereduction ofthetopologybringsbenetstothenetwork,mainlyinenergyconsumption. Eventhoughtherearemanywaystoperformsuchtasks,eachprotocolinthiscategory modifydifferentlytheavailableparametersthetransmissionpowerandthelevelof activityofthenodes;andusesdifferentinformationtomakedecisionsnodelocation, numberofneighbors,etc.Thissectionisfocusedonthedescriptionofthemostimportant typesoftopologyconstructionalgorithms,withexamplealgorithmsforeachcategoryof thedetailedtaxonomypresentedinFigure2.2. 23

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Figure2.2:Taxonomyofconnectivity-orientedtopologyconstructionprotocols. 2.2.1ControllingtheTransmissionPower Thissectiondescribesthemostimportanttopologyconstructionalgorithmsandprotocols thatbuildthereducedtopologybycontrollingthetransmissionpowerofthenodes.The rstcaseconsideredinthissectionisonewhereallnodesinthenetworkaresimilar, i.e.,assuminganhomogeneousinfrastructure.Forthiscase,centralizedalgorithmsand distributedprotocolsarepresented.Thesecondcaseincludesprotocolsthatconsidera networkwithheterogeneousdevices,intermsofenergyandtransmissionrange.Thiscase willbeexplainedwithmoredetaillaterinSection2.2.1.3. 2.2.1.1CentralizedApproaches Controllingthetransmissionpowerinacentralizedmannerisperhapsthemostmature topologyconstructiontechnique,giventhatmanytechniquesfromclassicalgraphtheory 24

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couldbeappliedalmostdirectly.Underthecentralizedparadigmtherearethreewellknownapproaches: Findingtheminimalcommunicationrangeforallthenodesinthenetworkthatwill preservenetworkconnectivity.Thisapproachisbetterrepresentedbytheproblem ofthe CriticalTransmissionRangeCTR Findingtheoptimaltransmissionpowerforeachindividualnode,whichisthe RangeAssignmentRAproblem Theuseofgeometricalpropertiesinordertondreducedglobaltopologiesbased onlocaloptimalsolutions Therstapproachwaspresentedin[6].ThisideaisbasedontheideathataMinimal SpanningTreeMSTonagraphprovidesconnectivity.Ifthecommunicationrangeof everynodeisguaranteeingtobeaslargeasthelongestedgeoftheMST,itwillimply thatthenetworkisconnected.Inthissense,Penrosedeterminedthatfordensenetworks, thelengthofthelongestedge,fromwhichthevalueoftheCTRcanbecalculated,is determined withhighprobability w : h : p byEquation2.1. CTR dense = r logn + f n n p .1 where f n isanincreasingfunctionof n ,suchthat lim n f n =+ ,and logn isthe naturallogarithmof n lnn 1 Equation2.1isvalidonlyfortwo-dimensionaldeployments.Othersimilarformulascan beseenin[4]forone-andthree-dimensionaldeployments,basedontheoremsfrom[6 8].However,thisequationhasseverallimitations.First,itonlyappliestodensenetworks. 1 Unlessotherwisespecied,alllogarithmsinthissectionarenaturallogarithms. 25

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Theasymptoticvalueofthelongestedgeisfoundinaxedareaasthenumberofnodes goestoinnity.Second,itisnotveryaccurate.Experimentsin[1,4]showthateven foralargenumberofnodes,thetheoreticalvaluegivenbyEquation2.1hasarelative differenceintheorderof28%whencomparedwithexperimentalresults. Anotherformulawaspresentedin[9]whichguaranteesconnectivityinbothsparseand densenetworks.Itusesthelengthofthesideofthedeploymentareaassumingthatit isasquare,andcalculatestheoptimumradiusandnumberofnodestoobtainafully connectedsparsenetwork.Fortheone-dimensionalcase,theCTRisgivenby: CTR = k llogl n .2 where k isaconstantwith1 k 2,and l isthelengthoftheline.TheasymptoticbehaviorofthisCTRhasbeenshowntobeveryaccuratewhencomparedwithexperimental resultsin[4]for k = 1,ifcertainassumptionsareconsidered.Forinstance,therelative magnitudeofthetransmissionrange r andthenumberofnodes n whenexpressedasa functionofthelengthoftheline l havetobesuchthat r = r l << l and n = n l >> 1. Theauthorsalsoprovidedapartiallyprovenformulaford-dimensionalcases. Ford-dimensionalcases,with d = 2 ; 3 ;::: ,Santi[4]proposesapartiallyprovedresultto ndtheCTRforconnectivityas: CTR = k l d logl n .3 where k isaconstantwith0 k 2 d d d 2 + 1 Ingeneral,theproceduretondtheCriticalTransmissionRangemaybeahardandcostly operation,especiallyifcompleteconnectivityisdesired.Also,insomecases,theCTR 26

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mightbeveryclosetothemaximumtransmissionrange,andtherefore,therewillbe neithermajordifferencesinthetopologynorenergysavings. Ifthehomogeneousrangeconstraintisremoved,thesolutionutilizedtondtheCTRcan provideanevenbettersolution.Amoreinterestingandenergy-efcientmethodwouldbe tondthemaximumenergyneededpernode;inotherwords,a non-homogeneouspower assignment tobuildareducedconnectedtopologywithoutthedrawbacksofhavingan homogeneousrange.Thisisthesecondapproachonthecentralizedparadigm:thewellknownRangeAssignmentRAproblem,whichisdenedasthefunctionthatndsa stronglyconnectedgraphandminimizesthetotalcostofthenetwork,whichisgivenby thesummationofthetransmissionpowerusedbyall n nodes. Thealgorithmpresentedin[10]tosolvetheRAproblemhasacomputationalcomplexityof O n 4 forone-dimensionalnetworks.SolvingtheRAproblemintwo-andthreedimensionalnetworksisNP-hard[10,11].Therefore,symmetryconstraintshavebeen addedtotheRAproblem,andtwonewproblemsemerged:The WeaklySymmetricRange AssignmentWSRAproblem andthe SymmetricRangeAssignmentSRAproblem ThesolutiontotheWeaklySymmetricRangeAssignmentWSRAproblemremoves unidirectionallinksanddeterminestherangeassignmentforeachnodesuchthatthe reducedgraphisconnectedandsymmetric,andthetotalcostofalltheassignmentsis minimum.NotethatinthecaseoftheWSRAproblem,theresultingtopologymaystill containsomeunidirectionallinks,whicharenotneededforconnectivity.TheSymmetric RangeAssignmentSRAproblem,ontheotherhand,isstrongerinitsrequirements,as alllinksintheresultingtopologymustbebidirectional.Thisimpliesthatsomenodeswill havetoincreasetheirtransmissionpowertoproducethesymmetrictopology. TheWSRAproblemappearstobemoreconvenienttosolveinwirelesssensornetworks becauseitpresentsthesamecomputationalcomplexityastheothersolutions,anditcre27

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atesaconnectedbackboneofbidirectionallinks,whichiswhatnodesneedtocommunicate.Inaddition,WSRAhasbeenprovedin[4]thattheenergycostoftheWSRAproblemhasamarginaladditionalenergycostcomparedwiththeRAproblem,andagreat gaincomparedtotheSRA. Thethirdapproachtakesadvantageofthreeverywellknownalgorithmsthatarebasedin geometricalpropertiesoftheEuclideanspace:the RelativeNeighborGraphRNG [12], the GabrielGraphGG [13]andthe DelaunayTriangulationDT [14].Itwasdecided toincludethesealgorithmsinthissectionofthetaxonomybecauseintheiroriginalversionstheyworkinacentralizedmanner,eventhoughseveraldistributedimplementationsexist.Theycouldhavebeenincludedunderthelocation-baseddistributedprotocols categoryaswell,astheyallassumethatinformationaboutdistancesbetweennodesor relativepositionsisavailable. TheRelativeNeighborGrapheliminatesthelongestedgefromeverytriangleformedby twoofitsneighborsanditself.TheRNGcanbeeasilydeterminedusingalocalalgorithm withmessagecomplexity O n andcomputationalcomplexity O n 2 .Also,iftheoriginal graph G isconnected,thenthereducedgraph G 0 isalsoconnected.However,nodesthat areafewhopsawayin G canbecomeveryfarapartin G 0 .TheGabrielGraphconnects nodes u and v ifthediskhavinglinesegment uv asitsdiametercontainsnoothernode thanthetwoneighbors u and v .TheGGgraphalsomaintainsconnectivityandhasthe samemessageandcomputationalcomplexityofRNG. AsitcanbeseenRNGsandGGsareverysimilar;theybothremoveeverylinktoaneighbornodethatcouldbereachedthroughanotherneighbor.Distributedimplementations oftheRNGsandGGsonlyrequirenodestosharetheirlocationswiththeirneighbors andtesttheseconditionstoverifyeachedgeinordertodeterminetheminimalsetof neighbors.Forexample,adistributedversionoftheGGcanbefoundin[15].Although 28

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thesetwographshavelowmessagecomplexity O n ,theirnodedegreecanbeashigh as n )]TJ/F19 11.9552 Tf 10.95 0 Td [(1. Anothergraphborrowedfromcomputationalgeometrythatisusefultobuildreduced topologiesistheDelaunayTriangulation.Ifalltheneighbornodesareconnectedbased onthevicinityoftheVoronoidiagram,aDelaunayTriangulationwillbeobtained.The Voronoidiagramisageometricconstructionthatdenestheareaofcoverageandthe vicinityinagraph.Traceanimaginarylinebetweentwonodes.Rightinthemiddleof thisline,traceanorthogonallinethatwilldenethelimitbetweentheareas.Repeatthe processbetweeneverypairofnodesinthegraph.Thesmallerintersectedareadened aroundanodefromthelimitswitheveryothernodeinthegraphdeterminesthenal diagram.TheDelaunayTriangulationdiagramisformedbyconnectingadjacentvertices intheVoronoidiagram.Withthisapproacheachnodecanchooseasitstransmission powerthepowerneededtoreachitsfarthestneighbor. Thisapproachrequiresglobalinformationand,ifappliedwithoutrestrictions,itmay connectnodeswhicharemoredistantthanthemaximumcommunicationrange.DT hasamessagecomplexityof O n andcomputationalcomplexityof O nlogn .Italso guaranteesconnectivityandmayhaveanodedegreeashighas n )]TJ/F19 11.9552 Tf 11.117 0 Td [(1.In[16],alocalized versionoftheDelaunaygraphisdescribed. 2.2.1.2DistributedApproaches Distributedtopologyconstructionprotocolsaredescribednext.Here,themainconcern ofthesealgorithmsisaboutbuildingaqualitytopologywhilebeingabletoimplementitinanefcientfashion;whereefcientmeanswithlowenergyconsumption,low computationalandmessagecomplexity,andsoon.Theseprotocolsmakeuseofloca29

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tion,direction,neighbor,androutinginformationtoachievetheirobjectives.Finally, thesectionalsoincludesmechanismsthatndthereducedtopologybycontrollingthe transmissionpowerinheterogeneousnetworks,i.e.,withoutassumingsimilarityofnodes inthenetwork,whichisinfact,averyplausiblescenario. Thealgorithmsthatsolvethetopologyconstructionproblemusinglocation-basedtechniquesassumethateverynodeknowsitsownpositionwithahighdegreeofcertainty. Thisinformationallowsthemtousegeometricpropertiesinordertodeterminethebest congurationofthetopologyintermsofdistancebetweennodes,whichattheenddeterminesthebesttransmissionrangeforeachofthem.Forexample,distributedversionsof thealgorithmsfromcomputationalgeometrydescribedinSection2.2.1.1canbeincluded here.Someofthemostimportantlocation-basedprotocolsaretheLocalMinimalSpanningTree,orLMST[17],andtheR&Malgorithm[18]. Indirection-basedtechniquesitisassumedthatthenodesareabletodeterminethedirectionofthesignalsreceivedfromtheirneighbors,andinsomecases,thedistancebetweenthem.Thedirectionoftheincomingangleofthesignalinthecircularcommunicationrangecanbeprovidedbydirectionalantennaeinstalledinthenodes.Distance information,ontheotherhand,canbeobtainedusingdifferenttechniqueslikeReceived SignalStrengthIndicatorRSSI,TimeofArrivalTOA,TimeDifferenceofArrival TDOA,oranyothersimilartechnique.Moreinformationaboutlocalizationtechniques canbefoundin[19].Someofthemostimportantdirection-basedprotocolsarethe YaoGraphYG [22],theCone-basedTopologyControlprotocolCBTC[23],theDistributedRelativeNeighborGraphProtocolDistRNG[24]andtheAngularTopology ControlwithDirectionalAntennasDi-ATCprotocol[25]. Inallthelocation-anddirection-basedtechniques,thetopologyconstructionalgorithms requireextrainformationfromtheneighbornodesotherthantheirownpresence,suchas 30

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accurateCartesiancoordinatebi-ortri-dimensionallocationorpolarcoordinatedistanceandangle.However,localizationinformationisnotalwaysavailableoraccurate, anditcouldbeveryexpensivetoobtain.Forexample,locationfromGPS-enablednodes canonlybeobtainedinplaceswherethereisdirectaccesstothesatellitesignals.Other localizationtechniques,likeultrasonicorultrawideband-based,notonlyneedalocalizationprotocolontopofthetopologyconstructionprotocol,butcouldalsoincreasethe communicationsoverhead,astheirrangeisverysmallcomparedwiththeradiocoverage. Inthecaseofpolarcoordinates,theuseofdirectionalantennaeincreasesthepriceand complexityofthewirelessdevices.Inaddition,eachoneofthosetechniquesalsocarries anintrinsicerrorthatlimitsthereliabilityontheinformationtheyproduce.Neighborbasedtechniquesovercometheseproblems,astheyassumethatnodesonlyneedtohave theabilitytodeterminethenumberofneighbors,changetheirtransmissionpowerand,in somecases,calculatethedistancebetweennodes. Themainideaofthesealgorithmsistoproduceaconnectedtopologybyconnectingeach nodewiththesmallestnecessarysetofneighbors,andwiththeminimumtransmission powerpossible.Giventhatthenodesdonotpossesaccuratelocationinformation,their decisionsdependmostlyontheprobabilityofselectingtheappropriateneighbors,the onesthatwouldextendthenetworkasfaraspossible.Undertheassumptionthatthe nodesareeitheruniformlyorPoissondistributed,somepropertieshavebeenfoundin connectedtopologiesthatdeneaboundedminimumappropriatesizeoftheneighborhoodsofasinglenodethat w.h.p. wouldcreateaconnectedtopology.Asaresult,most neighbor-basedprotocolsfortopologyconstructionarebasedonthecreationofa Kneighborgraph Thedenitionoftheminimumnumberofneighbors k thateachnodemusthaveinorder topreserveconnectivityhasbeenawell-studiedproblem.Mostcommonlyusednumbers 31

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forthisparameterarebetween6and8,oranaverageof3neighbors,aspresentedin[26 28].Recently,in[29],itisdemonstratedthattoproduceaconnectedtopology,eachnode shouldbeconnectedto Q logn nearestneighbors.However,theonlywaytocompletely guaranteeconnectivityinaworst-casescenario,underthehomogeneousassumption,is bydening k = n )]TJ/F19 11.9552 Tf 11.364 0 Td [(1,whichwillproduceatopologysimilartotheoriginalMaxPower graph,assumingofcoursethatitwasconnectedfromthebeginning.Someofthemost importantneighbor-basedprotocolsarethe K-NEIGHprotocol [30]andthe XTCprotocol [31]. Theconnectivityofatopologyisoneofthemostimportantrequirementsofanytopology constructionprotocol.Onewaytodetectconnectivityisbymakingsurethataroutecan befoundfromonenodetoeveryothernodeinthenetwork.Thisisthemainobjectiveof theroutingfunction:tobuildroutingtablestoroutepacketsfromonenodetoallpossible destinations.Whenallthenodesareincludedintheroutingtablesitimpliesthattheycan bereached,andthetransmissionrangedoesnotneedtobeadjusted.Thisisthemainidea behindtherouting-basedtechniques.Oneofthemostwidelyknowntopologyconstructionmechanismsinthiscategoryisthe CommonPowerCOMPOWprotocol [32]. 2.2.1.3HeterogeneousDevices Thewidespectrumofpossibleapplicationswherewirelesssensornetworkscanbeappliedhasincreasedthepossibilityofmixednetworks,wheredevicesofdifferenttypes andcharacteristicsco-existandworkinthesameapplication.Inthistypeofheterogeneousenvironment,itisveryimportanttodevisealgorithmsandmechanismsthatwill allowdifferentdevicestocollaborate,eachtakingadvantageoftheabilitiesoftheothers. 32

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Althoughtopologycontrolproblemshavebeenstudiedinthecontextofheterogeneous wirelesssensornetworksbefore,mostexistingmechanismshavefocusedonvaryingthe nodes'transmissionpowerbasedontheassumptionthatallthewirelessdeviceshave identicalphysicalcharacteristics.Asaresult,topologycontrolproblemshavebeensolved asrangeassignmentproblems,whichnotonlyneglecttheheterogeneityofthenetwork butalsodonottakeadvantageoftheuniquecapabilitiesofdifferentdevices.Someexamplesoftopologyconstructionalgorithmsforheterogeneouswirelesssensornetworksare theDirectedLMSTDLMST,DirectedRNGDRNG,proposedbothin[33],andthe ResidualEnergyAwareDynamicREADtopologyconstructionalgorithm[34]. 2.2.2HierarchicalTechniques Theprevioussectiondiscusseshowchangingthetransmissionpowerofthenodesreduces thenetworktopology,savesenergy,andincreasesthelifetimeofthenetworkwhilepreservingconnectivityandcoverage.However,thisapproachdoesnotpreventthetransmissionofredundantinformationwhenseveralnodesareclosetoeachotherandmaynot simplifythenetworktopologyenoughinordertomakewirelesssensornetworksscalable forlargedeployments.Thissectionexplainsadifferentapproachtotopologyconstruction,thehierarchicaltopologyconstructionapproach,whichaddressesthescalability problemandfacilitatestheaggregationofinformationforadditionalenergysavings. Inthehierarchicaltopologyconstructionapproach,acommunicationhierarchyiscreatedinwhichareducedsubsetofthenodesisselectedandgivenmoreresponsibilities onbehalfofasimpliedandreducedfunctionalityforthemajorityofthenodes.This approachhasthepotentialtogreatlysimplifythenetworktopologyandtheopportunityto 33

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saveadditionalenergybyassigningusefulfunctionstothereducedsubsetofnodes,such asinformationaggregationandltering,androutingandmessageforwarding. Onedisadvantageofthehierarchicalapproachisthattheselectedsubsetofnodeswill workmorethantheirunselectedneighbors,andwillseetheirbatteriesdrainedsooner. Therefore,thisapproachmustbeaccompaniedbyagoodtopologymaintenancefunction thatwillrotatetheroleofthenodeswiththenalgoalofspendingtheirenergyevenly andextendingthenetworklifetime. TheclassicationoftopologyconstructionsmechanismsdepictedinFigure2.2shows thathierarchical-basedtopologyconstructionmechanismscanbeclassiedasbackbonebased,adaptive,andcluster-based.Inthefollowingsections,thesecategoriesalongwith themostimportantalgorithmsandprotocolsavailableintheliteraturearedescribedand explained. 2.2.2.1Backbone-basedTechniques Themaingoalofthecommunicationbackboneapproachistondaconnectedsubset ofnodesthatwillguaranteeconnectivitybyallowingeveryothernodeinthenetworkto reachatleastonenodeonthebackboneinadirectway.Itisimportanttomentionthat eventhoughonecommonassumptionofthisapproachistohavethenodestransmittingat fullpower,theycouldalsoreducetheirtransmissionrangetoreachonlytheirdirectactive neighbors,sotheapproachespresentedinSection2.2.1andthisonearenotmutually exclusive.Figure2.3bshowsanexampleofthisapproachinwhichonly35nodesout of500nodesinthenetworkwereselectedtobuildthebackboneandtoprovidecomplete connectivity. 34

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aMaxPowergraph. bReducedtopology. Figure2.3:Topologycontrolbyreducingthenumberofactivenodesandthecreationofa networkbackbone. Acommunicationbackbonecanbecreatedbysolvingawidelyknownmathematical problem:the ConnectedDominatingSetCDSproblem .A DominatingSetDS isaset ofnodes D V inagraph,inwhichallothernodesthatdonotbelongtothesubsethave alinktoatleastonenodeintheset D .InthespecialcaseoftheCDS,thenodesin D are connected.Mathematically,theformaldenitionofaDSisexpressedasinEquation2.4. Ofcourse,thesmallerthedominatingsetis,thebetterforenergyconservation,therefore, ndingthe MinimumDominatingSetMDS andthe MinimumConnectedDominating SetMCDS isofparamountinterest.TheseproblemshavebeenshowntobeNP-hard in[35,36],therefore,heuristicsareneededforpracticalpurposes. D = 8 v 2 V : v 2 D _9 d 2 D : v ; d 2 E .4 SomemathematicalformulationsoftheproblemhasbeenproposedfortheMCDSproblem.In[37],theauthorsproposetheseparationoftheproblemsoftheCDSintotwoparts towhichwell-knownlinearprogrammingdenitionsexist:theminimumdominatingset andtheminimumtreethatwillconnectthedominatingnodes.Someothervariationshave 35

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beenproposed,addingrestrictionstotheprobleminordertoreducethesolutionspace: in[38,39]wheretheauthorsrestrictedthetypeofnetworkstoberegularandrandom cubicgraphs,respectively.OthersolutionsextendtheCDSschemebyincludingother metrics,likein[40]wheretheauthorsincludethemaximizationofthethroughputofthe network.Inthisdissertation,anewmixedintegerprogrammingdenitionoftheMCDS problemisdenedinSection3.2asanewtoolforevaluationoftheprotocolsproposedin thisdissertation. InthecaseofapproximatesolutionstotheMCDSproblem,manyalgorithmshavebeen provedtobeapproximationalgorithmsoftheoptimalsolution.IntheworkofGuhaand Kuller[41],theauthorsproposedtwoschemestoapproximatetheMCDSwithratiosof O H D ,where H istheharmonicfunctionand D isthemaximumnodedegreeof thegraph.However,assumingthatthenodesaredeployedintheEuclideanspace,better approximationratioscanbeachieved.Forexample,thealgorithmsbasedonMaximal IndependentSetsMISpresentedin[42,43]and[44,45]havebeenprovedtohavean approximationratioof O n ,and7 : 8and6 : 91tothesizeoftheoptimalMCDS,respectively. Ingeneral,threemethodsarethemostcommonlyusedtocreateaconnecteddominating set,andtheywillbeexplainedindetail.Thesetechniquesare:growingatree,connectingindependentsets,andpruning-basedtechniques. AneasywaytoillustratetherstapproachtogrowatreeisbycomparingitwithPrim's algorithm[46],whichndstheminimumspanningtreeofagraph.Theprocessworks fromthesetofnodesthatarepartofthetreeattime t .Between t and t + 1,basedon certainparameters,thenodesinthesetevaluatealladjacentnodesinordertoextendthe tree.Theprocesscontinuesuntilallnodesonthegraphareevaluated.Ofcourse,inthe caseoftheCDS,noteverynodewillbeselectedtobepartofthetree,andthosewhich 36

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Figure2.4:Growingatreewith1-hopneighborinformation. werenotselectedwillgotosleepuntilanewtreeisrequested.Thisprocedureguarantees thattheextendedtreeat t + 1isstillconnectedsincethenewselectednodesarealways neighborsofatleastonenodeofthetreeset.Ingeneral,theprocessstartsonasingle node,usuallythesinknode,butiftherearemorethanonesinknodes,thenseveraltrees couldbebuiltinparallel,ifthenodessupportthatfunctionality.Thegrowingatree techniquehascharacteristicsthataredesirableforroutingprotocols,likeanorganized structurethatallowsimplementingroutingbasedonthesimpliedlogicalstructure,hierarchicaladdressing,queryingbasedontreesearches,etc. In[41],theauthorspresentacoloring-basedgrowingatreeapproachtocreateaCDS onagraph.Atthebeginning,allnodesaremarkedasWhite,andthealgorithmstarts atthenodewiththehighestnodedegree.ThisnodeismarkedBlack,andmarksallits neighborsGray.Graynodesareinspectedinordertocalculatetheiryield,orthenumberofWhitenodesthattheywouldaddtothetree.TheGraynodesthatincludemore unmarkednodesoneachiterationwillbeincludedonthetreebymarkingthemasBlack nodes.However,usingthetopologydepictedinFigure2.4,theauthorsshowedthatthis approachisineffectiveifGraynodeslookedattheirownneighborsonly.Asitcanbe seen,thealgorithmcreatesatreewith d + 2nodes,where d isthenodedegreeofthe initialnode,insteadoftheexpectedtreewithonlyfournodes.Theauthorsalsoshowthat theimplementationofthisalgorithmrunsin O m steps,where m isthenumberofedges intheoriginalgraph. 37

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Inordertosolvethisproblem,theauthorsproposedamodicationofthealgorithm,consistingofscanningpairsofnodesina2-hopmanner.AGraynodeandaWhitenodewill bemarkedasBlackiftheirjointcontributionisthegreatestontheiteration.First,the algorithmmarksaGraynodeBlack,whichmakesallitsneighborsGray.Then,oneof theGraynodesisalsocoloredBlack,whichmakesitsneighborsGray.Here,theyield isgivenbythetotalnumberofGraycolorednodes.Finally,thepairofnodeswiththe highestyieldistheoneselectedaspartofthetree.Thislookaheadgreedysolutionnot onlyproducestheexpectedfour-nodetreebutalsolettheauthorsprovethattheprocedure producesaconnecteddominatingsetwithatmost2 1 + H D j OPT DS j nodes,where D isthemaximumdegreeofthegraph, H istheharmonicfunction H k = k i = 1 1 = i lnk + 1,and j OPT DS j isthesetofnodesinanoptimaldominatingset.Theauthorsshow thattheimplementationofthismodiedgreedyalgorithmcanberunin O nm steps, where n isthesetofnodesand m thesetofedgesintheoriginalgraph. Adistributedversionofthistechniqueispresentedin[47]withanapproximationofat most2 H D nodesthantheoptimalsolution,and O j C j D + j C j timeand O n j C j messagecomplexity,where C isthedominatingsetproducedbythealgorithm. Thetopologyconstructionprotocolsintroducedinthisdissertation,theA3familyofprotocols,usethegrowingtreetechniquetobuildaconnecteddominatingset.Adetailed explanationoftheprotocolswillbepresentedinChapters4and5. ThesecondapproachtobuildingaCDStreeistocreateindependentsetsrst,andconnectthesetslater.Duringtherstphase,theideaistoforma MaximalIndependentSet MIS .An IndependentSetIS ofgraph G isasubset W 2 V wherenotwonodesin W haveanedge.AnMISisanindependentsetthatisnotasubsetofanyotherindependent set,i.e.,anMISof G isanISthatcannotincludemorenodesin V .Therefore,anMISisa DominatingSet,whichmaynotbeconnected.Duringthesecondphase,thesealgorithms 38

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ndawaytoconnecttheDSwiththeminimumnumberofnodes,andtherefore,formthe CDStree. The EnergyEfcientConnectedDominatingSetEECDS algorithmisanimportant exampleinthiscategory.Proposedin[44],theEECDSalgorithmcreatesamaximal independentsetintherstphase,andthenselectsgatewaynodestoconnectthetheindependentsetsduringthesecondphase. EECDSalsousesacoloringapproachtobuildtheMIS.TheEECDSalgorithmbegins withallnodesbeingWhite.AninitiatornodeelectsitselfaspartoftheMIScoloring itselfBlackandsendingaBlackmessagetoannounceitsneighborsthatitispartofthe MIS.Uponreceivingthismessage,eachWhiteneighborcolorsitselfasGrayandsends aGraymessagetonotifyitsownWhiteneighborsthatithasbeenconvertedtoGray. Therefore,allWhitenodesreceivingaGraymessageareneighborsofanodethatdoes notbelongtotheMIS.ThesenodesneedtocompetetobecomeBlacknodes.Thecompetitionconsistsofsendingan Inquiry messagetoitsneighborstoknowabouttheirstate andweightsandwaitfortheirresponsesforaspecicamountoftime.Ifduringthistime, itdoesnotreceiveanyBlackmessageinresponse,andithasthehighestweight,itbecomesaBlacknode,andtheprocessstartsagain.Otherwise,itstaysasaWhitenode. Theweightisametriccalculatedbyeachnodebasedonthebatterypowerandeffective nodedegree.TheauthorsshowthatthesetofBlacknodesproducedbytheabovealgorithmformsaMIS. ThegoalofthesecondpartofthealgorithmistoformaCDSusingnodesthatdonot belongtotheMIS.Thesenodes,called connectors ,areselectedinagreedymannerby MISnodesusingthreetypesofmessages.Anon-MISnodethatbecomespartofthe CDSsendsaBluemessagetonotifyitsneighbors.MISnodessend Invite messagesto non-MISnodestoinvitethemtobeconnectors.Inresponsetoinvitemessages,non-MIS 39

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calculatetheirweightsandsend Update messages.Finally,thenon-MISnodewiththe highestweightbecomespartoftheCDS.TheauthorsprovethatphasetwoofEECDS buildsaCDS. ThemaindisadvantageoftheEECDSalgorithmisitsmessagecomplexity.Inbothphases ofthealgorithm,competitionisusedtodeterminethebestcandidatestobeincludedin theindependentsetsandthenaltree.Thisprocessisverycostlyintermsofmessage overheadbecauseeachnodehastoconsultitsneighborsfortheirstatusinordertocalculateitsownmetric.Thislargeoverheadisparticularlydetrimentalindensenetworks becauseofthenetworkcongestionandcollisionsthatitgenerates.Theauthorsclaim thatthemessagecomplexityoftheEECDSalgorithmis O n ,asduringeachofthetwo phaseseachnodeatmostsendsoutonemessage.Thetimecomplexityofthealgorithm isgivenbytheconstructionoftheMIS,whichhasa O n worsttimecomplexity.The authorsalsoshowthatEECDShasanapproximationfactorofnothigherthan7.6,i.e.,the EECDSproducesaCDSwithatmost7.6timesthenumberofnodesgivenbytheoptimal solution,whichistheMCDS.Finally,theauthorsproposeabackbonerecalculationproceduretoswitchthebackbonewhentheminimalenergyofthecurrentonedecreasesby 50%.Thisprocedure,unfortunately,isnotwell-explainedinthepaperanditisunkonwn whetheritneedsglobalinformationorifitcanbetriggeredinadistributedmanner.Further,theclaimthattherecalculationprocedurebalancestheenergyconsumptionofthe nodesisnotsupported. Otheralgorithmsthatworkusingthistechniquearethe Distance-2D2Coloringalgorithm [48]and SPAN [49].AmodiedversionoftheSPANalgorithmthatincludesthe useofdirectionalantennasandpresentsthesamemessageandcomputationalcomplexity oftheoriginalversionispresentedin[50].Otheralgorithmsthatbelongtothiscategory canbefoundin[51],and[41]. 40

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Finally,thethirdapproachtocreateaCDSworksdifferentlythatthetwoothersapproachesdescribedabove;thegrowingtreeandtheindependentsets-basedtechniquesstart withareduced,non-connectedtopologyandthenaddnodestoconnectit.InthePruningbasedtechniquesapproach,thealgorithmscalculateatopologythatguaranteesconnectivitybyincludingmostofthenodes,andthenpruningunnecessarynodesout.ThisapproachisusedintheConnectedDominatingSetundertheRuleKalgorithmproposed in[52,53]andtheExtendedConnectedDominatingsetsintroducedin[54]. The ConnectedDominatingSetunderRuleKCDS-Rule-Kalgorithm proposedin[52, 53]isanexampleofadistributedalgorithmunderthiscategorythatuseslocalinformation.Thealgorithmworksintwophases.TherstphaseinvolvescreatinganinitialCDS treeusingthefollowingmarkingprocess[52]: S = 8 v 2 S : x ; y 2 N v ; :9 x ; y 2 E .5 where N v isthesetofneighborsof v Inotherwords,ifnode v hastwoneighborsthatarenotconnected,itwillincludeitself ontheinitialset.Inthisrstphase,thenodesexchangeHELLOmessagesinorderto gettoknowtheirneighborsandexchangetheirneighborlists.Onceanodereceivesthe listsfromitsneighbors,itintersectsthelistswithitsownlistofneighborsandcountsthe numberofelementsinbothlists.Ifthisnumberislessthantheamountofneighborsin thenode'sownlist,thenthisnodewillmarkitselfaspartoftheinitialset;otherwise,the nodewillturnitselfoff. Forthesecondphase,thealgorithmprunesunnecessarynodesapplyingoneofthethree pruningrulesdescribedin[53].Atemporarilymarkednodedecidestounmarkitselfifit determinesthatallitsneighborsarecoveredbymarkednodeswithhigherpriority,which mightbegivenbythelevelofthenodeinthetreeassumingthatalowerlevelmeans 41

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higherpriority,ortheprioritycouldhavebeendenedbeforeastotheexecutionofthe protocol.Aninitiatornoderequeststhelistofallmarkednodesinitsneighborhoodwith lessorequalprioritythanitself.Theneighbornodesupdatetheirlistofmarkednodesand respondwiththeupdatedlist.Then,basedonthereplymessages,theinitiatorchecksif allitsneighborsarecoveredbyatleastoneactivenodedifferentfromitself.Ifthisisthe case,itunmarksitselfandannouncesthis,sotheothernodescanupdatetheirstatusof coveredneighbors.Ifthenodehasatleastonenodethatiscoveredexclusivelybyitself, thenitmarksitselfasapermanentelementofthetree.Thenaltreeisaprunedversion oftheinitialonewithallredundantnodesthatwerecoveredbyothernodeswithhigheror equalpriorityremoved. Otherpruningrulesarealsopresentedbytheauthorsin[52,53]: Rule1 and Rule2 .In Rule1,amarkedhostcanunmarkitselfifitsneighborsetiscoveredbyanothermarked host;thatis,ifallneighborsofagatewayareconnectedwitheachotherviaanothergateway,itcanrelinquishitsresponsibilityasagateway.Inthe Rule2 pruningapproach,a markedhostcanunmarkitselfifitsneighborhoodiscoveredbytwootherdirectlyconnectedmarkedhosts.Finally,thethirdandlastrule, RuleK ,generalizestheapproachand buildsabettersmallerCDSrelaxingtheconstraintonthenumberofmarkedhosts,i.e., RuleK unmarksgatewayscoveredby k othergateways,where k canbeanynumber. Thecasesofthequeryingofneighbornode'sstatusandtheunmarkingannouncement processesintheEECDSalgorithmandtheCDS-Rule-Kmechanismsrespectively,show themainsourceofmessagescomplexityinthoseprotocols.Eventhoughtheauthors claimlinearityinthemessagecomplexity,thenalamountofmessagesisnotbounded andisaffectedbynodedegreeandnodedensityinthenetwork.IntheCDS-Rule-Kprotocol,onceanodedecidestounmarkitselfduringthequeryprocess,eachnodegeneratesaquerythatisbasedonitsownlevelandreceivesindividualanswers.Duringthe 42

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unmarkingannouncementprocess,itmustupdateallitsneighborstocorrectthemetrics inallpossibleactiveprocesses.Thisistwo-hopinformationthatmostofthenodessend oncetheygetprunedfromthetree.TheCDS-Rule-Kmechanismshasan O n 2 message complexity, O n 2 computationalcomplexity,andan O 1 DS opt approximation. 2.2.2.2Cluster-basedTechniques Thissectionpresentscluster-basedtechniques,whichsimplifythenetworktopologyeven furtherbycreatinggroupsofnodesmanagedbyspecialnodescalledClusterheads.Clustersarecreatedbyclassifyingobjectsintodifferentgroups,ormoreprecisely,partitioning thedatasetintosubsetssothateachclustersharessomecommonfeature,characteristic, ortrait.Cluster-basedtechniquesalsoincludealgorithmstoselecttheclusterheads,specialnodesthatnotonlyserveasfacilitatorsforcommunicationonbehalfoftheircluster nodesbutalsocanperformspecialtaskssuchasrouting,dataaggregation,scheduling, andotherswiththepotentialtosaveevenmoreenergy. Bothclusteringtechniquesandclusterheadselectionalgorithmsareveryimportantin thesetopologyconstructiontechniquessincetheyhavetobeimplementedinadistributed fashion,consumethenetworkenergyevenlyandefciently,andintroducetheleastamountofextraoverhead.Someofthemoreimportantalgorithmsofthiskindarethe Low EnergyAdaptiveClusteringHierarchyLEACHprotocol [55],whichisoneofthemost widelyknowncluster-basedtechniques,and HybridEnergy-EfcientDistributedHEED clustering ,ahybrid,energy-efcient,distributedclusteringapproachforadhocsensor networks[56]. 43

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2.2.2.3AdaptiveTechniques Adaptivetechniquesarethosemechanismsinwhichthenetworkisperiodicallyevaluatingthestateofthecommunication,and,whenaperformancemetricisnotatitsdesired level,thereducedtopologyadjustsinordertorecoverthenormalstate.Adaptivetechniquesfortopologyconstructioninwirelesssensornetworksarenotverycommoninthe literaturethusfar.Oneinterestingfeatureofthesetechniquesisthattheyperformboth, topologyconstructionandtopologymaintenancefunctions.Someofthemostimportant adaptiveprotocolsarethe AdaptiveSelf-ConguringsEnsorNetworksTopologiesASCENTmechanism [57],andthe MinimumPowerCongurationProtocolMPCP andthe MinimumActiveSubnetProtocolMASP bothproposedin[58]. 2.2.3HybridApproaches Thetechniquespresentedinprevioussectionscanbecombinedinordertodevelopa morecompleteandbettersolutiontothetopologyconstructionproblem.Forexample, clusteringtechniquesmightbeusedalongwithcontrollingthetransmissionpowerof eachnodetosimplifythetopologyandsolvetheRangeAssignmentproblem,saving additionalenergy. Anexampleofahybridtechniqueis CLUSTERPOW [59],inwhichtheauthorscombine clustering,router-based,andpowercontroltechniquestosolvetheRAprobleminnetworkswithnon-homogeneousdeployments.Otherexamplesofhybridprotocolarethe TopologyManagementbyPriorityOrderingTMPOprotocol [60],the Topologyand EnergyControlAlgorithmTECAforWirelessSensorNetworks [61],andtheprotocols proposedin[62,63]. 44

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2.3Coverage-orientedTopologyConstruction Ithasbeenstatedinthisdissertationthatthemaingoalsofawirelesssensornetwork aretomonitortheoccurrenceofeventsintheareaofinterest,reportthoseeventstothe users,andbeactivethelongestpossibletimewhilecoveringasmuchareaaspossibleand preservingconnectivity,sotheinformationgeneratedfromthenodescanbecollected. Thismeansthatinordertohaveaneffectivetopologyconstructionprotocol,noneof theseissuesshouldbeignored.Theprevioussectionincludedmultipletopologyconstructionprotocolsthatprovidedaconnectedreducedtopology,butdidnottakeintoaccount thelevelofcoverageoftheareaofinterest.Thissectionpresentstopologyconstruction protocolswhosemailgoalistoguaranteecoverage.Inordertopreservegeneralityand giventhatsomeoftheprotocolsincludedinthistaxonomydonotguaranteeconnectivity inthenetwork,thepropernameofthisbranchcouldnothavebeenconnected-coverageoriented,eventhoughthecontributionsinthisareapresentedinthisdissertationdoguaranteeconnectivity. Lookingatthealreadypresentedprotocols,twocasesofreducedtopologiescomesto attention:Therstoneiscasewhereallthenodesarekeptawakeandjusttheircommunicationrangesarereduced,andthesecondoneiswherethetopologyisreducedbyturning offredundantnodes.Intherstcasethecoverageoftheareadependsexclusivelyonthe actualdeploymentofthenodesbecausethecoverageofthereducedtopologyremains exactlythesameasintheMaxPowergraph.Inthesecondcase,eachnodethatisturned offdoesmostlikelyreducethedegreeofcoverageontheareaofinterest,whichimplies thattheselectednodesmustincludesomemetrictominimizetheimpactofthesleeping nodeswhileguaranteeingahighdegreeofcoverage. 45

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Figure2.5:Classicationofcoverage-orientedtopologyconstructionprotocols. Thegoalsoftotalcoverageandenergyefciencyaretightlyintegratedsinceanetwork thatprovidestotalcoveragemighthavetoomanyactivenodes,atopologythatissimply connectedmightnotprovidesufcientcoverageofthedeploymentarea,oranoptimaltotalcoveragewithminimumnumberofactivenodesmaynotbeconnected.Dependingon theapplication,anyofthesecasesmaybethedesiredsolution.Thissectionincludesaseriesofclassicationcriteriathatserveasastructureforageneraltaxonomyofcoverageorientedtopologyconstructionprotocols.Followingthetaxonomyanditsclassication criteria,someofthemostimportantcoverage-orientedprotocolsareintroduced. 2.3.1ClassicationFactors Coverage-orientedtopologyconstructionalgorithmscanbeclassiedaccordingtothe denitionoftheareaofinterestandtheredundancytheyprovide.Thetopologyconstructionprotocolsincludedinthischapterareorganizedbasedontheirclassicationinthe taxonomy,asshowninFigure2.5. 46

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2.3.1.1DenitionoftheAreaofInterest Thedenitionoftheareaofinterestisthemainfactorthatdifferentiatescoverage-orientedtopologyconstructionprotocols.Dependingontheapplicationandtheeventstobe monitored,thespecicationforcoveragechanges. Themostgeneralcaseisthe AreaCoverage ,inwhichthewirelesssensornetworkis inchargeofmonitoringthecompleteareafortheoccurrenceofevents.Sometypical examplesoftheseapplicationsareintrusiondetectionandmappingofenvironmental variables,liketemperature.Themainissuewiththeproblemofcompletecoverageis that,ifitsaverystrictpolicy,itmayrequirealargeamountofactivenodes,especially ifthedensityofthenetworkislow.Inadditiontothis,inordertohaveapreciseideaof thecoveredareaofanode,thepositionofthenodesisusuallyrequiredandthisincreases thecostofimplementationduetospecialhardwarelikeGPSoroverheadifadistributed locationalgorithmisused. However,sometimesitisnotnecessarytomonitortheentireareabutasetofsmaller regionsinwhichtherealinterestis.Insomecasesitmaybeassumedthattheseareas ofinterestmayevenchangeintime.Theprotocolsinthiscategoryareknownas Target Coverage protocols.Theirmaininterestistooptimizethecoverageofacertainnumberof targetsinsidethedeploymentareawhilepossiblyreservingtheenergyinareasinwhich thereisnointerestinkeepingthemcoveredbecausetheydonotcontainanytargets.An applicationthatbenetsfromtheprotocolsinthiscategoryistargettracking.Oneofthe issuesofthiskindofcoverageishowtoguaranteecoverageinthecaseswherethemobilityofthetargetsrequiretheprotocoltochangetheselectionofactivenodesfrequently. 47

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2.3.1.2Redundancy Giventhepromptnessforfailureinwirelesssensornetworks,coveragecanbeaffected inaveryunexpectedwaywhenanodefails.Someapplicationscanwithstandacertain degreeoffailureincoverageandwaitforamaintenancepolicytorestoreitlater.Inother applicationsthelossofcoverageisnotanoptionandsomelevelofrobustnessmustbe guaranteedinordertowithstandnodefailure.Oneofthewaysofprocuringrobustnessis byincreasingredundancy;i.e.,selectingmorethanonenodetocoverthesamearea. Themostcommoncaseofredundancyis 1-coverage ,inwhichtheprotocolsjustguaranteethatatleastasinglenodeiscoveringeachpointofthearea.Thisisthesolution thatrequiresfewerresourcesfromthenetwork,butisalsotheonethatismoresensitive tonodefailurebecauseitcanleaveareasuncoveredwiththelossofasinglenode.Non criticalapplicationsbenetfromprotocolsinthiscategorybecausetheycanreservemore energyforfutureuseandextendthelifetimeofthenetwork. Theprotocolsthatofferahigherdegreeredundancyareinthecategoryof K-coverage whereKisthenumberofnodesthatareguaranteedtooffercoverageovereachpoint intheinterestarea.ApplicationsthatneedcompletecoveragendtheK-coveragealgorithmsttedsotheycanstilloffercoverageevenwhenK-1nodesfail.Themainissueof theseprotocolsisthattheamountofresourcesneededtoofferredundantcoveragecanbe veryhigh,andalsomayhaveimplicationsconcerningthedensityofactivenodesinthe reducedtopology. 48

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2.3.2OtherConsiderationsinCoverage-orientedTopologyConstructionProtocols Someoftheprotocolsinthecoverage-orientedcategoryhavespecialconsiderationsrelatedtothecommunicationandsensingrangesofthenodes.Similarlytotopologyconstructionforconnectivity,bothcommunicationandsensingrangesareusuallyrepresented asdiskscenteredatthenode'spositionwithradius R Comm and R Sense ,respectively. Oneofthemostcommonassumptionsintheliteratureisthat,inordertofacilitatethe implementationofasolutionthatguaranteesbothcoverageandconnectivity,thecommunicationrangeissettobe R Comm 2 R Sense .Intheworkspresentedin[64],the authorsprovedthatifthecommunicationrangeisatleasttwicethesensingrange,acompletecoverageoftheareawillimplyconnectivityamongtheactivenodesinthetopology. ThisworkalsowasextendedtoK-coveragein[67]. Someotherprotocolsworkundertheassumptionthatthethecommunicationandsensing rangesareequal[68];however,inrealitycommunicationrangeisusuallygreaterthan thesensingrangeand,evenifthecommunicationrangecouldbereducedtomatchthe sensingone,itwouldimplyasubstantialincreaseinthenumberofnodesrequiredto coveragivenarea.Inbothcases,theprotocolsthatusetheseassumptionscannotguaranteeconnectivityiftheassumptionisnotaccomplished.Tosolvethisdependency,many protocolsassumeanarbitraryratiobetweenthecommunicationandsensingranges,includingtheonesintroducedinthisdissertation,A3CovandA3CovLite. Anotherconsiderationregardingthecoverage-orientedprotocolsiswhethertheyneed locationinformationornot.Themainadvantageofhavinglocationinformationisthat itiseasiertoguaranteetotalcoveragebecauseeachnodecancalculatetheareacovered byitselfanditsneighbors,checkredundancyanddeterminewhetheritisneededtostay activeornot.However,evenifthecostoftheoverheadisnotconsidered,theaccuracyof 49

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thelocationinformationmaynotbeenoughtoguaranteetheprecisioninthecalculation ofthecoverage;inotherwords,duetoanincorrectlocation,anodemayleaveazone uncoveredassumingtheareaiscoveredbyitsneighbors. Inthecaseoftheprotocolsthatlackanylocationinformationfromthenodesinthenetwork,guaranteeingcoverageisamorecomplextaskwhichusuallyissolvedbyproviding anapproximatesolution.Oneoftheseapproximationsispresentedin[71],whichstates thatinadensenetwork,ifallthenodesinthenetworkarecoveredbythesensingrangeof atleastoneactivenode,thentheareaofdeploymentiscovered w : h : p : Thisapproximation mayimplyasacriceincoveragearea,butwillalsodecreasethenumberofactivenodes requiredtoofferahighlevelofcoverage. 2.3.3ExamplesofCoverage-orientedTopologyConstructionProtocols TherstpartofthissectionwillbededicatedtoAreaCoverageprotocols,presentingboth 1-coverageandK-coverageprotocols.Differentapproacheswillbepresented,including theoreticaldeployments,andcentralizedanddistributedsolutions.Thesecondpartof thissectionwillcoversomeofthemostrelevanttargetcoverageprotocols,includingalso differentlevelsofredundancy. Therstandmostcommoncaseofcoverage-orientedprotocolsistheareacoveragecategory.Therstcasethatwillbeconsideredwillbetheprotocolsthatprovide1-coverage oftheareaofinterest.Sometheoreticalapproachesgenerateoptimalgriddeployments thatguaranteeconnectedcoveragewithaminimumnumberofnodes,anddifferentlevels ofconnectivity.Someexamplesofthistheoreticalapproacharepresentedin[69,72 75].Furthermore,thesolutiontothecirclepackingproblemisalsoconsideredasan approximationtotheconnectedcoverageproblem,basedontheresultsin[76],assuming 50

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that R Comm = 2 R Sense andthatoverlappingoftheareasofthecirclesispossible.Inthis dissertation,theA3,A3Lite,A3CovandA3CovLiteprotocolsarecomparedwiththe optimalsolutionspresentedin[69,72,76]. Basedontheassumptionsofverydensenetworksandacommunicationsradiusequalto thesensingradius R Comm = R Sense ,theauthorsin[69]provedthatnotopologycanguaranteeconnected-coveragetotheentireareawithanodedensitylowerthan 0 : 522 = r 2 where r isthecommunicationandthesensingradius. Inaddition,theauthorsusespecicgeometriestocreategrid-liketopologiesofactive nodestoprovideconnected-coverageofthedeploymentarea.Thegridstructuresare basedinsquare-,hexagon-,andstrip-likedistributions.Inordertocalculatetheamount ofnodesneededtobuildthistopologies,theauthorscalculatethenodedensityofeach typeofgrid.ThisformulasarepresentedinEquations2.6. d SQR = 1 = r 2 .6 d HEX = 0 : 769 = r 2 d STR = 0 : 536 = r 2 whichhaveapproximationratiosof1 : 916,1 : 473and1 : 027withrespecttotheoptimal connected-coveragetopology,andadegreeofconnectivityof4,3and1,respectively. Theauthorsalsopresentapproximationschemestoimplementthesetheoreticaldeploymentsindistributedfashion.Thesedistributedalgorithmsareallbasedontheassumption ofveryhighdensenetworkdeployments,theneedoflocationinformationandareferencelocationsystem,andmessageexchangesamongneighborstomakeon/offdecisions withoutfurthercoordination. 51

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aSquaredeployment. bHexagondeployment. cStripdeployment. Figure2.6:Differentdeploymentgeometriesforconnectedcoveragetopologieswith R S = R C 52

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Anotherinterestingresultshownin[69]isthatmoderatenodedensitiescanbeusedto coveralargefractionoftheareawhereastherequireddensityofnodesincreasesdrasticallyifcompletecoverageisneeded.Basedonthisresult,simulationexperimentsare presentedtoprovide90%connected-coveragetopologiesonly.However,theauhtorsdo notprovidedetailsofthedistributedimplementations. Similaroptimaldeploymentsarealsopresentedin[72]wheretheauthorsworkwithsquares,triangles,rhombuses,hexagons,andstripsbutproveoptimaldeploymentsforscenarioswhere R Comm 6 = R Sense ,withnodedensityfunctionspresentedinEquations2.7. Asshownin[72],once R Comm > p 3 R Sense ,mostoptimaltopologiesreachtheirminimal deploymentsize.Thiscanbeexplainedbytheworkin[77],wheretheauthorproved thattheoptimalcoveragestructureisbasedonatriangularpatterninwhichthreecircleswithsensingradiusradius r are p 3 r apartfromeachother.Inotherwords,smaller distancesbetweencircleswouldproduceoverlappingregionswhilegreaterdistances wouldproducenon-coveredareas.Therepetitionofthispatterncreatesa"honeycomblike"structurethatprovidestotalcoveragewithminimalnumberofcircles.Thisfactordeterminesthatthedistancebetweennodestoprovidetotalconnectivity-coverage shouldbe min p 3 R Sense ; R Comm .Ontheotherhand,iftheratiois R Comm = R Sense = 1, theoptimalsensingcoverageisequivalenttocommunicationcoverage,whichattheend determinestheconnectivityofthenetwork.Basedontheseideas,theexperimentsinthe performanceevaluationofthedistributedalgorithmsusetheratio R Comm = R Sense = p 3for theconnected-coverageprotocols,andtheratio R Comm = R Sense = 1fortheconnectivityonlyprotocols. 53

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d SQR = R 2 Sense min p 2 ; R Comm R Sense 2 .7 d RHO = R 2 Comm sin Q p 3 Q p 2 and p 2 R Comm R Sense p 3 d HEX = 3 4 p 3 R 2 Sense min 1 ; R Comm R Sense 2 d STR = 1 = b q R 2 Sense + b 2 = 4 b = min n R Comm ; p 3 R Sense o Afterobservingthedensityequationsfromtheprevioussolutions,if R Comm >> R Sense thesensingrangeultimatelydeterminesthenumberofactivenodestocoverthecompletearea.Inaddition,itwasmentionedthatanapproximationratioofthestrip-based deploymentisnogreaterthat2.7%oftheoptimalsolution,whichisdenitelyatight bound.Inthisdissertation,anewlowerboundmetricisproposedinordertosupportthe performanceanalysisofcoverage-orientedprotocols:the CirclePackingProblemCPP Thepackingproblemisverywell-knownbymathematiciansandgeometricians.Oneof themostimportantreferencestothisproblemcanbedatedbackto1900whenDavid HilbertpresentedattheInternationalMathematicalCongress,alistof23problemsthat wouldberelevantinthe20thcentury.AmongtheproblemsHilbertpresented,theproblemofpackingwasoneofthose.Thefollowingquotewastakenfromhislecture[78] 2 : Howcanwearrangemostdenselyinspaceaninnitenumberofequal solidsofgivenform,e.g.sphereswithgivenradii[ ::: ]thatis,howcanone 2 AcopyofHilbert'scompletelecturecanbefoundat http://aleph0.clarku.edu/ djoyce/hilbert/problems.html 54

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sotthemtogetherthattheratioofthelledtotheunlledspacemaybeas greataspossible? Thesolutionofthepackingproblem,ormorespecicallytheCirclePackingProblem, providestheminimumnumberofnon-overlappingcirclesthatcanbettedinsideageometricshape,inthecaseofstudyinthiswork,aunitsquare.Thesolutiontothisproblem thereforeprovidesalowerboundfortotalcoveragebasedonthefactthatnoneofthecirclesoverlapeachother,whichlimitsthenumberofcirclestoacertainoptimalvalue.The optimalsolutionstothisproblemwillbeusedinthisdissertationforevaluationpurposes. Theoptimalvaluesprovidedbythecirclepackingproblem[76]willbeusedasthelower boundfortheconnected-coverageproblem.Inaddition,amodicationisbeingproposed inordertogeneratetotalareacoveragebasedontheresultsofthenon-overlappingversion:Let R Comm >> R Sense sothatthegraphisconnected.Let n bethenumberofcircles ofasolutiontothepackingproblemforradius r = R Sense .Ifthesensingradiusofthe samecirclesismultipliedbyafactor c andoverlappingisallowed,theunitsquarecould becomecompletelycovered. AnexampleofthiscanbeseeninFigure2.7,inwhichthewhitesectionsaretheoriginal coveredareas,theblacksectionsareareasnotbeingcovered,andtheoutercirclesrepresentthemodiedsensingarea c R Sense .Figure2.7ashowstheoptimaloriginalcircle packingfor R Sense = 1 = 6oftheareaside.Figures2.7b,2.7cand2.7dshowhowthe coveragewouldlookiftheradiusisaugmentedbyafactorof2, p 3and1 : 5,respectively. Asitcanbeseen,theunitsquareisnowcompletelycoveredinallscenarios,andthe optimalvalueforpackingcanbecomparedwiththeonesobtainedusingthedensityfunctionsoftheoptimaldeploymentswithradiiof2 r p 3 r ,and1 : 5 r .Figure2.8showsthis comparisonwhereitcanbeseenthatthesolutionstothepackingproblemwith2 R Sense p 3 R Sense and1 : 5 R Sense areequivalenttothesquare,hexagonandstripgeometricoptimal 55

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aOriginalcirclepackingwith R Sense = 1 = 6oftheareaside. bModiedcirclepackingwith2 R Sense cModiedcirclepackingwith p 3 R Sense dModiedcirclepackingwith1 : 5 R Sense Figure2.7:Exampleoforiginalandmodiedsolutionsofthecirclepackingproblem. 56

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Figure2.8:Theoreticalcomparisonbetweenthepackingproblemandtheoptimal deployments. deploymentspresentedin[69],intermsofnumberofactivenodes,whichvalidatesthe useofthesolutionsoftheCPPproblemasatoolforanalysis. Themainissuewiththeoptimaldeploymentsisthattheauthorsassumethepossibility ofmanuallocationofthenodesintheexactpatterngeneratedbythesolutions.Whenthe topologieshavebeendeployedrandomly,theoptimalsolutionscannotbeapplieddirectly. Inordertosolvetheconnectedcoverageprobleminrandomtopologies,thefollowing centralizedanddistributedsolutionshavebeenproposed. Someexamplesofcentralizedalgorithmsarethefollowing:theauthorsin[79,80]ta randomnodedeploymenttoapredenedgrid.Theauthorsin[79,80]utilizedtheTriangleLatticedeploymentpatterninordertondthelowerboundforthecoverageproblem. Thedrawbackisthatalthoughthetightallocationofcirclesintheareaprovidesanalmost completecoverageofthearea,whichisalowerboundforthetotalcoverage,itresults 57

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inanunconnectednetwork.Inordertosolvethisproblem,thesolutiontothepacking problemisusedheretocreateadeploymentthatassuresaminimumamountofnodes with R Comm = 2 R Sense In[81],theauthorsgrowatreeandaddnodesaccordingtotherateofnewinformation thattheyprovideaboutthemonitoredarea.Inthecaseof[82,83],bothsolutionsare basedonmetaheuristics.Whiletherstworkusesgeneticalgorithmstondaconnectedcoveragetopologythatwillcoverasetofcriticalpoints,thesecondusesanevolutionary multiobjectiveapproachtocreateanoptimaldeploymentconsideringconnectivity,coverageandtransmissionpower. Someexamplesof1-coveragedistributedprotocolarethe ProvingEnvironmentand AdaptiveSleeping PEASprotocol, OptimalGeographicalDensityControl OGDCprotocolandthe Area-basedCollaborativeSleeping ACOSprotocol.ThePEASprotocol, presentedin[84],offerscoverageandconnectivityasymptoticallyalmostsurely a : a : s in thecaseswhere R c 1 + p 5 R s .Itworksbasedontwoalgorithms:ProbingEnvironmentandAdaptiveSleeping.Intherstone,nodeswakeupfromasleepingperiodand probetheirenvironment;ifnonodeisactiveonapredenedprobingrange,thenthenode willwakeup,otherwiseitwillgobacktosleep.AdaptiveSleepingisusedtocalculate oftheoptimalwakeuptimeforthenodes.Thisprotocolisadistributedheuristictocover area,basedon1-hopawayinformationfromneighbors,anddoesnotguaranteeneither1ork-connectivityorcoverage.However,itdoesnotrequirelocationinformationandit doesprovidesamaintenancepolicy. TheOGDC[65]isbasedonanoptimalityconditionpresentedonthesamepaperfor coverageandconnectivity,whichistheassumptionthat R c 2 R s .Themainideaisto trytondclustersofnodeswhoselocationsareascloseaspossibletothearrangements denedintheoptimalitycondition.Nodeswillstarttheprocessofselectionbyvolunteer58

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ingthemselves,basedonarandomvariableproportionaltotheirremainingenergyand thecurrentstateoftheirneighborhoods.Oncethevolunteernodehasannounceitself,a neighborattheproperdistancewillselectitandthentogethertheywilllookforathird nodethatcompletesthearrangement.Thisprotocolisadistributedheuristicforcovering thedeploymentarea,basedoninformationfromneighbors1-hopaway,anddoesguaranteeonly1-connectivityandcoverage,assuming R c = R s .Itrequireslocationinformation anddoesnotprovidesamaintenancepolicy. TheACOSprotocol,presentedin[85],isalocalizedprotocolthatcalculatesthenetarea coveredbyasensor,whichisdenedastheareathatiscoveredexclusivelybyasinglenodes.Anodeisselectedtoremainactiveiftheitsnetareaisgreaterthatacertain thresholdvaluedenoted j ,denedbetween0and1.Thisprotocoluses1-hopawayinformationfromneighbors,offers1-coverageandassumesthat R c 2 R s SomeexamplesofareacoverageprotocolswithK-coveragelevelofredundancyarethe StandGuardAlgorithm StanGAprotocol,the CoverageCongurationProtocol CCP andthe AccurateK-CoverageEligibility AKCEprotocol.TheCCPprotocol[66]uses apropertythatstatesthatanareaAisK-coveredifthefollowingthreeconditionsare followed:rst,theareacontainintersectionpointsbetweensensingareasofnodes,and betweenthesensingareaonodesandtheboundariesoftheareaA;second,alltheintersectionpointsbetweensensingrangesofnodesareK-covered;andthird,ifallintersectionpointsbetweensensingrangesandareaboundaryareK-covered.Basedon theneighbornodes'locationinformation,eachnodecandeneifallitsareahasbeen coveredbyitsneighbors.The EnhancedCoverageCongurationProtocol ECCP[86]is anenhancedversionofCCPthatincludestwomorestatesintheirautomatoninorderto guaranteeabetterselection. 59

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TheAKCE,presentedin[87],isaprotocolinwhicheachnodechecksalltheintersectionpointswithitsneighborsbasedon R s ,calledR-neighbors.Thenitfusesallthearcs formed,creatingsectorswiththesamecoveragedegreek's.Ifallsectorsarecoveredby neighbornodes,thenodewillbeeligibleforgoingintosleepingstate.Allthesectorsthat havelesscoveragethatK,arecalledDecisionAreas.Thenodecalculatesallintersection pointsbetweenR-neighborsandbetweenR-and2Rneighbors.Ifalltheintersection pointslocatedintheDecisionAreashaveacoveragestrictlyhigherthanK,thenthenode willbeeligibletogotosleepmode.IfatleastoneintersectionpointisnotK-covered,the thenodewillbeselectedtobeawake. TheStanGAprotocol[88]worksbasedonthenodecoverageapproximation.Eachnode setsarandomtimeoutduringwhichitlistensforactivenodeswhosedistanceislessthan R SG ,whichisaproportionalvaluetothesensingradius.Ifthenumberofnodesinside thediskwithradius R SG islessthanK,thenthenodewillremainactive;otherwise,if thenumberofneighborsisatleastK,thenthenodewillturnitselfoff.Thisprotocol iscomparedwithPEAS[84],andthreeschemespresentedin[89]:Nearest-neighbor, Neighbor-numberandprobability-basedselection.ThemaindisadvantageofStanGAis thatitdoesnotguaranteeconnectivitywhen R SG R c = 2.Thecoverage-orientedprotocols introducedinChapter5ofthisdissertationuseasimilareligibilitymetrictoselectactive nodesforcoverage,butguaranteeconnectivityinallcases. Otherexamplesofprotocolsinthiscategoryareasfollows:theauthorsin[90,91]calculateamaximalindependentsetandthenndappropriatenodestoconnectthesets. In[92]thenodesareselectedascloselyaspossibletoapredenedoptimaltopologyand thenholedetectionandcorrectionalgorithmsareexecutedtoguaranteetotalcoverage. In[93,94]theauthorsuseCDStechniquestoprovidecoverage.Theworkpresented in[69]includesatechniquebasedontheBreadth-FirstSearchBFS,inwhichnode 60

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y isselectedtobeevaluatedbynode x if d x ; y 1 : 914 ap with0 : 5 a 0 : 6and R Comm = R Sense Thesecondmaincategoryforcoverage-orientedprotocolsisTargetCoverage.Theprotocolsinthiscategoryarespecializedincoveringasetofpointsinsideaninterestarea. Someexamplesofprotocolsinthiscategoryaretheonespresentedin[95]. IntheEvenCoverprotocol[97]eachnodeevaluatestheexpecteddensityinitsareabased onthedistanceofallitsneighborsinordertoprovide1-coverageinthearea.Thismetricservesasanestimateofthequalityofcoverage.Thevalueofthedensitymetriccan determinethreeoptionsforthenode:rst,iftheareaisverydense,thenthenodewill gotosleep;second,iftheareaissomewhatdense,thenodewillbesenttosleepbased onarandomprobability;andthird,iftheareaisnotdenseenough,thenodewillremain active.TheprotocolassumesthatthenodesareuniformlyorPoissondeployedinthe area.Theauthorsin[95]proposeasolutionbasedontheconstructionofaConnected DominatingSetasin[52],offeringbothcoverage-onlyandconnected-coveragesolutions, includingk-coverage.In[96]theauthorsproposeanenergy-efcientsolutiontotheKcoverageofmultipletargetsindensenetworksbyndingdisjointtopologiesthatcoverall thetargets,andthenrotatingtheminordertopreservecoverageanddistributetheenergy usageamongdifferentsetofnodes. 2.4TopologyMaintenance Givenacertainnumberofnodesdistributedinaspecicarea,topologyconstructionaims atbuildingareducedtopologythatwillsaveenergywhilepreservingnetworkconnectivityandareacoverage.Oncetheinitialreducedtopologyhasbeencreated,thenetwork startsperformingthetasksitwasdesignedfor.Everyactivityinvolvedinthenetwork's 61

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tasks,likesensing,processing,anddistributingofinformationhasanassociatedcost thatwillconsumetheenergyoftheactivenodes.Therefore,inaniteamountoftime, allnodeswillinexorablyseetheirenergysourcedepletedcompletely,nomatterhow optimaltheinitialreductionwas.Thismeansthatinordertoincreasethetotalnetwork lifetime,thesetofactivenodes,theonesinthereducedtopology,cannotbeactiveall thetime.Rather,atopologymaintenancemechanismshouldbeinplacetorestorethe currenttopologyorbuildanewonewiththecollaborationofformerlyinactivenodes sothatallnodescanparticipateinthenetwork,consumetheirenergyinafairmanner, andincreasethelifetimeofthenetwork.Accordingly, TopologyMaintenance isdenedastheprocessthatrestores,rotates,or recreatesthenetworktopologyfromtimetotimewhenthecurrentreduced oneisnolongeroptimal.Itinvolvesrotatingtheroleofnodesasmuchas possibletoincreasethenetworklifetime. 2.4.1ClassicationFactors Topologymaintenancecanbeexercisedindifferentwaysdependingonwhenthetopologiesarebuilt,thescope,andthetypeoftriggeringeventormetric.Theseoptionsare explainednext. 2.4.1.1SelectionPolicy:Static,DynamicandHybrid Statictopologymaintenancetechniques calculatedifferentreducedtopologiesduringthe rsttopologyconstructionprocess.Thesetopologiesarebuiltandstoredinmemoryand switchedoutforeachotherwhenneeded.Assuch,statictechniqueshavepre-planned 62

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topologies.Themaingoalofthisapproachistodistributetheactivityofthenetwork amongdisjointsetsofnodes.Thebestexampletodescribethesetechniquesismakingan analogytoastringofholidayblinkinglights:theentirestringcontainsanumberofpredeneddisjointsubsetsoflightsthatarelitoneatatime,andtaketurnsovertime.Ascan beinferred,statictechniquestakeadditionaltimeduringtheinitialtopologyconstruction phasetocalculatealladditionaltopologies,butoncethisprocessisnished,theswitching processisfasterthanifanewtopologyconstructionphasehadtotakeplace.Further,the communicationoverheadofeachsubsequenttopologyconstructionphaseisalsosaved. Statictopologymaintenancetechniquesmayhavesomedrawbackstoo.Forexample, itisdifculttoknowapriorihoweachofthetopologiesandtheirnodeswillconsume theirenergy.Therefore,themechanismmaychoosetousesomenodesinmorethanone topologythatmaynotbeavailableorwillmakethetopologylastashortertimeperiod thanexpected. Oneimportantdecisiontomakeintheconstructionofthepre-plannedtopologiesiswhetherornottobuildcompletelynode-disjointtopologies.Thisaspectmustbeseenalong withthedensityofthenetwork.Forexample,inaverysparsenetwork,itmightbevery difculttondmorethanonecompletelydisjointtopology,andinthatcase,thetopology maintenancemechanismwouldbeswitchingthesametopologyoverandoveragain. Theoppositeistrueforhighlydensenetworks,inwhichmanynode-disjointreduced topologiesmightbefound.Nonetheless,regardlessofthenetworkdensity,inmostsituations,itmightbeagoodideatoallowshared-disjointtopologies.First,theremightbe criticalnodesthat,ifnotincludedinthetopologies,wouldmakestatictechniqueslook liketopologyconstructionalgorithms.Second,shared-disjointtopologiesallownew nodestobeincludedinthenetworkwiththepossibilityofextendingitslifetime.Ineither case,aseriesofpre-plannedtopologiesarestoredinthenetworkandswitchedbasedon 63

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Figure2.9:Multiplenode-disjointCDStreesoverthesamenetwork. theestablishedtriggeringcriteria.Figure2.9showsanexampleofthenumberofnodedisjointreducedtopologiesthatcanbecreatedtoimplementtheStaticTopologyRotation approach. Contrarytostatictopologymaintenancetechniques, Dynamictopologymaintenance techniques donotmakeaprioricalculationstodeterminethetopologythatwillbecome activewhenthecurrentoneisnolongerappropriate.Instead,dynamictechniquesmake thosecalculationson-the-y.Assuch,dynamictechniquesareusuallymoretimeand energyconsumingsincetheymayhavetorunthetopologyconstructionprocessseveral times.Therefore,theenergyefciencyoftheunderlyingtopologyconstructionalgorithm playsanimportantrole.However,sincedynamictechniquesconsiderthecurrentstatusof thenetworkwhenmakingthenewcalculations,thetopologyconstructionprocessusually 64

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choosesanoptimalorclosetooptimaltopologyeverytimeitisrun,resultinginbetteror moreadequatesubsequenttopologies,ascomparedwithstatictechniques. Finally, Hybridtopologymaintenancetechniques areacombinationofstaticanddynamic techniques.Thealgorithmsinthiscategoryworkintwodifferentstages.Intherststage, theprotocolcalculatesalldifferentreducedtopologiesduringthersttopologyconstructionphasestaticapproach.Thesecondstageiswhenthenetworkdeterminesthatthe currentreducedtopologycannotbeestablishedbecausethesinkhasnoconnectivitywith anyactivenodesdeadtopology,thenmechanismexecutesatopologyconstructionprotocolinordertondanewtopologyontheydynamicapproach.Theprotocolsin thiscategoryshowsomeadvantagescomparedtotheprevioustechniques,likeitcanuse resourcesthatthestatic-onlyprotocolswillnotbeabletouse,andthatthenetworkmay lastlongerthanwhenusingadynamicapproachbecausetherotationprocessconsumes lessoverheadthanacompletenewconstructionprocess.However,thehybridtechniques alsoshowadisadvantagethatnoneofthestatic-ordynamic-onlyhave:dependingonthe selectionofthetriggeringcriteria,acrippledreducetopologycanlastalongtime,affectingthelevelofserviceinconnectivityandcoverage,beforeitgetstothepointwhereit needstoberestoredglobally.TheseissueswillbeaddressedindetailinChapter6. 2.4.1.2LevelofInvolvement:GlobalandLocal Thesecondaspectisrelatedtothescopeofthetechnique:whichnodes,orwhichpartof thenetwork,areinvolvedintheexecutionofthetopologymaintenancealgorithm.The scopecanbeglobalorlocal.While globaltechniques considerallthenodesinthenetworkinordertomakeaglobal-optimaldecision, localtechniques onlyconsiderasmall subsetofthenodesinordertomakeadecisioninalocal-optimalfashion.Therefore, 65

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globaltechniquesswitchtheentiretopology,andlocaltechniquesonlyswitchaportion ofthenetwork,suchasabranchofatree,acluster,orevenjustasinglenode. Statictechniquesareusuallyglobalinnature,asthecalculationofreplacementsformore localizedportionsofthenetworkmaytakeanexcessiveamountofresources.Onealternativetomakestaticlocaltechniquesmoreattractiveistoincreasethescopeofthe portionofthenetworktoswitch.Forinstance,inatree-basednetwork,severaldifferent treebranchesmightbefoundduringthersttopologyconstructionphaseand,uponthe triggeringcriteria,anentirebranchisswitched.However,asthescopeisincreased,local techniquesbecomemoreandmoresimilartoglobaltechniques. Globaldynamictechniquesrunanetwork-widenewtopologyconstructionprocessevery timethetopologyneedstobechangedand,therefore,switchtheentiretopology.Local dynamictechniques,ontheotherhand,runamorelocalizedprocessmeanttocalculate andestablishanewbranchofatree,acluster,oraspeciclinkorsmallsetoflinks.Contrarytoglobaltechniques,localdynamictechniquesmightbeabletoincreasethenetwork lifetimemorethaneitherstaticordynamicglobaltechniques,asitmaybepossibleto restorealocalfailurewithjustafewcomputationsandasmallnumberofmessages. 2.4.1.3TriggeringMechanisms Whetherthetopologymaintenancemechanismisstatic,dynamic,orhybrid,globalorlocal,thereisoneimportantquestionrelatedtoall:whatisthecriterionorcriteriathatwill beusedtotriggertheprocessofchangingthecurrenttopology?Thetriggeringcriteria, whichmayhaveimportantimplicationsintermsofenergysavingsaswellascoverage, reliability,andotherimportantmetrics,maybebasedononeofthefollowingchoices: 66

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Time-based: Intime-basedtopologymaintenance,thecurrenttopologyischanged whenatimerexpires.Theamountoftimeisusuallyxedandpre-dened,andisa verycriticalvariable.Tooshortatimebetweenchangesmaycauseunwanted,extra overheadasaconsequenceofswitchingthetopologymoreoftenthannecessary. Ontheotherhand,averylongtimebetweenchangesmayuseasuboptimalnetworklongerthannecessary,withthepossibilityoflosingimportanteventsduetoits poorcoverage. Energy-based: Giventheenergylimitationsofwirelesssensordevices,itmakes sensetoswitchthetopologywhentheenergylevelofthenodesgoesbelowacertainthreshold.Again,thechoiceoftheenergythresholdisverycriticalforthesame reasonsexplainedbefore.Changingthetopologytoooftenmayendupspending moreenergythantheenergythatissupposedtobesavedbytopologymaintenance, therebydefeatingitspurpose.Averylowthreshold,ontheotherhand,willmake certaincriticalnodesunavailableforupcomingtopologies. Random: Inrandom-basedtopologymaintenance,thecurrenttopologyisswitched usingarandomvariable. Failure-based: Afailure-basedtechniquetriggerstheprocessofchangingthecurrenttopologyafteranode,oranumberofnodes,havefailed.Thesetechniques requiretheexistenceoffailuredetectionandnoticationmechanisms. Density-based: Anothercriterionmightbebasedonthedensityofthenetwork.A similarmetricmightbethenodedegreeofthenetworkorthenodedegreeofsome importantnodes. 67

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Figure2.10:Classicationoftopologymaintenance. Combinations: Combinationsofthesecriteriacouldbeusedaswell.Forexample, thetopologymaintenancecouldbeactivatedbasedonenergyandfailure,ortime andenergy. Figure2.10showsacompletetaxonomyoftopologymaintenancethatalsoincludessome ofthepossibletriggeringcriteria. 2.4.2ExamplesofTopologyMaintenanceAlgorithms ThetopologymaintenancealgorithmsthatareintroducedinthisdissertationwillbedescribedinChapter6.Inthissection,someofthemostrelevanttopologymaintenance protocolswillbepresented.Inliterature,therearenotmanytopologymaintenancetechniquesthatcouldbeclassiedasstaticglobal.Oneapproach,presentedin[69,96],is basedonthestaticmaintenanceconcept.Ingeneral,thestaticmaintenanceschemerequiresspecialattentionintheuseoftherandom-andpattern-basedapproachesforsynchronizedradiostowakeupthenodesandbuildthereducedtopologies. 68

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Oncetheinitialreducedconnected-coveragetopologyisbuiltusinganyofthemechanismsmentionedabove,thechosenmechanismisruniterativelyusingonlytheremaining nodes,orthosenodesthathavenotbeenpartofanyreducedtopologycalculatedbefore. Sincetheworkfocusesonbuildingthemaximumnumberofnode-disjointtopologies, itdoesnotincludeanyperformanceevaluationofthepresentedtechniqueintermsof numberofactivenodes,nordoesitmentionanythingaboutthetriggeringcriteriathat couldbeutilizedtoswitchthetopologies. Inthecaseofdynamicglobaltopologymaintenancetechniques,therearemanytopology constructionmechanismsthatembedandutilizethistechniquewithoutformallycallingittopologymaintenance.OneexampleisthatoftheLEACHprotocoldescribedin Section2.2.2.2.LEACHchangestheentirenetworktopologyperiodically,in rounds ; therefore,itisadynamicglobaltechniquewithatime-basedtriggeringcriterion.As describedinSection2.2.2.2,italsoincludesaclusterheadselectionmetricthatguarantees thatthenodesconsumetheirenergyinanevenandfairmanner. Thereareseveraltechniquesavailableintheliteraturethatperformdynamiclocalmaintenanceofthenetworktopologywithoutbeingexplicitlycategorizedasdynamiclocal topologymaintenancetechniques.Forexample,in[98],theauthorsproposeafaulttoleranttopologymaintenancemethodologyinwhichtheyselectasetofbackupnodes thatwillmaintainbackboneconnectivityreplacingnodesincaseoffailure.Theselected backupnodeswillturnonwhenafailureisdetectedinoneoftheactiveneighborsofa nonadjacentactivenode,creatinganalternateroutetoreachtheactivenodeincaseit wasdisconnectedfromthenetwork.Anotherdynamiclocalfailure-basedtechniqueis presentedin[99].Theworkproposestoincreasethetransmissionrangeofaneighbor ofthefailednode.Theneighborisselectedeitherrandomlyorbasedontheremaining energyofthenodes. 69

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In[100],theauthorspresentanevaluationschemefornodefailureinstaticwirelessnetworks.Theevaluationconsistsofperiodicalrequestsfromeachnodetoalltheneighbors inrange.Therecipientoftherequestmustexecuteatesttaskandreturntheresulttothe requester.Iftheresultiscorrectandthemessageisreceivedduringanexpectedinterval, thenthenodeisconsideredavailable.Theauthorsin[101]extendedthisevaluationproceduretomobileunits,includingrecoveryafterfailure. TheGeographicalAdaptiveFidelityGAFalgorithmintroducedin[102]isanotherexampleofadynamiclocaltopologymaintenancetechnique.GAFisbasedontheknown observationthatindensenetworksmultiplepathscanbeestablishedbetweennodes, therefore,thereisthepossibilityofturningsomenodesoffwithoutjeopardizingthenetworkconnectivity.GAFusesnodelocationinformationandavirtualgridtointroducethe conceptofnodeequivalenceinwhichallnodeswithinthesamevirtualgridsquareare consideredequalintermsoftheirabilitytoroutepackets.Nodesinthesamegridthen coordinateamongthemselvestodeterminewhowillperformtheroutingfunctionontheir behalfandforhowlong.Thisnegotiationisbasedonanapplication-dependentranking procedurethatchoosesastheactivenodetheonewiththemostenergy.Theactivenode thenbroadcaststheamountoftimeitwillbeactive,whichiscalculatedbasedonthe amountofremainingenergy.Oncetheactivenodeconsumeshalfitsenergy,thenodes wakeupandthenegotiationprocedurestartsagain.Atthattime,itisveryunlikelythat anodewhohasbeenactiverecentlywillbeselectedagainsinceitwasactivewhilethe otheronesweresleeping,achievingthedesiredenergyconsumptionbalance. TheSPANalgorithmintroducedin[49]issimilartoGAFinthesensethateachnodedecidestobepartoftheroutingbackbonebasedonthenumberofneighborsanditsamount ofenergy.InSPAN,backbonenodesarecalledcoordinators,andalsorotatewithtime. OnedifferencebetweenthetwoalgorithmsisthatSPANdoesnotneedlocationinfor70

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mation.SPANisbasedonHELLOpacketsbywhichnodesknowwhotheirneighbors andcoordinatorsare.Iftwoneighborsofanon-coordinatornodecannotreacheachother eitherdirectlyorthroughoneortwocoordinators,thenthenodeshouldbecomeacoordinator.Inordertoresolvecontentionproblemswhenmorethanonenodevolunteers asacoordinator,SPANdelaysthecoordinatorannouncementsbyatimethatconsiders thenumberofnodesamongtheseneighborsthatwouldbeconnectedifthenodewere tobecomeacoordinator,andtheremainingenergyinthenode.Then,periodically,each coordinatorchecksifitshouldcontinuebeingacoordinator.Inordertoensurefairness, thecoordinatorwithdrawsitselfasacoordinatorifeverypairofneighbornodescanreach eachotherviasomeotherneighbors. TheAdaptiveFidelityEnergy-ConservingAlgorithmAFECAproposedin[103]isalso verysimilartoGAFandSPAN.AFECAsharesthesamemotivationandapproachto topologymaintenanceofGAFandSPANbutusesadifferentswitchingmetric:neighbor density.Eachnodeestimatesitsneighbordensitybymaintainingalistofthenodesitis abletohear,then,itcalculatesitssleepingtimeusingaproportionalfactorofthenumber ofneighbors. 71

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Chapter3:Methodology Thischapterdescribesthemethodologyusedfortheperformanceevaluationofthedifferenttopologyconstructionandmaintenanceprotocolsintroducedinthisdissertation. Bothanalyticalandsimulation-basedevaluationsareincluded.Thischapterisdivided intwosections.TherstsectionpresentsanewanalyticalsolutiontotheminimalconnecteddominatingsetproblemusingamixedintegerprogrammingapproachMIP, whichservesasacentralizedoptimalalternativetotheheuristicsproposedlaterinChapter4.Thesecondsectiondescribesmetrics,factorsandlevelsutilizedinthesimulationbasedperformanceevaluationoftheprotocols,plusthedenitionofthemodelforenergy consumption.Theperformanceevaluationsarethenincludedintheappropriatechapters 3.1AnAnalyticalSolutiontotheMCDSProblem Previously,inSection2.2.2.1,theMCDSproblemwasformallydenedasaconnected setofnodes D V inagraph,suchthateverynodein V eitherbelongsto D orhasatleast onelinktoanodein D .TheMCDSproblemisaparticularcaseoftheMinimalDominatingSetMDSproblem,thathasbeensolvedusingbothanalyticalandapproximation approaches.However,inthecaseoftheMCDSproblem,notmanyanalyticalsolutions havebeenproposedtosolvethisproblem,comparedtothegreatmajorityofapproximate solutionsavailableintheliterature. 72

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Figure3.1:ExamplesofMDSsolutions. Twoapproacheshavebeenfoundintheliterature.Therstone,usedin[37],dividesthe MCDSproblemintotwosub-problems:ndingtheMDSofthegraph,andthenndinga spanningtreeoverthegraphthatconnectstheMDSnodes.Thedivideandconquerapproachmayreducethetotalcomplexityoftheproblem,whichisanimportantadvantage inlargescenarios;however,animproperlydividedsolutioncouldleadtoscenarioslike theonepresentedinFigure3.1. Theinitialgraphisaverysimpleone.TwoMDSscanbeobtainedfromthegivengraph and,giventhattheMDSlinearprogrammingformulationhasnoweightsontheobjective function,asin[37,104],anyofthetwosolutionsarefeasibleoptimalsolutions.However, ifsolutionMDS1isfedtothesecondstage,itwillneedtoincludemoreactivenodes inordertoprovideconnectivityamongthedominatingnodes,whichasitcanbeseenin thesolutionMDS2,isnotnecessary.Assaidbefore,anadequatedecompositionofthe MCDSproblemcouldprovideasuccessfulformulationthatwillovercomethisscenario andprovidetheoptimalsolution. ThesecondapproachforananalyticalsolutiontotheMCDSproblemispresented in[105].Thisformulationisbasedontwoconditionsthatmustbeaccomplishedbyevery CDS:Oneverysubsetofnodes S 2 V ,theremustbeatleastonegatewaynodethathas alinktoanodeintheset V = S vertex-cutcondition,andforeverynon-gatewaynode u 73

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amessagegeneratedfromanyneighborof u ,saynode v ,musthaveawaytoreachevery otherneighborof u neighborconnectivitycondition. Theformulationproposedbytheauthorsisbasedonthesolutionoftheminimumvertex cutproblemforallpossiblesubsets S of V withthevertex-cutcondition,whichtheyprove willproduceaMCDSset.Giventhatthenumberofallpossiblesubsetsof V growsexponentiallywith j V j ,theauthorsproposeaniterativeandincrementalconstraintgeneration schemethatincreasesthenumberofsubsetsconsideredoneveryiterationinalinearfashion.Theiterativeprocessstartswiththeoptimalsolutionbasedonthecurrentsubsets.If theoptimalsolutionofthevertexcutproblemisaCDS,thenitmustbeaMCDS,andthe programstops.Ifthesolutionisnotconnected,thentheauthorsincludenewconstraints basedonthenon-optimalsolutionandwillreruntheoptimalsolution. Boththepreviousformulationsdonotshowenoughclarityintheirimplementationto allowaneffectivereplicationoftheirmodel,andtheyalsoshowdependenceonheuristic processesinordertoprovideanapproximationtotheoptimalsolutionoftheMCDS problem,andnottheoptimaloneitself.Thislackofguaranteeinndingtheoptimal solutionisthemainmotivationfortheintroductionofthenewformulationpresentedin thisdissertation. MIP-MCDSisamixedintegerprogrammingformulationthatndstheoptimalsolution totheMCDSproblem.Therearetwomainsetsofconstraintsthatguaranteedominance overthenetworkandconnectivityamongthedominatornodes.Theformulationisbased onthebasicdenitionoftheMCDSproblem,whichmakesitverycleartounderstand andreplicate,ascanbeseeninSection3.2whereitisintroducedindetail. TheapproachusedintheMIP-MCDSsolutionisbasedontheassumptionthataMCDS canbedenedastheminimumcardinalitysubsetofnon-leafnodesamongallpossible 74

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treesthatcanbeobtainedfromaconnectedgraph.Inordertoprovethisstatement,some otherstatementsmustbealsoproved. Theorem1.Everypossibletreethatcanbeconstructedfroma connectedgraphwith n > 2 ,willcontainatleast4solutionstothe CDSproblem .Itisknownthateveryconnectedgraphcontainsatleastonetreethatincludesallnodes.Thisissimplyprovenbythefactthatacyclicstructurescanbeobtained fromsimplealgorithmsliketheBreathFirstSearchBFS,DepthFirstSearchDFSor theMinimalSpanningTreeMST.Furthermore,bydenition,thecompletesetofnodes ofagraphisalsoaCDS.Thenetworktopologythatofferstheworstcaseforaconnected dominatingsetcanbeseeninthelineargraph,inwhichalltheintermediatenodesbetweentheextremesmustbeselectedasdominatorsinordertoguaranteeconnectivity. Asstatedbefore,thisisasolutionoftheCDSproblemforthisgraph.Theotherthree solutionscomefromthescenariosinwhichthenodesintheextremesaredominated,and intwoscenariosinwhichjustoneofthemwasselectedtobeadominatorandtheother isdominated.ThesefourscenariosaretheonlypossiblesolutionsforaCDSinapath topology.Anyothertopologyisexpectedtohavemoreleafnodes,whichcanproduce morecombinationsforsolutionsoftheCDS. Corollary1.Everypossibletreethatcanbeconstructedfroma connectedgraphwith n > 2 willcontain 2 L solutionstotheCDSproblem where L isthenumberofleafnodesinthetree .Ingeneral,thetotalnumber ofconnecteddominatingsetscontainedinatreecanbecalculatedbyallthepossible combinationsofdominating-dominatorstatesontheleafnodes.Thisvalueisequivalent to2 L ,where L isthenumberofleafnodesinthetree,i.e.,allnodeswithcardinality1in thetree. 75

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Corollary2.TheminimalcardinalityCDSinatreeis n )]TJ/F42 11.9552 Tf 11.048 0 Td [(L .Allnon-leaf nodesarenecessaryintheCDSbecausetheyhaveatleastonenodeundertheirdominance.TheinclusionofanyleafnodeinthesolutionofaCDSwillresultinaredundant solution.ThismeansthattheexclusionofallleafnodeswillproducetheminimalcardinalityCDSofatree.Inthecasewhenagraphisapath,itistrivialtoobservethatonly onetreecanbeconstructedfromtheoriginaltopology,inwhichthenumberofleaves correspondstothetwonodesintheextremesthatdonotofferdominanceoveranynode; therefore,havingthat L = 2,thentheminimalcardinalityCDSsolutionofthattreewill betheminimalCDSofthegraphwhichis n )]TJ/F19 11.9552 Tf 11.036 0 Td [(2.Now,theotherextremecaseiswhenthe initialgraph G isafullyconnectedgraphinwhicheachnode u hasanedgetowardevery othernodeinthegraph.Itiseasilyseenthatifthetreeisselectedtobeastartopology, asinglenodeisabletodominateeveryothernodeinthegraph,sotheMCDSsolution tothisparticulartreehasacardinalityof1.Thisstatementimpliesalsothattheoptimal solutionoftheMCDSproblemisasubtreefromoneormoreofthepossibletreesthatcan begeneratedfromaconnectedgraph.TheconclusiononthisCorollaryissupportedalso byTheorem6.16in[104]. Theorem2.Notallpossibletreesthatcanbeconstructedfroma connectedgraphcontainasolutiontotheMCDSoftheoriginalgraph BasedontheresultofCorollary2,itcanbeseenthateverypossibletreeobtainedfrom agraphcontainsaCDSwithminimalcardinalityof n )]TJ/F42 11.9552 Tf 11.32 0 Td [(L dominantnodesfortheirparticulartree;however,theminimalcardinalityCDSsolutionforaparticulartreeisnot necessarilytheminimalcardinalityCDSoftheinitialgraph.Assumegraph G asafully connectedgraph.AsshowninCorollary2,whenhavingastartopologytree,theminimumcardinalityCDSandtheoptimalCDSofthegraphhasasizeof1.Nevertheless,one ofthepossibletreesthatcanbeconstructedfromafullyconnectedgraphisapathgraph 76

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which,asitwasshownalsoinCorollary2,hasaMCDSwithaminimumcardinalityof n )]TJ/F19 11.9552 Tf 11.128 0 Td [(2whichisgreaterthantheminimumcardinalityoftheMCDSfromthetreewithstar topology. BasedonCorollary2,itcanbeseenthattheconstructionofaminimumtreethatprovides dominanceofthegraphisalegitimateapproachtondingtheoptimalsolutionofthe minimalconnecteddominatingsetproblem.However,Theorem2showshowtheprocess ofndingthetreethatcontainstheoptimalCDSisnottrivial. Themainadvantageofincludingbothconnectivityanddominanceasasingleproblemis thatallnodesselectedtobeactivearepotentialdominators,asopposedtothedominatorsgatewaysapproachinwhichthedominancecapabilityofthegatewaynodesisnotused. ThischaracteristiceliminatedthepossibilityofhavingcasesliketheoneinFigure3.1bin whichnodeBcouldhavebeenselectednotonlyasagatewaybutalsoasadominator. Theformulationpresentedinthenextsectionisbasedonthesearchofthedominating subtree.Thestructureofatreewasselectedbecause:rst,thenumberoflinksisknown tobealways n )]TJ/F19 11.9552 Tf 10.761 0 Td [(1,being n thenumberofnodesinthetree;andsecond,becausenomatter whatshapethenalgraphofthedominatorstakes,ifitisaconnectedgraph,thenatree canbecalculatedfromthetotalsetofedges. 3.2TheMIPApproachfortheMinimumConnectedDominatingSetProblem ThesolutionpresentedinthissectionisbasedonamixedintegerprogrammingMIP formulationoftheMinimumConnectedDominatingSetproblemstartingfromthesink node.Thisvariationisbasedonthefactthat,inrealapplications,thesinknodemust bealwaysactiveandthatitshouldbethecenterofthelogicalinfrastructureinorderto 77

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reducethedistancefromallthenodestoitself.AgeneralsolutiontotheCDSproblem canbesolvedusingasimilarapproach,butitwillnotbeincludedinthisdissertation. Asstatedbefore,thisformulationisbasedontwoconstraints:dominationandconnectivity.ThedominationconstraintisbasedontheMinimumTotalDominatingSetMTDS problem,aspresentedin[104].TheMTDSproblemdiffersfromtheregularMDSprobleminthesensethateverynode,includingthedominatornodes,musthaveatleastone dominatornodeintheirneighborhoods.Thisconstraintguaranteesthattherewillbeno isolateddominatornodes,whichisanecessaryconditionofanyMCDSsolutionbutinsufcient,becauseitdoesnotguaranteeconnectivityinthesubsetofdominantnodes;for example,thenalreducedtopologymaybeaforestgraphmadeofislandsofconnected componentsbuiltfromdominatornodes,inwhichthedominatornodesarenotisolated, butdisconnected. Theconnectivityconstraintisbasedonatechniquecalledtheowoftokens.Thetokensrepresenttherightforanodetobecomeadominatornode,andtheyowthough thenetworkcreatingatreeofdominatornodes.Theminimumtreethatdominatesall nodesinthenetworkwillbetheMCDSthatstartsinthesink.Theowoftokestechniqueisdenedbasedonthefollowingrules: Thesinknodeisassumedtobetheuniquesourceofthetokensanditwillposses n 0 tokens,where n 0 isassumedtobetheminimumnumberofrequireddominator nodestocoverthecompletenetwork,includingthesinknode. Thedistributionprocessstartswiththesinkconsumingonetokenanddistributing n 0 )]TJ/F19 11.9552 Tf 10.949 0 Td [(1tokensamongitsneighborsselectedtobedominators. 78

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Figure3.2:Exampleoftheowoftokenstechnique. Eachdominatornode w willreceiveanumberoftokens n 0 w n 0 )]TJ/F19 11.9552 Tf 11.676 0 Td [(1 from anotherdominatornode,willconsume1andthenitwilldistribute n 0 w )]TJ/F19 11.9552 Tf 11.075 0 Td [(1tokens amongitsneighbornodesselectedtobedominatorsalso. Dominatornodesaretheonlyoneswhocandistributetokens. Adominatornodethatreceivesjust1tokencannotselectanymorenodestobe dominators. Anodecannotbeadominatorifitdoesnotreceiveatokenfromanotherdominator node. Therecanbeowoftokensonlywheredirectlinksexistbetweennodes AnexampleoftheexecutionoftheowoftokenstechniquecanbeseeninFigure3.2. Thesinknodeinthecentergeneratestheowthatwillreachallactivenodes.Inthe exampleitcanbeseenhowthesinknodedistributes6tokensamongitsneighbors,which willdosimilarlywiththeextratokenstheyreceived. 79

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Themathematicalformulationassumesthatthereexistsaconnectedgraph G = V ; E where n = j V j istotalnumberofnodesinthenetworkand adj istheaadjacencymatrixof size n n whichcontains1ifthereisdirectcommunicationbetweenthenodes i and j ,or 0otherwise,foreverypair i ; j 2 V Theproblemhastwosetsofvariables:thebinaryarray y withsize n ,inwhich y i representsifthenodeisselectedtobedominatorwitha1,and0otherwise,andtheinteger array flow withsize n n inwhich flow i ; j containstheamountoftokensthatow fromnode i tonode j Equation3.1showstheformulationofthemixedintegerprogrammingversionofthe minimumconnecteddominatingsetbasedontheowoftokensapproach,whichisone ofthecontributionsofthisdissertation. minn 0 = i y i .1 s : t : j f s ; j )]TJ/F46 17.2153 Tf 10.95 -2.552 Td [( i f i ; s = n 0 )]TJ/F19 11.9552 Tf 10.949 0 Td [(1.2 8 i ; j f i ; j adj i ; j )]TJ/F46 17.2153 Tf 10.949 -2.552 Td [( k f k ; i adj k ; i = )]TJ/F19 11.9552 Tf 9.289 0 Td [(1 y i .3 8 i ; j f i ; j adj i ; j n y i .4 8 i ; j adj i ; j y j 1.5 Theobjectivefunctionofthisproblemistheminimizationofthenumberofactivenodes, asshowninEquation3.1.Theconstraintsoftheminimizationfunctionarethefollowing: 80

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Constraint3.2determinesthatthenumberoftokensthatowfromthesinkis n 0 )]TJ/F19 11.9552 Tf -384.673 -23.907 Td [(1,whichisthenumberofdominatorsminus1. Constraint3.3determinesthatthedifferencebetweenincomingandoutgoingow is )]TJ/F19 11.9552 Tf 9.289 0 Td [(1or0,dependingifthenodeisadominatorornot,respectively.Thisrestrictionalsocontrolsthatdominatednodeshavenoowandthatowcanonlyoccur betweennodesthatareadjacent. Constraint3.4determinesthattheoutgoingowsislessorequalthanthetotal numberofnodesinthetopologyforactivenodes,and0forinactivenodes.This restrictionalsolimitstheexistenceofowoftokensonlyifthenodesareadjacent. Constraint3.5determinesthateachnodemusthaveatleastonedominatorinits neighborhood.Thisconstraintguaranteesthatsetofselectednodesisatotaldominatingset. ThecurrentformulationoftheMIP-MCDSproblemisaninitialversiontotheanalytical solutionoftheMCDSproblem,whosepurposeisonlytoserveasatoolforcomparison andevaluationoftheapproximationalgorithmspresentedinthisdissertation.Theformulationstillhassomeroomforimprovementinordertoreducetheexecutiontime.A pre-processingschemecouldbeimplementedinordertoeliminatesometrivialdecisions; forexample,turningoffimmediatelyallnodeswithnodedegreeequalto1,becausethey aredestinedtobedominated.Amorecompleteanalysisandfurtherimprovementsare partofthefutureworkonthistopic.Inaddition,duetothe NP-Hard natureoftheMCDS problem,thisformulationisnotscalableforlargenetworks,whichiswhymostofthe discussioninthisdissertationrevolvesaroundheuristicsolutions. TheMIP-MCDSoptimizationmodelwastestedusingthetopologycontrolsimulator Atarraya,includedinthisdissertation,andtheoptimizationprogramcalledGurobi c de81

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velopedbyGurobiOptimization 1 .Theresultsoftheanalyticalcomparisonoftheoptimal solutionagainsttheproposedheuristicswillbeshowninSection4.4. 3.3PerformanceEvaluation:Assumptions,Metrics,FactorsandLevels Thissectionpresentsthegeneralassumptions,performancemetrics,factorsandlevels utilizedintheperformanceevaluationspresentedinthisdissertation.Theevaluationsas wellasthecharacteristicsoftheparticularscenariosusedforeachsetofexperimentswill bepresentedintheperformanceevaluationsectionofeachchapter. 3.3.1Assumptions Thefollowingaretheassumptionsmadeinthisdissertation: Allnodesarelocatedinatwodimensionalspaceandhaveaperfectcommunication coveragedisk. Allnodeshaveequalcommunicationrangesandalllinksarebidirectional. Allnodeshaveasinglesensorandhaveaperfectsensingcoveragedisk. Nodeshavenoinformationabouttheirposition,orientation,orneighbors. Theinitialgraph,theoneformedrightafterthedeploymentusingthemaximum communicationrange,isconnected. Distancesbetweennodescanbecalculatedasametricperfectlyproportionaltothe ReceivedSignalStrengthIndicatorRSSI. 1 http://www.gurobi.com/ 82

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ThereisnopacketlossattheDataLinkLayer. Thereisamechanismbywhichanodecanbeawakenedwhenitsradioisoff. Thenetworkdutycycleis100%Thenetworkisalwaysactive. Thetimeunitsofthesimulationclockareapproximately1second. 3.3.2PerformanceMetrics Inordertoprovideatangiblecomparisonamongtopologycontrolalternatives,thefollowingperformancemetricswerechosen.Someofthemareexclusivetotheconstruction orthemaintenanceprocesses. Numberofactivenodes: thismetricmeasuresthequalityoftheselectionpolicyfor nodes.Inaddition,theamountofactivenodesselectedbythealgorithmhasadirect impactonthelifetimeofthenetwork. Numberofmessages: thismetricshowstheoverheadoftheprotocolintermsof messagecomplexity,whichisalsorelatedwiththescalabilityoftheprotocoland theenergyconsumption. Ratioofenergyspent: thismetricshowsthecostoftheprotocolintermsofenergy; inotherwords,howmuchenergyisspentintheexecutionoftheprotocol. Ratioofcoveredarea: thisratioisimportantforcomparingcoverage-oriented protocolsinordertocompareeffectivenessoftheirselectionpolicies. Networklifetime: thismetricisusefulespeciallyincomparingtopologymaintenanceprotocols,andshowsthebehaviorofsomeofthepreviouslymentioned 83

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metricsinthetimedomain,inordertoobtainanaveragebehavioroftheuseofthe resourcesinthenetworkinthelongrun. 3.3.3FactorsandLevels Theevaluationoftopologycontrolprotocolswasperformedindifferentscenarios,in ordertoobtainageneralideaofthebehavioroftheprotocolsundercertainconditions. Thelistoffactorsthatwereusedtodenethedifferentscenariosisthefollowing: Numberofnodes: thisparameterdeterminesthesizeofthetopology.Thevariation ofthisparameterhelpstodeterminethescalabilityoftheprotocols.Thenetwork sizesusedontheexperimentsvariedbasedontheevaluatedmetric,fromverysmall topologieswithonly5nodes,toverydensetopologieswith4000nodes. SideoftheareaL :thisparameterdenesthesizeofthedeploymentarea.Thearea isassumedtobeasquareofsideL.Thisfactorvariedbetween50and600meters, dependingonthedenitionofeachparticularexperiment. CommunicationrangeR c : thisparameterisveryusefulbecauseithasanimplicationinotherparameterslikeaveragenodedegree.Thelevelsofthisfactorwere calculatedmostlyusingtheCriticalTransmissionRangeCTRformula[6].The CTRistheminimalradiusthat w.h.p. producesaconnectedtopologygiventhesize ofthenetworkandtheareaside L .BasedontheCTR,thecommunicationrange takesvaluesof1to3CTRs.Insomecases,thelevelswerecalculatedasaratioof thesensingrange.Inthisfashion,thisfactortakesvaluesof1, p 3and2. 84

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SensingrangeR s : thisparameterisimportantdeterminingtheareaofcoverageof asinglenode.Thelevelsofthisfactorwerestaticallydenedorweredenedasa certainratioofthesideofthearea L NumberofVirtualNetworkInterfacesVNIs: thisparameterisusefulfortopologyconstructionandmaintenanceprotocolsthatcontemplatetheuseofmultiple reducedtopologies.AlltheexperimentsthatusedmultipleVNIs,assumedavalue of3VNIsinthenetwork. LevelofredundancyK-CommandK-Cov: theseparametersdeterminethelevelof redundancyincommunicationandcoverage.Alltheexperimentsassumeavalueof K-Comm=1andK-Cov=1. Nodelocationdistribution: thedistributionofthenodesintheareaplaysavery importantroleintheperformanceoftheprotocols.Eventhoughmanyassume uniformlyrandomdistribution,somerequirespecicdensitiesineverysectionof thedeploymentarea. Networkload: theamountofmessagesthateveryactivenodewillbesendingduringtheoperationofthenetwork.Thiscouldbeconstantandperiodic,orcould bevariabledependingontheoccurrenceofanevent.Allexperimentsassumeda networkloadof1messageevery10secondsperactivenode.Inaddition,therewas nodataaggregationtechniqueinordertoreducetheloadonthenetwork. Packetsize: allexperimentsusetwodifferentmessagesizes:shortmessages,assumedtobecontrolpacketsof25Byteslong,andlongmessages,assumedtobe dataorspeciallongcontrolpacketsof100Byteslong. 85

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Initialenergy: thisparameterrepresentstheinitialenergyreservethatanodehasat thebeginningofthesimulation.Thevalueassumedforthisparameteris1Jouleper node,asin[55].Thisvalueisconsiderablysmallcomparedwiththerealamount ofenergyinanAAbattery,howeveritwasselectedforconvenienceinorderto reducethesimulationtime.Itisexpectedthattheperformanceevaluationofthe networkwithrealenergyreservevalueswillbeproportionallysimilartotheresults presentedinthisdissertation. 3.3.4EnergyModel Inordertoassessthelifetimeofagiventopology,itisimportanttoincludeamodelto drainthenodes'energyeverytimetheyperformanyaction.Theenergymodelusedin thisdissertationtomodeltheenergyconsumptionofthenodesisbasedonEquations3.6 and3.7,aspresentedin[55],whichismostlybasedontheactionsoftransmmitingor receivingdata. E Tx = E elec + E amp R 2 comm p .6 E Rx = E elec .7 where E Tx istheenergyspenttotransmit1bit, E Rx istheenergytoreceive1bit, E elec is theenergyusedbytheelectroniccomponentsoftheradio,and E amp istheenergyused bytheradioamplier.Thesecondtermisproportionaltothesquareofthetransmission rangethatwantstobeachievedbytheradiosignal.Despitethesimplicityofthisenergy model,itisstillcommonlyusedintheliteratureofwirelesssensornetworks.Intheperformanceevaluationspresentedlaterinthisdissertation,itisassumedthatidlelistening 86

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Table3.1:Parametersfortheenergymodel. Initialenergysource 1Joule E elec 50 nJ = bit E amp 10 pJ = bit = m 2 energyconsumptionisnegligible.Thevaluesoftheparametersfortheenergymodelare summarizedinTable3.1. 87

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Chapter4:TheA3andA3LiteTopologyConstructionProtocolsforConnectivity InChapter2,alargenumberofsolutionsfortopologyconstructionwerediscussed,both forconnectivityonlyandforconnectedcoverage.Themaincontributionspresentedin thisdissertationarethedenitionandimplementationofanewfamilyofsimpletopologyconstructionprotocolsforwirelesssensornetworks.The A3 familyofprotocolsis composedoffourprotocols: A3 and A3Lite ,focusedonachievingconnectivitywhile reducingthenumberofactivenodesasmuchaspossible,and A3Cov and A3CovLite whichtrytoincreasetheamountofareacoveredbythereducedtopologyinthecases where R Comm 6 = R Sense ,withoutincreasingdramaticallythenumberofactivenodes. Thischapterwillbededicatedentirelytothersttwoconnectivity-orientedprotocols. Eventhoughitwasdiscussedthatcoveragemustbeacriticalconsiderationonanytopologyconstructionprotocol,theassuranceofconnectivityisalsofundamentalbecausea networkthatoffersperfectcoveragebutlacksthemeanstotransmittheinformationis useless.Thatisthereasonwhythe A3 and A3Lite connectivity-orientedprotocolsare thefoundationofthe A3Cov and A3CovLite coverage-orientedprotocolspresentedin Chapter5. 88

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4.1Introduction Thealgorithmspresentedinthischapterbelongtothecategoryofhierarchicalschemes thatcreateaConnectedDominatingSetCDStoreducethetopology,asdened in2.2.2.1.Amongthewiderangeoftopologyconstructionalgorithmsshownonthesecondchapter,thiscategorywasselectedbasedontheadvantagesitoffers: ThenodesselectedtobepartoftheCDSaresufcienttoprovideconnectivityto thenetwork.Thisgivesthepossibilityofturningoffeverynon-selectednode,while providingconnectivityandareduceddegreeofsensingcoverageofthedeployment area,dependingontheratiobetweenthesensingrangeandtheareaside. Ifthenon-selectednodesaresenttosleep,theirenergywillbeusedforfuturemaintenanceofthenetwork,whentheinitiallyselectednodesstarttonishuptheir energyreserve.Thesesavingsarenotpossibleontechniquesthatarebasedonjust alteringthetransmissionpower. Whenmostofthenodesareturnedoff,thenodedegreeisreduced,sointerference andcollisionsarereducedconsiderably.Thissurelyhasanimpactonthepacket delayandthroughputofthenetwork. Thefocusofthischapteristopresenttwosimpletopologyconstructionalgorithmsthat guaranteeconnectivity,withlowmessageandcomputationalcomplexity:A3andA3Lite. TheA3algorithm,whosenamecomesfromATree,istherstmemberofthefamily oftopologyconstructionprotocolspresentedinthisdissertation.Asitnameimplies, thisalgorithmcreatesatreethatcoverseverysinglenodeinthetopologyandprovidesa communicationbackboneforthenetwork,andallthenon-selectednodesaresenttoalow 89

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energyconsumptionstatesotheirenergywillbepreservedforfutureuse.Eventhough theideaisdenitelynotnew,themethodologyandselectionmetriccertainlyare. ThesecondalgorithmistheA3Liteprotocol,whichisanevolutionoftheA3protocol. Theideawiththesecondprotocolisthat,whileusingthesamebasicprincipletocreate thetree,A3Liteuseslessmessages,reducesthecomputationalcomplexityandevenproducesareducedtopologywithlessactivenodesthanitspredecessor. Theseprotocolswillbetestedagainsttwowell-knowntopologyconstructionprotocols alsopresentedonChapter2:EECDS[44]andCDS-Rule-K[52].Furthermore,the performanceofA3andA3LitewillbealsocomparedtotheirextendedversionforcoverageA3CovandA3CovLiteandwiththeoptimaldeploymentsforconnectedcoverage presentedin[69]inChapter5,basedonthefactthatwhen R Comm = R Sense ,theproblemof connectivityissimilartotheproblemofconnectedcoverage,whichdiscussedinthenext chapter. 4.2TheA3Algorithm Usingamoreformaldenition,theA3protocol[106]producesatreethatisanapproximatesolutiontotheMinimalConnectedDominatingSetproblemMCDS,whichis provedtobeNP-Hardin[36].Oneoftheadvantagesoftheheuristicnatureofthissolutionisthatitcanbeexecutedinadistributedwayinthetopology,opposedtoacentralizedprocessingthattheoptimalmixedintegerprogramingsolutionpresentedinSection3.2.Asexpectedthecostoftheapproximatesolutionisrepresentedbytheextra activenodesselectedthattheoptimalsolutionswouldnothavechosen.Thistopicwill bediscussedindetaillaterinSection4.4,inwhichthesolutionsprovidedbytheMIPandheuristic-basedapproacheswillbecompared. 90

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Figure4.1:TheA3algorithm. TheA3algorithmassumesthatthenodeshavenoknowledgeaboutthepositionororientationoftheirneighbors;therefore,thenodeslackanexactgeometricviewofthetopology.Ontheotherhand,nodesareabletodeterminethedistancetotheirneighborsbased onthesignalstrength.Thedistanceplaysamajorroleintheselectionofthenodesbased onthebeliefthat,themorespreadoutthenodesare,themoreareaandunvisitednodes theywillcover.TheA3algorithmconsistsofthe NeighborhoodDiscovery Children Selection ,and SecondOpportunity processes. 4.2.1TheNeighborhoodDiscoveryProcess Oncethenodesaredeployed,thetreebuildingprocessisstartedbyapreselectednode, usuallythesinknode.Thesink'sinitialstateis ActiveCandidate ,whilealltheother nodesareinthe Initial state. 91

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Figure4.2:TheA3protocolnitestatemachine. Thesink,nodeAinFigure4.1a,startstheprotocolbysendinga HelloMessage .This messageallowstheneighborsofAtorecognizetheirdominantor"parent"node.InFigure4.1a,nodesB,C,D,andEreceivethemessage.NodesFandGareoutofreach fromnodeA. Ifanodehasreceiveda HelloMessage previously,itignoresanyothermessagesofthis kind;otherwise,thereceiversetsitsstateas Child ,adoptsthesenderasits"parentnode", calculatestheselectionmetricexplainedlaterinSection4.2.3.1andanswersbackwith a ParentRecognitionMessage ,asshowninFigure4.1b,whichincludesthecalculated metric.Theselectionmetriciscalculatedbasedonthesignalstrengthofthereceived HelloMessage andtheremainingenergyinthenode,andwillbeusedlaterbytheparent nodetosortthecandidatesandchoosethemostappropriateones.Attheendofthisrst stage,nodeAhasthelistofallthenodesthatitiscovering,andtheirrespectivemetrics. Inaddition,eachofthecoverednodesknowswhichnodewillbeitsparentnode. 4.2.2ChildrenSelectionProcess Justafterhavingsentthe HelloMessage ,the ActiveCandidate nodechangesitsstate to WaitingCandidate andsetsatimeouttoreceivetherepliesfromitsneighbors.Ev92

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erytimea ParentRecognitionMessage isreceived,theselectionmetricisstoredinalist ofcandidates. Ifa WaitingCandidate nodedoesnotreceiveany ParentRecognitionMessages from itsneighbors,itturnsoffbecausetherearenonewnodestocoveronitsneighborhood. ThisisthecaseofnodesEandBinthenaltopologyshowninFigure4.1g,giventhat theyhavenochildren.Ifatleastonenoderepliestothe HelloMessage ,the Waiting Candidate willchangeitsstateto ActiveNode becauseitiscoveringatleastonenode inthetopology. Oncethetimeoutexpires,theparentnodechangesitsstatusto ActiveNode andsortsthe listindecreasingorderaccordingtotheselectionmetric.Theparentnodethensendsa ChildrenRecognitionMessage thatincludesthecompletesortedlistofcandidatestoall itsdominatednodes.InFigure4.1c,nodeAbroadcaststhesortedlisttonodesB,C,D, andE. Afterthechildrennodesreceivethelist,theychangetheirstatusto Candidate node andsetatimeoutproportionaltotheirpositioninthecandidatelist.Duringthattimeout thecandidateswaitfor SleepingMessages comingfromtheir"brother"nodes.Ifanode receivesa SleepingMessage duringthetimeoutperiod,itturnsitselfoffforacertain periodoftimeandchangesitsstatusto SleepingCandidate ,meaningthatoneofits brothersisbetterqualiedtobecomepartofthetree.Basedonthisscheme,thebest nodeaccordingtothemetricsendsa SleepingMessage rst,blockinganyothercandidate brotherinitsrange.Therefore,onlytheothercandidatenodesoutsideitsareaofcommunicationhavetheopportunitytostarttheirowngenerationprocess.Forexample,in Figure4.1d,nodeDreceiveda SleepingMessage fromEbeforeitstimerexpired,soit turneditselfoff.A CandidateNode thatdoesnotreceiveany SleepingMessage changes 93

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itsstateto ActiveCandidate andstartsitsownprocessoflookingforunvisitednodes bysendinga HelloMessage ,asin4.2.1. 4.2.3SecondOpportunityProcess Althoughthersttwostagesaresufcientinmostscenariostoproduceaconnectedreducedtopology,therearesomecasesinwhichthisdoesnothappen.Oneexampleis thecaseofnodeDinFigure4.1d,whichissenttosleepbynodeE,becauseEsends the SleepingMessage rst.IfnodeDneverwakesup,nodeGwillnotreceivea Hello Message fromanyothernodesoitwillnotparticipateinthetreecreationprocess.This casewillbethesameforallnodessenttosleepwhichhaveabottlenecklinkinthegraph. Inordertoavoidthissituation,whenanodereceivesa SleepingMessage ,insteadofgoingdirectlytothe SleepingNode mode,itsetsatimerthat,onceexpired,thenodeturns backon,changesitsstatusto ActiveCandidate andsendsa HelloMessage tostartits ownneighborhooddiscoveryprocess,asseeninFigure4.1e.InFigure4.1f,nodeD becomespartoftheCDSaftergoingthroughtheSecondOpportunityProcess,because itdiscoversnodeGandgoestothe ActiveNode mode.Thisoperationincreasesthe overheadofthealgorithm,butguaranteesconnectivityofallthenodesinthegraph,as provedinLemma1. L EMMA 1.I FTHEINITIALGRAPHISCONNECTED THEREDUCEDGRAPHISALSO CONNECTED Proof: Assumethataconnectedoriginalgraphisgiven.Ifatthenalstageofthealgorithmthereexistsatleastonenodethathasnotbeencovered,itisbecauseitdidnot receiveany HelloMessage .Giventhateverynodeisforcedtosenda HelloMessage ,each nodeexploresallitsneighborsfromtheoriginalgraphlookingforunvisitednodes.The 94

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algorithmcontinuesuntilallnodesarevisitedinthetotalareaofcoverageofthetree, exploringalledgesfromthissetofnodes.Thismeansthatthenaltreeisaconnected subgraphitselfbecauseithasnoedgetounvisitednodes.Ifanuncoverednodeexistsat theendoftheexecutionofA3,itmeansthatthereisnoedgebetweenanyofthecovered nodesandtheuncoverednode.Thentheinitialgraphcannotbeconnectedbecauseithas atleasttwonon-connectedsetsofnodes,whichcontradictstheinitialassumptionofa connectedgraph. ItisworthemphasizingthatA3iscompletelydistributedandneedsnosynchronization schemenorlocalizationinformation.Theprocessnisheswhenthelastnodenishesits owncreationprocess.Eachnodeisresponsibleforitsownprocessandneedsnoinformationaboutthestatusoftheoverallprocess.Actually,assoonasanodeisselectedaspart oftheCDStree,itcanstartitsapplication-relatedtasks.Figure4.2.1showsthenitestate machineofanoderunningtheA3protocol.Asitcanbeseen,theA3algorithmguaranteesthat,oncethealgorithmisrun,everynodeisineither ActiveNode or Sleeping Node state. ThecomputationalcomplexityoftheA3algorithmcanbeeasilycalculatedbasedonthe factthatthesortingfunctionexecutedbytheparentnodesisthemostexpensiveoperation.Therefore,thecomplexityofthealgorithmisgivenbythecomplexityofthesorting routine,whichcanbeboundedas O nlogn .Themessagecomplexityisboundedbythe worstcaseof4messagesinthecaseofanodethatbecomesaparentnodeattherst opportunity: Hello ParentRecognition ChildrenRecognition ,and Sleeping messages. Therefore,themessagecomplexityis O n foranetworkwith n nodes,withaworstcase scenarioof4 n messages. 95

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4.2.3.1TheSelectionMetric Severalmetricshavebeenutilizedintheliteraturetoselecttheactivenodes,suchasthe distancebetweenthenodes,thenodedegreeofthecandidatenodes,andthepotential coverageofthecandidatenodes,beingamongthemostimportantones.Forexample, inthetheworkof[41],theauthorsusetheamountofunvisitednodesthateachcandidateneighborwouldprovidetothediscoveredtopology.However,thesemetricsusually havetwomaindrawbacks.First,theydonotconsidertheamountofresidualenergyin thenodes,sotheycouldselectnodesthatmightdiesoon.Second,thegeometryofthe topologyisalsoignored,whichcoulddrivetoanonappropriateselectionofnodes.For example,ifallcandidatesincludethesameamountofnodes,probablytheIDwillbeused asatiebreaker,whichmaydevolveintotheselectionofnodesthatinterferewithother activeneighbors.Finally,thesemetricsusuallyrequiresendingmessagestonodesthatare twohopsaway,increasingtheoverheadconsiderably. TheselectionmetricutilizedbytheA3algorithmissimple,requiresonlyonehopinformation,andalsoconsiderstheresidualenergyofthenodes.NodesonlyneedtomeasuretheReceivedSignalStrengthIndicatorRSSIofthe HelloMessage sentfromtheir dominantnodes.Then,usingtheirresidualenergy,thenalmetriciscalculatedusing Equation4.1,whichisaconvexcombinationoftheresidualenergyinthechildnode anditsdistancetotheparentnode.Themetric,sentbacktotheparentnodeinthe Parent RecognitionMessage ,iscalculatedasfollows: Mx ; y = W E E x E max + W D RSSI y RSSI .1 where x isthecandidatenode, y isitsparentnode, W E istheweightfortheremaining energyinthenode, E x istheremainingenergyinnode x E max isthemaximuminitialen96

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ergy, W D istheweightforthedistancefromtheparentnode, RSSI y isthereceivedsignal strengthfromtheparentnode,and RSSI istheminimumRSSItoensureconnectivity, whichisgivenbythesensitivityofthereceiver.Notethat,giventhat W E + W D = 1, Equation4.1producesavaluebetween0and1thatisassignedtoeachneighborwhen addedtothelist;thehigherthevalueofthemetric,thehigheraprioritythenodewill receiveintheselectionprocess,increasingitsprobabilitytobeactiveinthetree. AsitcanbeseenfromEquation4.1,theselectionmetricgivesprioritytothosenodes withhigherenergyandwhicharefartherawayfromtheparentnode.Thenaleffect ofthischoiceistohaveatreewithfewernodesandbettercoverage.However,proper weightmanipulationcansatisfydifferentcriteria,asneededbythenetworkoperator.If communicationcoverageistobeoptimizedandtheaverageheightofthenodeinthe treenumberofhopsneedstobereduced,thedistancemetricmustbeweighedmore heavily.Thedownsideisthatlowenergynodesmaybeincludedinthetree,whichmay introduceearlyfailuresofnodes,reducingreliability;andmayincreasethenumberof callsofmaintenanceprocesses,thereforereducingthelifetimeofthetree.Ontheother hand,ifreliabilityofthetreeisdesired,energymustbeweighedmore.Thedownsideis thatthetreemaypresentmoreactivenodes,duetothefactthatthegeometricdistribution ofthenodesisnottakenintoaccount.Inthisdissertation,abalancedaveragewithboth weightssetto0 : 5,isusedinallperformanceevaluations.Furtheranalysisoftheimpact oftheweightsintheperformanceoftheprotocolsispartofthefutureworkafterthis dissertation. 97

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Figure4.3:TheA3Liteprotocolnitestatemachine. 4.3TheA3LiteAlgorithm EventhoughA3isaverysimpleprotocolandoffersaverylowmessageandcomputationalcomplexity,itcanbemadeevensimplerbyrelaxingtheneedofacentralized selectionprocessintheparentnodesinordertodeterminethepriorityofitscandidate neighbors.ThisistheideabehindA3Lite,whichonlyneedsatotalof2 n messagesto createatreesimilarorbettertotheonecreatedbyA3. 4.3.1TheNeighborhoodDiscoveryProcess SimilartoA3,apreselectednode,letussaynodeX,startsthetreecreationprocessby sendinga HelloMessage .Each HelloMessage includestheIDoftheparentnode,except inthecaseofthesinkwhichinthateldwillhaveitsownID.Whentheneighborsof nodeXreceivethemessage,theychangetheirstatusto WaitingActive ,calculatethe 98

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selectionmetricofA3Equation4.1inthesamemanner,andregisterthesenderasits parentnode.Then,eachnodesetstimeoutAinverselyproportionaltotheirselection metric, t 0 + 1 )]TJ/F42 11.9552 Tf 11.409 0 Td [(metric t 1 ,where t 0 << t 1 tosenda HelloMessage andtimeoutB, settohalfthevalueoftimeoutA,tosenda ParentRecognitionMessage 4.3.2ChildrenSelectionProcess Atthispoint,duringthe WaitingActive stateseveraleventsmayhappen: Thenodemayreceivea ParentRecognitionMessage fromoneofitsbrothersall nodesundertheareaofcoverageofthesameparentnode.Inthiscase,thereceiver nodecancelstimeoutBandremainsinthe WaitingActive state. Thenodemayreceivea HelloMessage fromanon-brother,inwhichcasethenode resetstimeoutAtoitsoriginalvalueandremainsinthe WaitingActive state.This meansthatanon-brothernodestartedaneighborhooddiscoveryprocessandneeds sometimetoexploreandletitsbranchgrowtocoverasmanynodesaspossible, decreasingtheprobabilityofthereceivernodehavingunvisitednodesinitsneighborhoodandbecomingactive. TimeoutAmayexpire.Whenthishappens,thenodesendsa HelloMessage and goestothe ActiveCandidate state. TimeoutBmayexpire.Inthiscase,thenodesendsa ParentRecognitionMessage andremainsinthe WaitingActive state. Thenodemayreceivea HelloMessage fromabrother,inwhichcasethenodegoes tothe SleepCandidate state.Uponreachingthisstate,thenodeturnstheradio offtemporarily,cancelstimeoutAandsetstimeoutC,equalto t 2 + 1 )]TJ/F42 11.9552 Tf 11.212 0 Td [(metric 99

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t 1 ,where t 0 << t 2 t 1 .WhentimeoutCexpires,thenodewillwakeupandstart its SecondOpportunityProcess ,inwhichthenodegoestothe ActiveCandidate statetoexploreitsneighborhoodforunvisitednodes. Oncethenodeisinthe ActiveCandidate state,itsendsa HelloMessage andsetstimeoutD,equalto t 3 ,where t 1 < t 3 ,inordertowaitfor ParentRecognitionMessage from itschildren.IftimeoutDexpiresandnomessagehasbeenreceived,thenodegoestothe SleepingNode state.Ifthe ActiveCandidate receivesatleastone ParentRecognition Message fromachild,thenthenodegoestothe ActiveNode state,whichmeans,thatit willbepartoftheCDStree. ComparedtoA3,A3Literequiresonlyamaximumoftwomessagespernode,whichisat mosthalfthemessagecomplexityofitspredecessor.Also,asitcanbeseeninFigure4.3 thatdepictsthenitestatemachineoftheA3Litealgorithm,A3LitekeepstheconnectivitypropertyfromA3describedinLemma1,giventhatinA3Liteeverynodesendsa HelloMessage withtheaddressofitsparentnode,soifanyunvisitednodeexistedatthe endoftheexecutionitisbecauseitwasnotconnectedintheoriginalgraph. 4.4PerformanceEvaluation InthissectiontheresultsoftheperformanceevaluationcomparingtheA3andA3Lite algorithmswiththeEECDSandtheCDS-Rule-KheuristicsalgorithmsandwiththeMIPMCDSoptimalsolutionsarepresented. Threesetsofexperimentsareincluded.Therstsetmaintainsthenumberofnodesxed andincreasesthenodedegreebychangingthecommunicationrangeofthenodes.The communicationrangesusedintheexperimentareproportionaltothecriticaltransmission 100

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Table4.1:Simulationparametersforconnectivity-orientedprotocols. Experiment1 Experiment2 Experiment3 Deployment area 200mx200m Numberof nodes 100 10,20,40,60, 80and100 50and101 Transmission RangeDistances basedonRSSI 1,1.5,2and 3xCTR equivalent to:27m, 41m,54m, 68mand81m Eqn.2.1 60m equivalent to1xCTR 30m Node Distribution Uniform ,200 Uniform ,200 GridHVand GridHVD Instancesper topology 50instances E max 1Joule A3Weights W E = 0 : 5 ; W D = 0 : 5 Energy Consumption Eelec=50 nJ = bit ;Eamp=10 pJ = bit = m 2 ShortMessages=25 Bytes Hello,ParentRecognitionandSleepingMessages LongMessages=100 Bytes ChildrenRecognitionandDatamessages Idlestateenergyconsumptionassumednegligible rangeCTRformulainEquation2.1presentedinSection2.2.1.1,calculatedbasedonthe denednetworksizeandtheareaofdeployment. Thesecondset,ontheotherhand,variesthenetworkdensitybychangingthenumber ofnodeswhilemaintainingaxedcommunicationrange.Inthesetwoexperiments,the nodesareuniformlydistributedintheareaofdeployment. Thethirdsetofexperimentsincludesanadditionaltheoreticalcomparisonconsideringan idealgridtopologyinwhichallnodeshavethesamenumberofneighbors.Twodifferent gridtopologiesareused:theGridHVtopology,inwhicheachnodecanlistentoitshorizontalandverticalneighbors;andtheGridHVDtopology,inwhicheachnodecanlisten 101

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toitshorizontal,vertical,anddiagonalneighbors.Therefore,thenumberofneighbors inthosetopologiesisatmost4and8,respectively.Figure4.6showsthesescenarios. Alloftheexperimentsshowtheaverageresultof50randomscenariosforthersttwo experiments,and50replicatesofthegridtopologiesforthethirdexperiment. Threeperformancemetricsareutilizedtoassesstheperformanceofthetopologyconstructionalgorithms:1numberofactivenodes;2numberofmessagesusedintheCDS buildingprocess;and3amountofenergyusedintheprocess.Therstmetricshows howthetopologyconstructionmechanismcaneffectivelyreducetheamountofactive nodeswhilepreservingnetworkconnectivity.Theothertwometricsshowhowefcient thealgorithmisintermsofoverheadandenergyconsumption. Thealgorithmsareevaluatedinscenariosthatgofromsparsetodensetopologies,and fromlowtohighnodedegree.Thenodedegreeandthedensityofthenetworkaremodiedbyincreasingthecommunicationrangeofthenodesandthenumberofnodesin thenetwork.ThefouralgorithmswereimplementedinaJava-basedevent-drivensimulationtoolcalledAtarraya[107],designedforthepurposeoftestingtopologycontrol algorithms.MoredetailsonthesimulationtoolcanbefoundinAppendixA.Table4.1 presentsasummaryofthesimulationvariablesusedintheexperiments. 4.4.1Experiment1:ChangingtheNodeDegree Themaingoalofthisexperimentistocomparethealgorithmswhenthenodedegreeof thenetworkischangedbyincreasingthetransmissionrangeofthenodes.Giventhat thesealgorithmsworkbasedoninformationfromneighbors,itisimportanttomeasure theirperformancewithneighborhoodsofdifferentsizes. 102

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aNumberofactivesnodes. bEnergyusedintheCDScreation. cNumberofmessagessent. Figure4.4:Resultsofexperiment1:changingthenodedegree. 103

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AsitcanbeseenfromFigure4.4a,thethreealgorithmsproduceasimilarnumberof activenodes.A3andEECDSproducealmostthesamenumberofactivenodesandCDSRule-Kproducesthelargestreducedtopologies.Thetrendinallthealgorithmsistodecreasethenumberofactivenodeswiththenodedegree,asexpected,giventhatwith largercommunicationranges,eachnodecoversmorearea,andthusmorenodes,soless activenodesarerequiredtocoverthewholenetwork.Thegapbetweentheoptimalsolutionandtheapproximationalgorithmsstartsatvenodesandthendecreases,whenthe communicationrangeandthenodedegreeincrease,toanalmostonenodedifference. Thisresultseemstoimplythattheperformanceoftheapproximationalgorithmstend toprovidereducedtopologiesveryclosetotheoptimalwhenthenodedegreedensity ishigh.Thisbehaviorcanbeexplainedbythefactthathavinglargercommunication rangesandlargersetsofnodestochoosefrom,theselectioncriteriaofthenodesinthe approximationalgorithmsdoesnothavemuchimpactwhilestillpracticallycoveringall nodesofthedeploymentarea;inotherwords,theoptimalnumberofactivenodeswould veryhardtomiss. Figures4.4band4.4cshowtwoimportantmetrics:thetotalenergyandnumberof messagesusedtobuildtheCDStrees,respectively.Inthiscase,theA3andA3Liteprotocolsshowtheirsuperiorperformance,withA3Litehavingtheleastamountofsentmessagesandenergyusedinthetopologyconstructionprocess.TheA3andA3Liteprotocols presentaslightly-increasinglinearenergyconsumptionwhencomparedwiththeCDSRule-KandEECDSalgorithms,whichshowaveryfastincreaserate. ThefastincreasinguseofenergyoftheCDS-Rule-Kprotocolisexplainedbyitspruning processinwhicheverynodemustupdatenodestwohopsawaywhenitisunmarked. Theoverheadofthisnoticationincreaseswiththenumberofneighborsbecausemore 104

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nodeswillretransmitthemessage.Also,whenthenodedegreeincreases,morenodesget unmarkedandwillproducethisextraoverhead. InthecaseoftheEECDSalgorithm,thefactorthatincreasestheamountofmessages andenergy,consequentlyisrelatedtothecompetitionusedinbothphasesofthealgorithm.Thisisduetothefactthatwithahighercommunicationrange,morenodesare covered,andthetreehasfewernodesinhigherlevels.This,atthesametime,reducesthe amountofnodescompetingtobecomepartofthetreeintheouterregionsofthetopology.However,EECDSshowsareductioninnetworkswithhighnodedegree,which meansthatitbenetsfromhavinglargecommunicationrangesbecauseitmayavoid havingtocalculatemanylevelsinatalltree,whichalwaysinvolvesagreatnumberof messages. ThelinearityoftheA3andA3Liteprotocolsisaconsequenceoftheboundednumberof messagesthateachnodeneedstotransmit,whichremainsalmostidenticalandnevergoes over4 n and2 n inidealconditions,respectively.Furthermore,thenumberofmessages intheA3andA3Liteprotocolsdecreaseswhenthedensityishigher;thisfactcanbe explainedbythefactthatlessnodesarerequiredtoprovideconnectivityinthenetwork, somorenodeswillbeturnedoff,andtheywillnotsendanymoremessages.Inthecase oftheenergy,theincreasingbehaviorisduetoimpactofoverhearingmessagesfrom neighborsnodes,wheretheneighborhoodsgrowwiththenodedegree. 4.4.2Experiment2:ChangingtheNodeDensity Themaingoalofthisexperimentistocomparetheresultsproducedbythealgorithms whenthenetworkdensityischangedbyvaryingthenumberofnodesintheareawhile keepingaxedcommunicationrangeof60 m ,equivalentinthisexperimentto1 xCTR of 105

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aNumberofactivesnodes. bEnergyusedintheCDScreation. cNumberofmessagessent. Figure4.5:Resultsofexperiment2:changingthenodedensity. 106

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10nodes.Thisexperimentisimportanttoshowhowscalablethealgorithmsareindense topologiesandhowtheresourceusagedependsonthenumberofnodes. Theresults,showninFigure4.5,showsimilarresultsintermsofenergyandmessages, butaslightlydifferentscenario,asseeninFigure4.5a.Inthiscase,theCDS-Rule-K showsthebestresultsinthesparsenetworksuptoscenarioswith40nodes,withsome advantageofthisprotocolinsmalltopologies.From60nodesandabove,itproducesa similarorworsenumberofactivesnodescomparetoA3.TheA3andA3Liteprotocols showaverysimilarbehaviorinthedifferentscenarios.EECDSappearstobehavea goodperformanceindensenetworks;however,thedifferenceinactivenodesislessthan oneactivenode,soitcanbeeasilyassumedthattheytendtoproducethesamevalue. Comparedtotheoptimalsolution,theapproximationalgorithmsproducereducedtopologiesthatareveryclosetotheoptimalinsmallnetworks,andthenstarttoshowagreater advantagewhenthesizeofthenetworkincreases.Itcanbeseenthattheoptimalsolution convergesrapidlytoanaveragevalueofseventoeightactivenodesforthescenarios shown,despitethenumberofnodes.Theconvergenceisshownalsobytheapproximation algorithms,butitisbetweentenandelevennodes,whichrepresentsanaverageof35% errorfromtheapproximatesolutionstotheoptimal,withastandarddeviationof0.19for A3.Thishighvariationcouldbeappreciatedwheninspectingtheresultsofindividual topologieswith100nodes,inwhichA3andA3Litecouldobtaintheoptimalsolutionina fewcases,whileinothertopologiestheapproximatesolutionsincludedtwicetheamount ofactivenodesintheoptimalsolution. Intermsofthemessagecomplexityandenergyefciency,theCDS-Rule-Kpresentsan almostexponentialincrease,theEECDSafastlinearincrease,andtheA3sshowlow andlinearlyboundednumbersofmessagesandenergyconsumption,asshowninFig107

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Figure4.6:Squaregridsdeployment. ures4.5band4.5c. ThisshowsthattheA3andA3Litealgorithmsarescalableandare nothighlyaffectedbythenumberofnodesdeployedorthenodedegreeinthenetwork. 4.4.3Experiment3:IdealGridTopologies Thethirdexperimentconsiderstheidealgridscenariowithitstwovariants:HVand HVD,asshowninFigure4.6.Thisexperimentshowstheperformanceofthealgorithms inaperfectlyhomogeneoustopology,withidealconditionsofdensityandnodedegree, whichcouldbeconsideredapredenedscenariosuchasasensornetworkdeployedinan ofcebuilding.FromFigure4.7,itcanbeseenthattheA3andA3Litealgorithmshow similarityinthenumberofactivesnodes,withA3Liteselecting54%ofthenodesinthe gridHVand31%inthegridHVDscenariostobeactive,versus58%and33%fromA3, 57%and31%fromEECDS,58%and32%fromCDS-Rule-Kalgorithms,and42%and 25%fromtheMIP-MCDSsolutions.Thismeansthattheapproximationprotocolswere atleast12%fromtheoptimalintheHVgrid,andaround6%intheHVDgrid.Theother 108

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twometricsshowanincreasingtrendforEECDSandCDS-Rule-KwhileA3andA3Lite showaboundedcostinoverheadandenergy. 109

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aNumberofactivesnodes. bEnergyusedintheCDScreation. cNumberofmessagessent. Figure4.7:Resultsofexperiment3:idealgridtopologies. 110

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Chapter5:TheA3CovandA3CovLiteTopologyConstructionProtocolsfor Coverage TheprotocolspresentedinChapter4areintendedtobuildaconnectedtopologywiththe minimumamountofactivenodes;however,asitwasdiscussedbefore,connectivityis nottheonlydesiredfeatureintopologyconstructionprotocols.Thesensingcoverageis averycriticalfactorthatdeterminesthesuccessofaprotocolbecauseitguaranteesthat mostoftheareaofinterestwillbemonitoredbythenetwork.Thetwoproblemscanbe assumedsimilarwhen R Comm = R Sense ,inwhichcasetheconnectivity-orientedprotocols usuallyofferagoodcoverageratio,butthisisnotaveryrealisticassumptiontomake. Inthissectiontwonewprotocolswillbeintroduced,asextensionsoftheA3andA3Lite algorithmsdescribedbefore:theA3CovandA3CoveLiteprotocols.Themainideabehindthenewprotocolsistousetheconnectedstructureproducedbytheoriginalalgorithmsasastartingpointandthenincludemorenodesthatwillextendthecoverageratio oftheareaofinterest.TheA3CovandA3CovLiteprotocols,asintheoriginalversion, donotneedanylocationinformation,workinadistributedmannerandalsoworkin scenarioswhere R Comm 6 = R Sense ,incomparisonwithmanycoverage-orientedprotocols whichcanonlyguaranteeconnectivitywhen R Comm 2 R Sense Thenewprotocolswillbecomparedagainsttheirpredecessorsinordertoshowtheconsiderablegainincoverage.Inaddition,theywillbecomparedwiththetheoreticaloptimal 111

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griddeploymentsfrom[69,88]andalso,withtwoothercoverage-orientedprotocols ACOSandStanGA,bothdescribedpreviouslyinSection2.3.3. 5.1TheA3CovAlgorithm FromthedescriptionoftheoriginalA3algorithmitisknownthatA3sendstosleepall nodesinthereducedtreetopologythatareunderthecommunicationrangeoftheircorespondentparentnodes.Whilethistechniquemayworkjustneinthecasewherethe communicationandsensingradiiareequal,itmaynotprovidesatisfactoryresultswhen thesensingradiusissmallerthanthecommunicationradius;inotherwords,manynodes willbeputtosleepbecausetheyarereachableviacommunicationrangebutthearea wheretheyaremaynotbecoveredsufcientlybytheirsensors. Therefore,ifsensing-coverageistobeincreased,morenodeswouldhavetobeselectedto remainactive.Onequestioncomestomindhere:whichnon-CDSnodesshouldtheprotocoladdtotheactivesubsetsothatcoverageissubstantiallyincreasedwithoutincluding toomanyextraactivenodes?Intherstplace,andgiventhelackoflocationinformation,thegenerationofanaccurategeometricmapofcoveragecanbeveryexpensivein bothmessageandcomputationcomplexity.ThisisthemainreasonwhybothA3Covand A3CovLiteworkbasedonthestatementpresentedin[71],wheretheauthorspropose that,inadensenetwork,thecoverageofthenodes'locationsisagoodapproximation ofthecoverageofthecompleteareaofinterest.Thismeansthatasimilarapproachtothe oneadoptedforconnectivitycanbealsoappliedforcoverage,andthatisthefoundation ofA3CovandA3CovLite. Focusingonthedescriptionoftheprotocols,A3CovinheritsmostoftheA3protocolin ordertoobtainaninitialconnectedtopology.Themaindifferencebetweentheproto112

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Figure5.1:TheA3Covprotocolnitestatemachine. colsisthatA3Covappliestwodifferentselectionmetrics,oneforconnectivityandone forcoverage.TherstonewasmaintainedfromtheA3protocolbecauseitproducesa connectedreducedtopologywhichfavorstheselectionofneighbornodesthatarefarther awayfromtheparentnode,decreasingasmuchaspossibletheoverlappedsensingarea betweenthem.Thesecondselectionpolicykeepsomeoftheleafnodesactiveinorder toextendthecoverageprovidedbythecommunicationbackbonealone.Thisselection policyisbasedontheideathatifanodeisinsidethesensingrangeofanactivenodeit willnotbeeligibletoremainactive,unlessitisrequiredforconnectivitypurposes. Assumingthesensingrangeasaperfectdiscwithradius R Sense andcenteredatthenode's position,ifthedistancebetweenanactivenodeandaregularnodeislessthat R Sense ,then theregularnodeisconsideredsensing-covered.Thiscriterionisevaluatedtwiceduring theexecutionoftheprotocol:whenthenodereceivesthe ChildrenRecognitionMessage fromitsparentnode,inwhichittestsifithasbeensensing-coveredbytheparentnode, andwhenanodereceivesa SensingCoverageMessage fromanyneighbor.The Sensing CoverageMessage canarriveatanymomentduringtheexecutionoftheprotocoland,if 113

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thesensingcoveragecriteriaisaccomplished,thatis,if d x ; y R Sense ,thenthereceiver issaidtobesensing-coveredbythesender. Anodecanbeselectedtobecomeactiveforcoveragepurposesjustafterthenodewas inthe WaitingCandidate stateandhavesenta HelloMessage withnoanswerfrom unvisitedneighbornodes.Atthismoment,theoriginalA3wouldwouldhavesentall thosenodestothe SleepingNode state,whileA3Covveriesrstifthenodeshave beensensing-coveredbyanotheractivenode,inwhichcasetheyaresentdirectlytothe SleepingNode state. The WaitingCandidate nodesthatwerenotsensing-coveredbytheirparentnodesand thatlackanychildrennodes,become CandidateNodesforCoverage andareasked tostayawakeforanextraperiodoftimeinordertolistenfor SensingCoverageMessage fromtheirneighbors.Thenewtimeoutusedbythesenodestowaitforthe SensingCoverageMessage isalsoproportionaltothemetricusedforconnectivity,whichconsiders distanceandenergy,sobothselectionprocessessharethesameprioritypolicy. Ifa CandidateNodeforCoverage receivesa SensingCoverageMessage beforethe timeoutexpires,and x ; y 2 V ; d x ; y < R Sense ,thenodeisconsideredsensing-covered, andgoestothe SleepingNode stateimmediately.If d x ; y > R Sense itmeansthatthe receivernodeisunderthecommunicationcoverageofthesenderbutnotwithinitssensingcoverage,sothemessageisignoredandthereceivernodekeepswaitingformessages untilthetimeoutexpires. Whenthetimeoutexpires,ifthenodehasnotbeensensing-covered,i.e.,ithasnotreceivedany SensingCoverageMessages ,thenoderemainsactive,changesitsstateto ActiveNode ,andsendsa SensingCoverageMessage toitsneighborsinordertonotify itsnewstate.Inaddition,each ActiveNode broadcastsa SleepingMessage inorderto delaytheneighborhooddiscoveryprocessofitsneighbornodesanddecreasetheproba114

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Figure5.2:TheA3CovLiteprotocolnitestatemachine. bilityofhavingtoomanyactivenodesinitsneighborhood.Thenodeswhowereselected intherstplaceaspartoftheCDStreeactivenodesforconnectivitypurposes,are askedtobroadcasta SensingCoverageMessage alsoinordertoupdatetheirneighbors' sensing-coveragestatus. Asitwillbeshownlaterintheperformanceresults,thecoverage-basedprotocolsimprovethecoverageinthosecaseswhere R Comm 6 = R Sense ,comparedtotheirpredecessors. Figure5.1depictsthenitestatemachineoftheA3Covalgorithm.A3Covhasthesame computationalcomplexityofA3andthesamemessagecomplexity O n ,onlythateach nodemaysenduptovemessages 5 n .Inaddition,theproofofLemma1isalsovalid forA3CovduetothefactthateverytreeproducedbyA3Covcontainsanunderlyingtree fromA3withextranodesaddedforcoveragepurposes,soconnectivityisnotaffected. 115

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5.2TheA3CovLiteAlgorithm A3CovLiteistherespectiveextensionofA3Liteinordertoprovidebettercoverageofthe area. A 3 CovLite worksexactlylikeA3Lite,exceptforthefollowingtwomoments:when anodereceivestherst HelloMessage andwhentimeoutDexpiresforanodein Active Candidate state.Intherstcase,whenanunvisitednodereceiveda HelloMessage ,it evaluatesifitissensing-coveredbyitsparentnode.Inthesecondcase,timeoutDissetto listenfor ParentRecognitionMessages fromchildrennodes.Ifthenodedoesnotreceive anymessagesofthiskind,itmeansthatitdoesnotprovideconnectivitytoanynode,and intheoriginal A3Lite thatwouldhavebeenenoughtosendthenodetothe Sleeping Node mode.However,inthisprotocol,thatdecisiondependsonknowingifthenodewas sensing-coveredbyanyothernode.Inthecasewherethenodewassensing-covered,the nodewillbesenttothe SleepingNode mode;otherwise,thenodewillchangeitsstate to ActiveNode Everynodethatreachesthe ActiveNode statewillsenda SensingCoverageMessage to itsneighborsinordertonotifythatithasbeenselectedtobeactive.Themessagecomplexityofthisprotocol,comparedtoA3Lite,isatmost3 n inthecaseallnodesareselectedtobeactive.Figure5.2showsthenitestatemachineoftheA3CovLitealgorithm. 5.3The a -CoverageSensingCoverageDenition AftercomparingtheperformanceofthedistributedA3-basedalgorithmsforconnectedcoverage,itwasobservedthatwhilethealgorithmscoveredalmost99%oftheareain densenetworks,theyneededmanymoreactivenodesthantheoptimaldeployments.In fact,thenumberofnodeswassimilartothatofthehexagon-basedgridshowedin[69, 116

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Figure5.3:Exampleof a -coverage. 72],whichistheonethatrequieresthegreatestnumberofactivenodesamongtheoptimalgrids.Aftersomeinsightintothewaythedistributedprotocolsworked,itwasconcludedthattheselectioncriteriawasmainlyresponsible.Rememberthatthenodesthat aretobeaddedtotheactiveset,arethosewhicharefartherawayfromtheirparentsand withthemostremainingenergy.Theselectionofthesedistantnodescreatessmallholes inthecoveragethatarelledbyadditionalnodes,althoughthesedonotnecessarelycontributemuchintermsofnewlycoveredarea. Figure5.3showsanexampleofthissituation.NodesB,C,DandFwouldbecomeactiveunderthecurrentdenitionofsensingcoverage;however,itiseasytoseethatthe contributionofnodeDtothecoveredareaisminimal,becauseitislocatedrightafterthe sensingradiusofA. Inothercases,theoppositecanbehappening.Someapplicationsrequireahigherlevelof coveragethantheoneofferedbytheoriginalselectionpolicy.Forexample,thesameFigure5.3showstheexampleofnodeEwhichisnotselectedbecauseithasbeensensing117

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coveredbyitsparentnodeA,butEisanodethatcouldextendconsiderablythesensing coverageofthetopologyduetothefactthatnoothernodeisofferingcoveragenearits position. Onesolutionisto"virtually"denethesensingcoverageinordertoincreaseordecrease thenumberofeligiblenodesforcoverage,dependingontherequirementsoftheapplication.Underthisnewidea,anodeissensing-coveredif 8 x ; y 2 V ; d x ; y a R Sense where0 < a R Comm = R Sense .Themaincaseswillbetheonesof a 0,whichwill selectmostnodestoremainactive;thecaseof a = 1whichwillproduceasimilarresult totheoriginalversionofsensingcoverage,andthecaseof a = R Comm = R Sense whichwill produceasimilarresulttothecasewhenthecommunicationandsensingradiiareequal. AnexampleoftheapplicationofthisnewdenitionisalsoshowninFigure5.3.Ifthe newdenitionisusedwith a = 1 : 3,nodeDwouldnotbeincluded.Themainsource ofsavingsinnumberofnodesisthatmostofthenodesinthebeltbetween R Sense and a R Sense willbellingupholesleftbytheselectionofthenodeswithhigherpriority, fartherawayfromtheparentnode.If a = 0 : 7,thennodesDandEwouldbeselected tobeactive,whichwillnotrepresentanysavingsinenergy,butwillprovidethebest coverageratioforthetopology. Itisobviousthatthisnewdenitionaffectsthetotalcoveredareabythetopology,thereforetheselectionofthe a parameterisveryimportant.Intheperformanceevaluation oftheA3CovandA3CovLiteprotocols,twodifferent a valuesweretestedinorderto illustratetheimpactofthisparameterintheselectionpolicy: a = 1 : 3and a = 0 : 7. Afterperformingexperimentsinasmallsampleofscenarioswithdifferent a values,an interestingtrendwasfound:from a = R Comm = R Sense = 1 : 7until a = 1 : 3,thegrowth ofcoveredareaversusthenumberofnodesfollowedalinearbehavior;however,from a = 1 : 3until a = 1,thenumberofnodesincreasedconsiderablyfasterthanthearea 118

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coverage.Eventhoughthischaracteristicmaynotapplyforallpossiblescenarios,it providesagoodstartingpointforanalysis.Inthecaseof a = 0 : 7,thevaluewasselected becauseitwasatthesamedistancefromthe a = 1,butintheoppositedirection,andjust asawayofcomparison. Intheperformanceevaluationsectionitwillseenthatthecoveredareafor a = 1 : 3falls between80%and90%insparsenetworksandbetween93%and95%indensenetworks, whilereducingconsiderablythenumberofactivenodes.Intheothercase,thecovered areafor a = 0 : 7inwhichfallsbetween90%and100%insparsenetworksandbetween 99%and100%indensenetworks,havingasaconsequenceasubtantialincreaseinthe numberofactivenodes.Moredetailsontheperformanceusingthemodiedsensing coveragewillbepresentedinthenextsection. 5.4PerformanceEvaluation Inthissection,thecompleteA3familyofdistributedprotocolsiscomparedwiththe theoreticalboundsforconnectivityandcoverage,andtwootherdistributedcoverageorientedprotocols,allofthempresentedinSection2.3.3. Forthecomparisonwiththetheoreticalbounds,threesetsofexperimentsareincluded. Therstsetofexperimentsincludesthoseexperimentsinwhichthecommunicationand sensingradiiarethesame R Comm = R Sense .Inthiscase,theA3protocolsarecompared withtheoptimaldeploymentsdescribedin[69]andsolutionstothepackingproblem foundintheliterature.Thiscasealsoprovidesascenariotocompareconnectivity-orientedandcoverage-orientedprotocolsasequals. Thesecondsetconsidersthecaseinwhichthecommunicationradiusis p 3timesthe sensingradius R Comm = p 3 R Sense .Asexplainedbefore,thisistheradiusthatguarantees 119

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connectivityandcoveragewiththeminimumnumberofnodes.Here,theoptimaldeploymentsdescribedin[72]areusedforcomparison.Finally,thethirdsetofexperiments considersthe a -coveragecaseswith a = 1 : 3and a = 0 : 7,usingacommunicationrange of R Comm = p 3 R Sense Eachoftheexperimentsdescribedbeforewereperformedinsparseanddensenetworks. Inalltheexperimentspresentedinthissection,theconceptsofsparseanddensenetworks isnotonlyrelatedtothenodedensityinthearea,buttothelevelofconnectivity,which ismorerelatedtothenodedegreenetworks.Inotherwords,insparsenetworkseach nodehasasmallerneighborhoodthaninthedensenetworks.Thedenitionofthese parametersisbasedontheCriticalTransmissionRangeCTRconcept,i.e.theminimal communicationrangeneededtoprovideaconnectedtopologyindensenetworks.In thisexperiment,theCTRformulafromPenroseandSanti,denedinEquation2.1,was utilized. Theevaluationundersparseanddensenetworksisveryimportantbecausemostofthe centralizedoptimalsolutionsforconnected-coveragepresentedinSection2.3.3assume verydensenetworkscenarios.Asitwillbeshownlater,thisisnotarestrictionfortheA3 familyofdistributedprotocols,whichalsoperformverywellinsparsescenarios. Inallscenarios,thenumberofactivenodesandthepercentageofcoveredareagiven connectivityareutilizedasthemainperformancemetricsforcomparison.Thecomplete setofexperimentswiththeA3distributedalgorithmswereperformedwithAtarraya. 5.4.1ComparisonwithTheoreticalDeployments Theprocesstoplotandcomparetheresultsforthepackingproblem,theoptimaldeploymentsandthoseobtainedfromA3andA3Litesimulationresults,isperformedasfollows. 120

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Table5.1:Simulationparametersforcoverage-orientedprotocols. Parameter Value Deploymentarea 600mx600m Nodedistribution Uniformlydistributedwithinthearea Instancespertopology 50instances A3Weights W E = 0 : 5 ; W D = 0 : 5 Energyconsumption E elec = 50 nJ = bit ; E amp = 10 pJ = bit = m 2 Packetsizes ShortMsg=25 Bytes ;LongMsg=100 Bytes A3Timers t 0 = 1 : 5, t 1 = 30, t 2 = 15, t 3 = 60 EnergyParameters asdescribedinTable3.1 Inallcases,theareaofdeploymentwasestablishedtobe600 m 600 m ,andthesensingandcommunicationradiihavethevalueof R Sense R Comm = R Sense .Forthepacking problem,giventhesetwovalues,theplottedresultwasthemaximumnumberofnonoverlappingcirclesofradius R Sense thatcanbettedinthearea,whichwasdetermined basedonexistingsolutionsintheliterature[76].Itisworthmentioningthatthereisno "formula"orequationtosolvethisproblem.Thesolutiontothepackingproblemnumber isthelowerboundofconnectivityandcoverageforthatparticularscenario.Then,based onthenumberofcircles,theadditionoftheirindividualareasoverthetotalareaissensingcoverageratio,asshowninEquation5.1. Coverage Packing = n R 2 Sense p l 2 .1 where n isthepackingnumber,and l isthesideofthesquare. Theguresforalltheresultsinthissectionarestructuredinthismanner:thex-axisofthe resultsrepresentsthesensingradius R Sense asaratioofthesideoftheareaofdeployment. So,forexample,avalueof0.5meansthatthesensingradiusishalfthesizeofthesideof thedeploymentsquare,or300 m inourcase.Inthey-axis,thenumberofactivenodes 121

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andthecoveredareawillbeshownintheirrespectiveplot.Table5.1showsthemain parametersutilizedinthesimulationexperiments. Fortheoptimaldeploymentsdescribedin[69],itisalwaysconsideredthattheyachieve 100%coverage.Thenumberofnodesproducedbyeachdeploymentgridwasobtained fromtheinverseofthedensityEquations2.6and2.7withtheradiusasaratioofthearea side,asshowninEquation5.2,and Q = p = 2and R Comm = R Sense = p 3tocalculate d RHO n deployment = 1 F density R Sense l .2 where F density isthedensityfunctionofthegivendeploymentgrid,and R Sense l istheratio ofthesensingradiusversusthesideofthesquare.Thislastoperationisnecessarybecausethedensityfunctionsweredesignedtoworkwithaunitsquare. Finally,fortheA3algorithms,therstparameterneededwastheinitialsizeofthetopology.Thetwooptimaldeploymenttechniquesdonotneedaninitialtopologygiventhat theyprovideanoptimalonefromthebeginning.Inthecaseofthedistributedalgorithms, aninitialtopologyisnecessaryinordertohavespreadenoughnodestohavemostofthe deploymentareacovered,andenoughdensitytoguaranteeconnectivity. Asithasbeendiscussedearlier,Equation2.1providestheCriticalTransmissionRange CTRforascenariowherethenumberofnodesandtheareasideofthedeploymentarea areknown.Giventhatintheseexperimentsjusttheareaofdeploymentandthedesired sensingradiusareknown,thesizeofthetopologyiscalculatedbytestingdifferentvalues forthetotalnumberofnodesparameter,untiltheCTRformulaprovidesradiithatare equalto1and0 : 5timesthedesiredcommunicationradius,inordertoprovide1 CTR and2 CTR sparseanddensenetworks,respectively.Theprocesswasrepeatedforall thesensingradiiconsideredtheexperiments,inordertoassesstheperformanceofthe 122

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Table5.2:Radiiandtopologysizesforcoverage-orientedprotocols. R Sense R Comm N Dense N Sparse 300 520 21 5 180 312 83 12 150 260 129 21 120 208 225 39 105 182 311 56 90 156 445 83 75 130 683 131 60 104 1100 225 51 88 1650 332 45 78 2200 446 39 68 3040 623 34 59 4000 855 algorithmswithdifferentsensingranges.Theselectionofthedifferentradiiwasbasedon theavailableresultsforthecirclepackingproblemin[76]. Letitbesaidthatalltherandomtopologiesusedforthisexperimentwereinitiallyconnected.Thecoveredareawascalculatedusingagraphicmethod:assumingeachpixelas asquareof1 m 1 m ,thecoveredareacanbeobtainedbycountingallpixelscovered bytheactivenodesandthendividingthatamountbythetotalamountofpixelsonthe graphicalrepresentationofthetopology.Table5.2showsthecompletelistofparameters R Sense R Comm = p 3 R Sense n Sparse and n Dense .Thevaluesfor R Comm areonlyusedinthe secondandthirdsetsofexperiments. 5.4.1.1Experiment1:SameRadii Intheseexperimentsitisassumedthat R Comm = R Sense .Thisassumptionismadeby[69] andcreatesascenarioinwhichconnectivityandcoveragebecomethesameproblem. Figures5.4and5.5showtheresultsoftheexperiments.Severalgeneralobservations canbemadefromthegures.Forexample,theperformanceoftheoptimaldeployments 123

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completelyagreewiththetheoreticalexpectations.Thesolutiontothepackingproblem alwaysprovidesthelowerboundinnumberofnodesandcoverage,regardlessofthe networkdensity.Thestripdeploymentisthenextbest,rightafterthepacking,followed bythehexagonandthesquareinthatorder.Theoptimaldeploymentsalwaysprovide 100%coverage;theyaredesignedtodoso.Theonlydifferenceisthat,asexpected,the numberofactivenodesincreasesinverselywiththesensingradius.Withregardtothe familyofA3protocols,theyalsobehaveasexpected:thepairsof Non-Lite and Lite protocolsshowsimilarbehaviorsintermsofnumberofnodesinsidetheirowncategories. Thisisexplainedbythefactthattherespectivepairsofprotocolssharethesameinner mechanismsforselectionexceptforthesensingcoveringissue,butgiventhatinthiscase thecommunicationandsensingradiiarethesame,theconnectivityandthecoverageturn intothesameproblem:anodecoveredbythecommunicationrangewillbealsocovered bythesensingrange. Intermsofthenumberofnodes,insparsenetworksallfourA3algorithmspresentsimilar performance,whichisexpectedgiventhattherearenottoomanychoicestogrowdifferenttrees.Inthiscase,theyperformsimilarlytothehexagon,betweenthesquareandthe stripdeployments.Withthesmallestradiusof0.05,equivalentto34metersandof855 nodesinthesparsedeployment,theA3algorithmsutilizedaround250nodes,whichis around30%ofthetotalnumberofnodes.Indensenetworksitcanbeseenhowthe Lite versionsneedfeweractivenodesthantheir Non-Lite counterparts.Thisdifferenceisexplainedbythemethodologyofgrowingthetreeofthealgorithms:the Lite versionsgive moretimefornewbranchestogrow,whichtendstoreducethepossibilityofleavingunvisitednodesforotherwaitingcandidatenodes.However,inthiscase,theperformanceof thealgorithmscomparedtotheoptimaldeploymentsisworse.The Non-Lite algorithms performtheworstofall,abovethesquare,andthe Lite versionsjustbelowthesquare. 124

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aNumberofactivenodesinsparsenetworks. bConnectivity-coverageinsparsenetworks. Figure5.4:Performanceinsparsenetworkswhen R Comm = R Sense 125

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aNumberofactivenodesindensenetworks. bConnectivity-coverageindensenetworks. Figure5.5:Performanceindensenetworkswhen R Comm = R Sense 126

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Nonetheless,evenintheworstcase,thedistributedprotocolsutilizearound10%ofthe nodestobuildthereducedtopology,whichisaconsiderablereductionfromthesparse networks.Itisworthmentioningthattheperformanceoftheoptimaldeploymentsshown intheguresistheoretical,asitassumesthatthealgorithmsndnodesintheprecise locationsneededbythegeometryinquestion.Ofcourse,thisassumptionwillnothold trueinallcases,evenlesssoinsparsenetworks.Therefore,inarealimplementation,it isexpectedthattheperformanceofadistributedalgorithmimplementingtheseoptimal deploymentswillbeworse,whichinturnmakestheA3algorithmslookgoodbetter. Intermsofcoverage,insparsenetworkstheA3algorithmsimprovethecoverageconsiderablycomparedwiththelowerboundofthepackingproblembuttheyarestillaway fromthe100%coverageprovidedbytheoptimaldeployments,especiallywhenlarge sensingradiiareused.However,theA3algorithmsachieveacoverageof90%orbetter forsensingradiiequalorsmallerthan0.17.Itisworthnoticingthatthesimulationresults presentedin[69]alsoassumedatarget90%coveragebecauseotherwisethenumberof activenodestoprovide100%coverageincreasedconsiderably. ThebehaviorexperiencedbythepackingproblemandtheA3algorithmsaroundaradius of0.3isduetodifferentreasons:inthecaseofthepackingproblem,aradiusof0.3is veryinconvenientbecauseitonlyallowsplacing2circlesinsidethesquare,leavinga greatamountofuncoveredspace.Astheradiusgetssmaller,morecirclescanbepacked tighter,decreasingtheamountofuncoveredspace.InthecaseofA3,thatbehavioris morerelatedtothelowdensityofnodesinsparsetopologies:asmallnumberofconnectednodesusuallymakesitlikelythattheyarenottoospreadoutwithinthearea,implyingthattheyarecontainedinasmallconvexhullcomparedtothetotaldeployment area.RememberthatA3doesnotneedtocovermoreareathantheonenecessarytocover thenodesinthenetwork,soinaverage,theresultsshowthatacoveredareaof75%is 127

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enoughtocoverallthe12nodeswithradiusof0.3.Inthecaseofdensenetworks,as showninFigure5.5b,thecoveredareaisnearto99%inmostcasesbecauseinthiscase thenodesaremorelikelytobespreadthroughouttheentirearea,thustheconvexhull ismoreequivalenttothedeploymentarea,andcoveringthenodeswouldbealmostthe sameascoveringthedeploymentarea.Theseresultsalsoconrmthestatementfrom[71] inwhichthecoverageofnodepositionsisassumedasanapproximationofthecoverage oftheentirearea. Insummary,when R Comm = R Sense ,theA3Litedistributedalgorithmisthebestchoice,becauseA3Liteneedstheleastnumberofactivenodes,whileprovidingthesamecoverage andusingtheleastnumberofmessagesamongalltheA3protocols. 5.4.1.2Experiment2:DifferentRadii Asstatedbefore,itisassumedintheseexperimentsthat R Comm = p 3 R Sense andtheparametersinTable4.1areused.Similarlytothelastsection,thesolutiontothepacking problemisthelowerboundfornumberofactivenodesandcoverage.Eventhoughthe optimaldistributionsfromExperiments1and2sharesomegeometries,theyareranked differentlyintermsofnumberofactivenodes:therhombusistheclosestdistributionto thepacking,followedbythestrip,thesquareandthehexagon,inthatorder,regardlessof networkdensity.Thehexagonperformsworsethanthesquarebecauseofthedoubleline ofnodesneededtoprovideconnectivity. Asexpected,the Cov versionsneedmoreactivenodesinbothscenarios,beingcloseto thesquareinsparsenetworks,andtothehexagonindensenetworks.Ontheotherhand, the Non-Cov versionsnotonlyneedfewernodesbutperformveryclosetothestripand therhombusinsparseanddensenetworksrespectively,whicharethebestperformersin 128

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aNumberofactivenodesinsparsenetworks. bConnectivity-coverageinsparsenetworks. Figure5.6:Performanceinsparsenetworkswhen R Comm > R Sense 129

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aNumberofactivenodesindensenetworks. bConnectivity-coverageindensenetworks. Figure5.7:Performanceindensenetworkswhen R Comm > R Sense 130

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theoptimaldeployments.Thisisexplainedbythefactthatthe Non-Cov protocolsdonot includeanyextranodesforcoverage,becauseconnectivityistheironlygoal. Anotherfacttobeanalyzedisthat,ingeneral,thenumberofnodesrequiredtoofferconnectivityinExperiment2islessthaninExperiment1.Thiscanbeexplainedbythefact thatwithalarger R Comm ,theprotocolscanbuildamorespreadouttopologywithless overlappingofsensingareasandtherefore,aconnectedtopologywithfewernodes.For example,usingaradiusof0.05,A3Covneedsaround425activenodesinthecasethat R Comm = R Sense andonly200inthisscenariowith R Comm = p 3 R Sense .Thedisadvantage isthatsincethecommunicationsradiusislargerthanthesensingradius,theprotocols connectthenetworkwithveryfewnodesbutleavemanyspacesuncovered.Thisisin factshowninFigures5.6band5.7b,wherethepoorcoverageperformanceoftheA3 algorithmscanbeseen. Inthecaseofareacoverage,theresultsmatchtheexpectations.Nowthe Cov versions performconsiderablybetterthanthe Non-Cov versions,asthe Cov algorithmswakeup manymorenodesthatwerewithinthecommunicationrangebutnotwithinthesensing rangeoftheirparents.Ofcourse,thisisdoneattheexpenseofhavingmoreactivenodes, whichisalsoshowninFigures5.6aand5.7a.The Cov versionsprovidethebestcoverageinboth,sparseanddensescenarioswithacoveragebetween85%and97%,and between92%and99%,respectively,butwithaperformanceabove90%foraradiusof 0.25orsmallerinallcases.However,indensenetworks,thesealgorithmsperformvery closetotheoptimaldeploymentinmostcases.Thebehavioraroundthe0.3radiusseenin Figure5.4bisalsoobservedherebutinthesparsenetworkscenarioFigure5.6band forthe Non-Cov versionsonly.Giventhatthecommunicationrangeis p 3timeslarger thanthesensingrange,evenfewernodesarerequiredtokeepthenetworkconnected 131

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somewherearoundtwoandthreenodescomparedtotheresultsofExperiment1,which requiredaround5nodes.Itisnotpossiblefor2or3nodescoverthewholearea. Insummary,inthecaseofsystemswhere R Comm 6 = R Sense ,thereisnoclearwinner,and rather,tradeoffsexist.Ifcoverageisnotascriticalasenergynetworklifetime,the NonCov algorithmsneedfewernodestobuildthereducedtopology.Inthiscase,itwouldbe bettertouseA3Lite,asitneedsfewernumberofnodesandmessages.Ifcoverageisvery importantfortheapplication,thenthe Cov algorithmsshouldbeused.Inthiscase,the A3CovLiteisthebestoptionmostlybecauseofitslowermessagecomplexity. 5.4.1.3Experiment3:Different a -coverage Theseexperimentsareperformedtoshowhowthe a -coverageparameterintroducedin Section5.3modiesthebehavioroftheA3CovandA3CovLiteprotocols.Thetradeoff isclear. Whenthe a -coverageparameterassumevaluesgreaterthan1 : 0,the Cov versionsperform alittlebitworseintermsofcoveragebutalittlebitbetterintermofthenumberofnodes comparedwiththeresultsshowninExperiment2.TakingA3CovLitewitharadiusof 0.05asanexample,inthecaseofsparsenetworks,Figures5.8aand5.8bshowthat itcoversaround90%oftheareawithcloseto100nodeswhileFigures5.6aand5.6b showthatthesamealgorithmwithoutthe a -coverageparametercovers97%ofthearea bututilizescloseto150activenodes.Inthecaseofdensenetworks,thenumbersare93% and130nodesversus100%and200nodes. Asseenintheresults,thedifferencebetweenA3CovandA3CovLiteisnowmorenoticeableinbothnumberofactivenodesandcoverage.Inthesparsescenario,thenumberof activenodesofthecoverageprotocolsislocatedbetweenthestripandtherhombus,with 132

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aNumberofactivenodesinsparsenetworks. bConnectivity-coverageinsparsenetworks. Figure5.8:Performanceinsparsenetworkswhen R Comm > R Sense and a > 1. 133

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aNumberofactivenodesindensenetworks. bConnectivity-coverageindensenetworks. Figure5.9:Performanceindensenetworkswhen R Comm > R Sense and a > 1. 134

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A3CovLitetheclosesttotheminimum.Asexpected,thesenumbersaresmallerthanthe onesinExperiment2becausethevirtualcoverageofthe a factorrestrictsthenumber ofcandidatestobeselectedforcoveragepurposes.Indensenetworks,thenumberof nodesoftheA3Covprotocolissimilartothesquare;inthecaseoftheA3CovLiteand theA3protocols,thenumberofnodesisbetweenthestripandthesquare,andtheA3Lite protocolshowsabehaviorcomparabletothestripdistribution.Thecoveragesuffereda decreasebetween5%and7%comparedtotheresultsonExperiment2. Intheothercase,whenthe a -coverageparameterassumesvalueslessthan1 : 0,the Cov versionsofferanextendedareaofcoveragecomparedtotheothertwoversions;however, thisincreasecomeswithagreatcostinthenumberofactivenodes.InFigure5.10b itcanbeseenhowtheprotocolsofferaareaofcoveragenolessthan90%evenwitha sensingradiusof0 : 5inthesparsenetworks.Thislevelofcoverageisonlyreachedby the Cov protocolswith a -coverageparameterof1 : 0and1 : 3whenthesensingradiusis around0 : 15and0 : 05respectively,asseeninFigure5.12b,whichrepresentsagainof almost5%morecoverage. Inthecaseofthedensenetworks,inFigure5.11bitcanbeseenhowthe a -coverage parameterkeepsthecoverageratioatvalueshigherthan99%forallsensingradii,which competesdirectlywiththelevelofcoverageprovidedbytheoptimalsolutions.However, asinFigure5.13b,itcanbeseehowthegainincoverageisat8%fortherstradius andnotmorethan2%intherestofthescenarioscomparedtothevaluesoftheother a coverageparameters. Now,asitcanbeseeninFigures5.12aand5.13akeepingthat90%coverageinthe sparsenetworksandthe99%coverageinthedensenetwork,imposesaheavetaxtothe network:roughlydoublethenumberofactivenodesareneeded,comparedtotheones requiredwhenthe a -coverageparameteris1 : 0,andalmosttriplethenodeswhenthe a 135

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aNumberofactivenodesinsparsenetworks. bConnectivity-coverageinsparsenetworks. Figure5.10:Performanceinsparsenetworkswhen R Comm > R Sense and a < 1. 136

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aNumberofactivenodesindensenetworks. bConnectivity-coverageindensenetworks. Figure5.11:Performanceindensenetworkswhen R Comm > R Sense and a < 1. 137

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coverageparameteris1 : 3.Thisincreaseremovesthe Cov protocolsawayfrombeingthe wortoftheoptimalsolutions,asshowninFigures5.10aand5.11a.Thistradeoffmay beexcesiveformostapplications,butnotforthoseinwhichthecriticalfactoriscoverage andnotenergyorlifetime. Inconclusion,itcanbeseenthatthepowerofthe a -coverageparameterintermsofalteringthebehaviorofthe Cov protocolsdependsontheneedsoftheapplication:either uselessenergyandextendthelifetimebyselectingfewernodes,andtherebyreducingthe areaofcoverage;oruseagreatamountofenergyandactivenodesinordertoobtaincompletecoverageofthearea.Adetailedanalysisoftheimpactofthe a -coverageparameter inthelifetimeispartofthefutureworkanditisnotincludedinthisdissertation. 5.4.2ComparisonwithDistributedProtocols Twodistributedprotocolswereselectedtobecomparedwiththe A 3 Cov protocols: ACOS[85]andStanGA[88].ThesecondoneisabletoprovideK-coverage,butthe comparisonwillbefocusedon K = 1.Fortheexperimentswiththedistributedcoverageorientedprotocols,randomscenarioswerecreatedbasedontheparametersdescribedin therespectivearticlesthatpresentedtheprotocols.Thegurespresentedinthissection arereproductionsoftheresultsintheircorrespondentpapers,whichshowinthex-axis thenumberofactivenodesproducedbytheprotocols,andinthey-axis,theareacovered bythereducedtopology. 5.4.2.1ComparisonWithACOS Thescenariosusedin[85]totesttheperformanceoftheACOSprotocolarebasedona particularwayofdeployment:theauthorsassumethattheareaofdeploymentisdivided 138

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aNumberofactivenodesinsparsenetworks. bConnectivity-coverageinsparsenetworks. Figure5.12:PerformanceoftheA3CovandA3CovLiteprotocolsinsparsenetworkswith differentradiiand a -coverageparameter. 139

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aNumberofactivenodesindensenetworks. bConnectivity-coverageindensenetworks. Figure5.13:PerformanceoftheA3CovandA3CovLiteprotocolsindensenetworkswith differentradiiand a -coverageparameter. 140

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insquarecellsof R s R s .Thenineachcell,aconstantnumberofnodesaredeployedin auniformlyrandommanner.Theyworkwith1,2,4and8nodespercell.Thescenarios theauthorsdenedhaveanareaof400 m 400 m R s = 20, R c = 40,whichwiththedifferentdensitieswillproducethenetworksizesof400,800,1600and3200,respectively. Theevaluationinthissectiononlyconsidersthescenarioswith800nodes. Figure5.14isbasedontheoriginalresultsshownin[85]for800nodes.Thedifferent pointsintheplottedfunctionforACOScorrespondtotheresultsintermsofnumberof activenodesandcoveredarea,basedonthevariationofthe j parameter,thatrepresents thenetcoveragethresholdintheprotocol.Theactualvaluesoftheparameterusedin theexperimentswerenotexplicitlyshownintheoriginalarticleofACOS,buttheyare mostlikelychangingfrom0 : 01to0 : 1,withsmallincrements,andfrom0 : 1to1 : 0with incrementsof0 : 1.FortheresultsofACOSinthisgure,onlythevalueswithacovered areagreaterthat65%wereconsidered.TheresultsoftheA3CovandA3CovLiteprotocolsinthisgurecorrespondtotheresultsintermsofnumberofactivenodesandareaof coveragefor a -coverageparametervaluesfrom0 : 5to1 : 5. Asithasbeenseen,inallscenarioswithasimilarnumberofactivenodesselected, A3CovandA3CovLiteofferagaininratioofcoveredareaofabout10%overACOS. Also, ACOScannotreachahigherdegreeofcoveragethat92%,whilethe Cov protocolscan reachpractivallytotalcoveragewiththesamenumberofnodes.ACOScanprovidelevels ofcoveragecloseto100%onlywhenthedensityofthenetwoerkisveryhigh nodes.Itisexpectedthatwithhigerdensities,the Cov protocolswillcontinuetoproduce evenbettercoverage. Theperformanceofthe Cov protocolscanberelatedtotheuniform-griddeploymentof thenodesinthearea.Thischaracteristicproducesaveryevenlydistributedtopology, 141

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Figure5.14:ComparisonofperformanceoftheA3Cov,A3CovLiteprotocolsandthe ACOSprotocolfor800nodes. 142

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thatallowstheA3-basedprotocolstoselectamorespreadoutsetofnodestobeactive, reducingtheoverlappingofsensingareas,andthus,theneedforselectingredundant nodes.InthecaseofACOS,theprotocoltriestoguaranteecompleteareacoverageand itpaysspecialattentiontocoveringsmallholesproducedbythetopology;thisselection policymayincreaseunnecessarilytheredundancyofthecoverage,requiringACOSto includeagreatamountofnodes,butnotofferingagreatcoverageratio. 5.4.2.2ComparisonWithStanGA Thescenariosusedin[88]totesttheperformanceoftheStanGAprotocolaredened bythefollowingparameters:auniformlyrandomdeploymentof200nodes,asquare deploymentareaof50 m 50 m ,communicationrangeof R c = 20,sensingrangeof R s = 10,andthe R SG parameterchangingfrom1 0 : 1 R s to12 1 : 2 R s withincrement of0 : 5.InthecaseofA3CovandA3CovLite,the a -coverageparameterwassettostart at0 : 1,alsowithanincrementof0 : 5.Thesevalueswereselectedinsuchawaythatonly levelsofcoveragegreaterthat93%oftheareaofinterestwereconsidered. Figure5.15,showstheresultsintermsofnumberofactivenodesversuscoveredarea forallthedifferentcongurationsdescribed.Thepointsoneachfunctioncorrespond totheresultswhenusingthedifferentvaluesoftheirrespectivecoverageparametersin decreasingorder,whenreadingthemfromlefttoright.Itcanbeseenthatthelowestratio ofcoveredareaoccurswiththegreatestvalueofthecoverageparameters,andthatthe coverageincreaseswhenthecoverageparametersdecrease. Asitcanbeseen,theperformanceofthethreeprotocolsisverysimilar.Thisbehavior isexpectedduetothesimilaritiesintheselectioncriteriaofthenodesforcoveragepurposes.However,themaindifferencebetweentheprotocolsisthattheStanGAprotocol 143

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Figure5.15:ComparisonofperformanceoftheA3Cov,A3CovLiteprotocolsandthe StanGAprotocolfordifferentcoveragecongurations. 144

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cannotguaranteeconnectivityinthescenarioswhere R SG > R cmax = 2,aspointedoutby theauthorsintheirarticle.Thisisacleardisadvantageofthisalgorithmcomparedtothe A3-basedprotocolswhichalwaysguaranteeaconnectedreducedtopologythat,inthe caseofthe Cov protocols,islaterextendedtoimprovecoverage. 145

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Chapter6:TopologyMaintenanceProtocols 6.1Introduction ThischapterisdevotedtotheproposedTopologyMaintenanceprotocols,aspartofthe secondcomponent,afterTopologyConstruction,toexecuteTopologyControl.Themain motivationforthestudyofTopologyMaintenanceasaseparateproblemfromTopology Constructionisthefactthatmostofthetopologycontrolalgorithmsproposedinliterature arefocusedonthetopologyreductionportion,whiletheydedicatelittleornoeffortto themaintenancepolicyoftheiralgorithms;forexample,mostoftheprotocolsdenea newinvocationofthetopologyconstructionwhennodesstarttofail.However,thereisno analysis,theoreticalorempirical,behindthesedecisions,sotheoptimalselectionofthe maintenancepolicycannotnotguaranteed. Theideaproposedinthissectionisthatbyseparatingthetopologyconstructionandmaintenanceprotocols,andworkingbasedonamodulardesign,itispossibletotestdifferent combinationsofthesetwokindsofprotocols,inordertoselect,basedonexperimentation,themostappropriatemaintenancepolicyforthereducedstructurecreatedbythe constructionprotocol. Inthischapter,fourtopologymaintenancealgorithmswillbeintroduced:StaticGlobal TopologyRotationSGTRot,DynamicGlobalTopologyRecreationDGTRec,Hybrid GlobalTopologyRecreationandRotationSGTRecRotandDynamicLocalDSRDL146

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DSR,basedontheDynamicSourceRoutingDSRprotocol.Thersttwohavebeen usedinliteraturebutnotimplementedasindependentprotocols,andthenaltwoare completelynewprotocols. Theperformanceofthefourproposedtopologycontrolprotocolswillbetested,working jointlywithtwotopologyconstructionprotocols:A3,EECDSandCDS-Rule-K.Inaddition,asensitivityanalysisofperformanceisincluded,basedontheparametersofenergy threshold,inter-resettimeandnetworkdensity. 6.2StaticGlobalTopologyRotation TheStaticGlobalTopologyRotationSGTRotistheimplementationofaprotocolfor rotatingmultiplereducedtopologies.Themainassumptionthatthisprotocolmakesis thateachnodekeepstrackofseveralVirtualNetworkInterfaces,orVNI.TheseVNIs containinformationrelevantforanodeconcerningeachseparatereducedtopologycreatedinthenetwork:address,roleactive,inactiveorsink,communicationandsensing radiusinthecaseswherethesearevariables,routinginformation,etc.Inaddition,inthe occurrenceofarotation,eachnodeshouldbeabletochangethecurrentlyactiveVNIina shortperiodoftime. Theprotocolisverysimple.Assumethatthetopologymaintenancetriggerisactivated inoneofthenodes.Itwillsenda NoticationMessage tothesinknode,informingthat itstriggerwentoff.Whenthismessagearrivestothesinknode,itwilldecideiftheoccurrenceofthetriggeringeventisenoughofareasontostarttherotationprocess.Ifthat isnotthecase,thesinknodewillignorethemessage.Insomecasesthesinkistheonly noderesponsibleforthetriggeringofthemaintenanceprocedure,likewhenitdependson alocaldecisionoralocaltimer. 147

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Inthecasewherethesinkconsidersthatarotationisnecessary,thesinkwilldetermine theidofthenextavailableVNI,willsenda RotationMessage includingtheidofthenext VNI,anditwillchangeitscurrentactiveVNItothenextone,updatingalltherelevant informationaboutthenewnetwork.Oncethismessagearrivesatanode,thenodewill forwardthe RotationMessage andwillchangealsoitsVNI.Afterchangingtothenew VNI,anodewillnotforwardanymore RotationMessages withtheidofthecurrentVNI, whichproducesacontrolledoodinginwhicheverynodetransmitsthe RotationMessage justonce. Aftereveryrotation,thesinkwillevaluateifithasatleastoneactivenodeinitsneighborhood.Ifthesinkndsatleastone,thentheVNIwillbeactiveuntilanewtriggeringevent occurs.Inthecasewherethesinkisisolatedfromactivenodes,thenitwilleliminate thecurrentVNIandwillstartanotherrotationtothenextVNI.Thenetworkisnally deadwhentherearenoVNIsavailabletoperformarotation.Thecurrentversionofthis protocoldoesnotincludemechanismstoverifythestatusofconnectivityandcoverageof thenewVNI,orthatallthenodeswererotated,butithasbeenconsideredforfuturenew versionsofthisprotocol. 6.3DynamicGlobalTopologyRecreation TheDynamicGlobalTopologyRecreationDGTRecisperhapsthemostcommonly usedmaintenancepolicyintheliteratureoftopologycontrol,mainlybecauseitisthe simplestonetoimplementbecauseitdoesnotrequireanypre-calculatedinformationand becauseitistightlyrelatedtothetopologyconstructionprotocols,whichhavebeenthe mainfocusofresearchinthisarea. 148

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AsintheSGTRotprotocol,thetopologymaintenancetriggerisactivatedinthesinkitself orinoneofthenodes.Itthetriggeringeventhappenedinaregularnodeitwillsend a NoticationMessage tothesinknode,informingthatitstriggerwentoff.Whenthis messagearrivesatthesinknode,itwilldecideiftheoccurrenceofthetriggeringevent inenoughreasontostarttherotationprocess.Ifthatisnotthecase,thesinknodewill ignorethemessage. Inthecasewherethesinkconsidersthatarotationisnecessary,thesinkwillsenda Reset Message and,ifitistheonlysinkinthetopology,itwillscheduleanewexecutionofthe topologyconstructionprotocolitusedintherstplacetoreducethetopology.Whena nodereceivesa ResetMessage ,itwillforwarditimmediatelytoallitsneighbors,and thenthenodewilleliminateallinformationaboutthecurrentreducedtopology,andwill moveitselfintotheinitialstateofthetopologyconstructionprotocol,waitingforthe newexecution.AsintheSGTRot,acontrolledoodingisinchargeofresetingtheentire network. 6.4DynamicLocal-DSR Thisprotocolisanewimplementationofanenergy-baseddynamiclocaltopologymaintenancetechnique.TheDL-DSRisbasedonthewell-knownDynamicSourceRouting DSR[108]protocolforwirelessadhocnetworks.Thisprotocolwasdesignedtoallow anodewithverylowremainingenergytondreplacementsthatwillofferconnectivityto itssoon-to-be-orphanedchildren. Theprotocolworksintwophases.Duringtherstphase,theaffectednode, N i ,i.e.the nodewhoseenergylevelisbelowacertainthreshold,broadcastsa WakeUpMessage that includesthelistofallitschildrennodes.Thismessagewillreachallitschildren C i ,both 149

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activeandsleeping,whichafterreceivingthemessagechangetheirstatusto Semi-Active Thesenodeswillsenda WakeUp-3Message totheirneighborsandchildren,which,upon receivingthemessage,willturnthemselvesonandchangetheirstatusto TM-Initial whichleavesthemreadyfortheexecutionofthelocalmaintenanceprotocol. The WakeUpMessage isalsoheardby N i 'sactiveparent P i anditsotherchildren B i brothersof N i ,whowerepartofthereducedtree.Uponreceivingthe WakeUpMessage P i storesthelistofchildrenof N i andthen,withthebrothernodes B i ,broadcastsa WakeUp-2Message amongtheirrespectivechildrenandneighborstowakethemuptoo. Allthenodesthatreceivedthe WakeUp-2Message willchangetheirstatusto TM-Initial andwillsenda WakeUp-3Message totheirrespectiveneighborhoods.Thenodesthat receivedthe WakeUp-3Message willnotforwardanyothermessage,whichwillcontain theprocesstoanareadenedbyallnodestwohopsawayon N i 'schildren'sside,and threehopsawayonitsparent'sside.Thesenodearein Semi-Active or TM-Initial states. Eachnodecanbeawakenedonlyonce,andwillignoreanyother Wake-Upmessage ThisprocedureisdoneinthismannertoguaranteethatalgorithmslikeA3,whichbuilds treeswithveryspreadoutbranches,canverylikelyndalternatepathstorestorethe topology,whilecoveringallthenodesthatwerepreviouslycoveredbynode N i .Figure6.1showsanexampleofthetopologyafterexecutingtherstphaseoftheDSR-based dynamiclocaltopologymaintenancetechniquejustdescribed,showingtheareaofthe networkthathasbeenawakenedtorunthemaintenanceprocedure. Thesecondphaseoftheprotocolbeginswiththeparentnode P i doingarestrictedoodingofa RouteRequestMessage .Theoodisrestrictedbecauseithasanaldestination: allsemi-activenodesonly,whicharetheneworphannodesfrom N i .The RouteRequest Message includesadatastructurethatcontainsthelistofnode N i 'schildrenthatarenow 150

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Figure6.1:PhaseoneoftheDSR-baseddynamiclocaltopologymaintenancetechnique. disconnectedfromthenetworkaswellasthecurrentroutingandenergy-distanceinformationofthepaththatthemessagehasgonethrough. Uponreceivinga RouteRequestMessage forthersttime,thereceivingnoderegisters thecurrentpathinformationcontainedinthemessageandsetsatimeoutinordertowait formoremessagesofthiskind.Everytimethenodereceivesanew RouteRequestMessage ,itwillcomparethepathfromthenewmessagewiththebestpathithasfoundyet.If thenewpathisbetter,thenthenodewillupdatethepath;otherwise,themessagewillbe ignored. Oncethetimeouthasexpired,thenodewillupdatetheinformationofthebestregistered pathwithitsowncostinlengthandenergy,andwillsenda RouteRequestMessage ,includingnewpathinformation.Also,thenodewillchangeitsstatusto TM-Ready .Anode inthisstatewillignoreevery RouteRequestMessage andwillsetatimeoutinorderto 151

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waitforrepliesontherouterequests.Ifthistimeoutexpires,thenthenodewillreturnto itsnormalroleinthereducedtopologyactiveorsleepingmode. Itisexpectedthatthesemessageswilleventuallyreachatleastoneofthenodes C i .These nodes,justasthenon-orphannodes,willsetatimeoutinordertowaitforthearrival ofmore RouteRequestMessages fromdifferentpaths;however,thetimeoutinthese nodeswillbelongerinordertoallowahighernumberofpossibilities.Oncethetimeout expires,the C i nodesselectthebestroutebacktotheparentnode P i basedontheroute informationcontainedinthemessages,andwillincludethisinformationina RouteReply Message ,whichisaunicastmessageaddressedtotheprevioushopinthepath. Receivinga RouteReplyMessage meansthatthespecicnodehasbeenselectedaspart ofthenewpathtotheorphannode.Thereceivernodewillchangeitsstatusto TM-Active andwillforwardthemessagetotheprevioushoponthebestpathithasregisteredforthe orphannode.Asinglenodecanbeselectedtobepartofdifferentpaths. Thisprocesscontinuesuntil P i receivesthe RouteReplyMessages fromallthe C i nodes thathavebeenreachedbytheprotocol.Asthetimeouttoreturntonormalityexpires,all nodesthatwerenotselectedtobepartofanewpathwillreturntotheiroriginalroles: sleepingoractivenodes.Inthecasethatanodewasselectedaspartofanewpath,no matterwhichroleithad,thenodewillremainactiveinordertoguaranteeconnectivity. 6.5HybridGlobalTopologyRecreationandRotation TheHybridGlobalTopologyRecreationandRotationHGTRecRotprotocolisamixturebetweenthestaticanddynamicglobalapproachespresentedhere.Asastaticprotocol,itassumesthatthetopologyconstructionprotocolgeneratesmorethanoneVNI, whichwillberotated,asintheSGTRotprotocol,basedonthetriggeredeventfromthe 152

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nodesinthenetwork.Themaindifferencefromthestaticprotocolcomeswhenthesink detectsthatithasbecomeisolatedfromthenetwork,duetolackofactiveneighbornodes. Atthispoint,thesinksendsa ResetMessage thatinvokesthetopologyconstructionprotocolinordertorenewthecurrentVNI,asintheDGTRecprotocol.Ifthesinkisstill isolatedaftertherecreationprocess,thenthesinkwilleliminatethecurrentVNIfromthe listofavailableonesandwillrotatetothenextone.IftherearenomoreVNIsavailable, thenthesinkwilldeterminethatthenetworkisdead. 6.6PerformanceEvaluation Thissectionincludescommoninformationaboutthesimulation-basedperformanceevaluationthatwillbecarriedoutinthenextthreechapterstoassesstheperformanceofthe variousstatic,dynamic,andhybridtopologymaintenancetechniques.Thepurposeofthe experimentsistodeterminethebenetofimplementingtopologymaintenancetechniques inbothsparseanddensenetworks,andcomparetheirperformanceversusthechoiceof notimplementingtopologymaintenanceatall. Intheseexperiments,sparsetopologiesaredenedastopologiesinwhichthecommunicationradiusiscalculatedbasedontheCriticalTransmissionRangeCTRformula ofPenrose-Santi[4]Equation2.1describedinSection2.2.1.1.Thisguaranteesthat thenodedegreeisverylow,creatingaweakly-connectedtopology.Densetopologies aredenedassparsetopologiesinwhichtheoriginalnumberofnodesisdoubled.Each pointinthegraphsistheaverageofrunningthesameexperiment150times,i.e.with150 differenttopologies. InallsimulationstheA3,EECDS,andCDS-Rule-Ktopologyconstructionalgorithms describedinChapters2and4wereutilized.Theimplementationswerecodedandtested 153

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Table6.1:Simulationparametersfortopologymaintenanceprotocols. SparseTopologies DenseTopologies Deploymentarea 200mx200m Numberofnodes 50 100and400 Numberofsinks 1sink Numberoftopologiesruns 150 perexperiment TransmissionRange 1xCTRequivalentto:37m[4] NodeDistribution Uniform,200 TimeThreshold 1000timeunits EnergyThreshold 10%oftotalenergy Maxnumberofreducedtopologies 3reducedtopologies staticandhybridschemes E max 1Joule A3Weights W E = 0 : 5 ; W D = 0 : 5 intheAtarrayasimulationtool.Inallsimulations,thewirelesssensordevicesareuniformlydistributedinanareaofinterestof200 m 200 m ;thenumberofnodesisvaried tocreatesparseanddensenetworks;andallscenarioshaveonesink.Eachactivenodein thecurrentreducedtopologyisscheduledtosenddatamessagesdirectedtothesinkevery 10timeunits.Sincealltopologyconstructionalgorithmsproduceatree-basedreduced topologyrootedatthesink,averysimpleroutingalgorithmisimplementedinwhich nodesforwardthedatamessagestotheirrespectiveparents.Inallexperiments,nodata aggregationorsimilarstrategyisimplemented.Energyisdrainedwhenapacketiseither sentorreceivedaccordingtotheenergydissipationmodelpresentedinSection3.3.4. Table6.1includesasummaryofthemostimportantsimulationparametersusedinall simulations. 154

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6.6.1PerformanceEvaluationofStaticGlobalTopologyMaintenanceTechniques ThissectionpresentsaperformanceevaluationofthestaticglobaltopologyrotationtechniquecarriedoutinthesimulationtoolAtarraya,usingthesimulationparametersand assumptionsdescribedintheTable6.1.Thepurposeoftheexperimentsinthissectionis todeterminethebenetofimplementingstaticglobaltopologymaintenancetechniques inbothsparseanddensenetworks,andcomparetheirperformanceversusthechoice ofnotimplementingtopologymaintenanceatall.Thefollowingtopologymaintenance techniquesandtriggeringcriteriaareincluded: NoTopologyMaintenance-NoTM: Theinitialreducedtopologyworkspermanentlyuntilthesinkdetectsthatitdoesnothaveanymoreactivenodesinrange.In general,thisisthesameterminationpolicyforallthealgorithms. StaticGlobalTime-basedTopologyRotation-SGTTRot: Everypre-determined timeintervalthetopologymaintenancealgorithmrotatestheactivereducedtopologyforoneofthepre-plannedones. StaticGlobalEnergy-basedTopologyRotation-SGETRot: Everytimeanode reachesacriticalenergythreshold,thetopologymaintenancealgorithmrotatesthe activereducedtopologyforoneofthepre-plannedones. Forsimplicity,intheexperiments,thenumberofpre-plannedtopologiesislimitedto three 1 .Theprocessofselectingthesethreetopologiesisdifferentdependingontheunderlyingtopologyconstructionmechanism.InthecaseofA3,itsselectionmetricismanipulatedtolowertheprobabilityofselectingonenodeinmorethanonetopology.However,sincethesametopologyconstructionalgorithmisruneverytime,ifaparticular 1 Amorecomplexmechanismthatndsasmanyaspossiblecompletelydisjointtopologiescanbe foundin[69]. 155

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nodethathasbeenusedbeforeinanothertopologyisneededtoguaranteenetworkconnectivity,itmaybeselectedagain.Inotherwords,thestaticglobaltechniquebasedonA3 mayproduceshared-disjointtopologies. InthecaseoftheEECDStopologyconstructionalgorithm,italsousesanumericalmetric toperformtheselectionoftheactivenodes,whichallowstheapplicationofapenaltyin thismetrictoallnodesthathavebeenselectedtobeactiveinothersubsets.However, dependingonthedensityofthenetwork,themetriccannotbechangedinallthenodes. EECDSworksintwophases,selectingBlacknodesintherstphase,andBlueandGray nodesinthesecondphase.Blacknodesarebackbonenodesthatactasclusterheads,Blue andGraynodesarethenusedtointerconnecttheclusterheads.Asaresultofthistwophaseapproach,EECDScanonlyreducetheselectionmetrictotheBlacknodesthathave beenselectedpreviouslytobeactiveinothersubsets.Indensetopologiesitisexpected thatifthereisachangeintheselectionmetricoftheBlacknodes,thesetofelectedGray nodeswillalsochange.However,insparsetopologiesthecaseisdifferentbecausethere aresofewpossibilitiesofselectionofGraynodesthattheywilltendtobethesameones ineverysubset. Finally,inthecaseoftheCDS-Rule-Ktopologyconstructionalgorithm,sinceitdoes notincludeanynumericalmetrictoselectthenodes,thealgorithmisleftunchanged, meaningthatitmayproduceverysimilartrees. 6.6.1.1SparseNetworks Figure6.2showsnetworklifetimesimulationresultswhenperformingstaticglobaltopologymaintenanceinsparsenetworks.Twocommonobservationscanbemade.First, staticglobaltopologymaintenanceinsparsenetworkscaneitherimproveordegradethe 156

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networklifetimecomparedwiththeoptionofnotperformingtopologymaintenanceatall. Second,theperformanceisnotsignicantlybetterorworse,meaningthatapplyingstatic globaltopologymaintenancetechniquesinsparsenetworksmightnotbeuseful. Theseresultsaretotallyexpected,asinsparsenetworksnotmanydisjointtopologiescan becreated.Rememberthatinthisscenarioonly50nodesarespreadinanareaof200 squaremeters.Thismeansthatthetopologymaintenanceprocedurejustactivatesthe sametopology,oraverysimilarreducedtopology,everytimeandtheoverheadrelated tothechangingprocessdrainsextraenergy,killingthenodesearlier.Theimpactofnot havingdisjointsubsetscanbeappreciatedintheCDS-Rule-KalgorithmFigure6.2c, asbothstatictechniquesdidnotevenreachtheperformanceofhavingnotopologymaintenanceatall. Anotherimportantobservationisthattheperformanceofthestaticglobaltechniquesmay changeaccordingtothevalueofthetriggeringmechanism,i.e.,thevalueofthetimer andtheenergythreshold.Nonetheless,itisnotexpectedthatchangingthesevaluesto moreappropriateoptimaloneswillproduceconsiderablybetterorworseresults,as theeffectofthereducednumberofdisjointtopologieswillprevailoverthethreshold values.Asensitivityanalysislookingattheeffectofthesevaluesintheperformanceof thetechniquesisincludedinSection6.8fordensenetworks. Finally,Figure6.6.1.1comparesthebestperformingtechniquesforeachalgorithm.As itcanbeobserved,allenergy-basedtechniquesperformbetterthanthetime-basedtechniques.Thisresultisexpectedastheenergythresholddoesnotmakethetopologyto changeuntilthenodesarealmostwithoutenergy.Sincetherearenotmanydisjointtopologies,theenergy-basedtechniquesdonotwasteasmuchenergyasthetime-based techniquesintheswitchingprocess,whichswitchthetopologyevery1000timeunits.Of thethreetechniques,theonebasedontheA3algorithmisthebestperforming.Thisis 157

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aA3 bEECDS. cCDS-Rule-K Figure6.2:Networklifetimewithandwithoutstaticglobaltopologymaintenanceusing theA3,EECDS,andCDS-Rule-Ktopologyconstructionmechanismsinsparsenetworks. 158

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Figure6.3:Bestperformingstaticglobaltopologymaintenancetechniquesinsparse networks. becauseA3ismoreenergyefcientthanEECDSandCDS-Rule-K,asithasbeendemonstratedin[106]. Theresultsofalltheseexperimentsaresurprisingatrstglancesinceitwasexpected thatsomehowtopologymaintenancehadtoprovidesomesortofimprovement.However, thisisnotthecase.Foralltopologyconstructionalgorithms,astaticglobaltopology maintenancetechniquedecreasesthenetworklifetime.Theexplanationofthishastodo withtworelatedfactors.Inasparsenetworknotmanyifmorethanonecompletelydisjointtopologiescanbebuilt,reducingthecasetothesimplecaseofnothavingtopology maintenanceatall.Inthecaseoftopologieswithsharednodes,althoughmorethanone topologiescanbecreated,manyofthemifnotallsharethesamecriticalnodes,then reducingtheenergyevenfurtherbecauseoftherepetitionofthetopologymaintenance process.Thetime-basedschemeperformsbetterthantheenergy-basedtechniquebecause theformergivesmoretopologiesthechangetousethosecriticalnodes.Inthelattercase, 159

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thersttopologyusesthosecriticalnodesalmostuntiltheyaredepleted.Ofcoursethisis aconsequenceoftheenergythresholdusedinthesimulations,inwhichthenodesaskthe sinktochangethetopologywhentheyhaveconsumed90%oftheirtotalenergy.Better resultsmightbeobtainedwithhigherthresholds. 6.6.1.2DenseNetworks Theperformanceofthestaticglobaltopologymaintenancetechniquesisexpectedto improvewiththenetworkdensity,asitincreasesthechanceofhavingmorenode-disjoint topologies.Thisimprovementinperformanceis,infact,showninFigure6.4,which includestheresultsformoredensenetworks,thoseusing100nodesinsteadof50.ComparingFigures6.2and6.4,itcanbeobservedthatwhileinsparsenetworksthenotopologymaintenanceoptionwaseitherthebestperformingone,orveryclosetobethebest performingone,indensenetworkstheoppositeistrue.Actually,itcanbeseenfromthe guresthatalltopologymaintenancetechniquesunderconsiderationextendthenetwork lifetimeoverthenotopologymaintenanceoption,sotheiruseismorethanjustied. Twoadditionalobservationsareworthincluding.First,theperformanceofthetopology maintenancetechniquesdependsontheunderlyingtopologyconstructionalgorithm.It canbeseenthatwhiletheperformanceoftheA3-basedandEECDS-basedtechniques improvedwithrespecttothesameexperimentsinsparsenetworks,theperformanceimprovementoftheCDS-Rule-K-basedtechniqueisnotasbig.Thishastodowiththe wayofselectingthedisjointtrees,asexplainedatthebeginningofthissection.A3and EECDSallowthemanipulationofthenodeselectionmetric,and,therefore,theyare abletobuildmorenode-disjointtrees.Second,asinthecaseofsparsenetworks,the techniquesthatusedtheenergytriggeringmetricoutperformedthetime-basedtechniques. 160

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Again,thishastodowithchoosinganoptimalswitchingtimeorenergythreshold,which hasnotbeenattemptedthusfar.AsensitivityanalysisisincludedinSection6.8,which alsolooksattheeffectofincreasingthenetworkdensityevenfurther. 6.6.2PerformanceEvaluationofDynamicGlobalTopologyMaintenanceTechniques Dynamicglobaltopologymaintenancetechniqueschangetheentiretopologybyrunningthetopologyconstructionmechanismaneweverytimeitisneeded.Usingthesame networkparametersdescribedinTable6.1,simulationexperimentswerecarriedoutto assessthenetworklifetimewithdynamicglobaltopologymaintenancetechniquesin sparseanddensenetworksusingtheA3,EECDS,andCDS-Rule-Ktopologyconstruction algorithmscomparedagainstthecasewherenotopologymaintenanceisperformed.The followingtopologymaintenancetechniquesandtriggeringcriteriaareincluded: NoTopologyMaintenance-NoTM: Theinitialreducedtopologyworkspermanentlyuntilthesinkdetectsthatitdoesnothaveanymoreactivenodesinrange. Thisisthesameterminationpolicyfortherestofthealgorithms. DynamicGlobalTime-basedTopologyRecreation-DGTTRec: Everysettime intervalthetopologymaintenancealgorithmterminatesthepreviousreducedtopologyandinvokesthetopologyconstructionalgorithmtocreateanewone. DynamicGlobalEnergy-basedTopologyRecreation-DGETRec: Everytimea nodereachesacriticalenergythreshold,thetopologymaintenancealgorithmterminatesthepreviousreducedtopologyandinvokesthetopologyconstructionalgorithmtocreateanewone. 161

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aA3 bEECDS. cCDS-Rule-K Figure6.4:Networklifetimewithandwithoutstaticglobaltopologymaintenanceusing theA3,EECDS,andCDS-Rule-Ktopologyconstructionmechanismsindensenetworks. 162

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Figure6.5:Bestperformingstaticglobaltopologymaintenancetechniquesindense networks. 6.6.2.1SparseNetworks Figure6.6showsthenetworklifetimesimulationresultsusingdynamicglobaltopology maintenancetechniquesinsparsenetworksusingenergyandtimetriggeringcriteria. ContrarytothestaticglobaltechniqueresultsforsparsenetworksshowninFigure6.2, nowalltopologymaintenancetechniquesprovidebetterperformancethanthecasewith notopologymaintenance.Itisclearthatthenewtopologyconstructionprocessisable tondbettertopologiesthanthepre-plannedalgorithms,extendingthenetworklifetime, eveninsparsenetworks.However,theperformanceimprovementoverthenotopology maintenanceoptionisnotconsiderableeither,reinforcingtheconclusionreachedbefore that,insparsenetworks,topologymaintenancedoesnotprovideimportantbenets.ComparingFigures6.6and6.2again,itcanbeobservedthatdynamictechniquesprovidebetterperformancethanstaticones,whichisexpectedgiventhatmoreandbettertopologies 163

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canbebuiltusingdynamicmethods.Amoredetailedcomparisonamongthesetechniques isincludedinSection6.7. Asinthecaseofstaticglobaltechniques,fromFigure6.6.2.1,thesametwoconclusions canbedrawn.First,allenergy-basedtechniquesoutperformedthetime-basedtechniques. Again,theseperformanceresultsmightvarydependingonthetimeperiodandtheenergythresholdchosen.Similarly,inthecaseofA3,thebehaviorcanalsobechanged varyingtheweightsinEquation4.1,whichwouldgivepreferencetothosenodesthat containmoreenergy,orthosenodesthatareclosertotheparentnode.Thereareclear tradeoffsusingthesevariablesandweights,whicharebeyondthescopeofthebook atthistime.Second,thetechniqueusingtheA3topologyconstructionalgorithmisthe bestperformingone,althoughnotbyanimportantmargin.ThisisduetoA3'slowerand linearmessagecomplexitycomparedwithEECDSandCDS-Rule-K[106]. 6.6.2.2DenseNetworks Moreinterestingresultsareobtainedinthecaseofdensenetworks,ascanbeobserved fromFigure6.8.Nowthegureshowsthatbyincreasingthenumberofnodesfrom50 to100,dynamicglobaltopologymaintenancetechniquesareabletokeepactiveaconsiderablyhighernumberofnodescomparedwiththeoptionofnotopologymaintenance. ComparedwiththecaseofdynamicglobaltechniquesinsparsenetworksshowninFigure6.6,theperformanceindensenetworksisnearlytwiceasgoodastheperformancein sparsenetworks,meaningthatmoreandbettertreescanbefoundindensenetworks. Also,asinthecaseofstaticglobaltechniquesindensenetworks,heretheperformance providedbytheenergy-basedtechniquesoutperformedtheonesbasedontime.Asstated before,thisdoesnotmeanthattime-basedtechniquesarebetterorworsethanenergy164

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aA3 bEECDS. cCDS-Rule-K Figure6.6:Networklifetimewithandwithoutdynamicglobaltopologymaintenance usingtheA3,EECDS,andCDS-Rule-Ktopologyconstructionmechanismsinsparse networks. 165

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Figure6.7:Bestperformingdynamicglobaltopologymaintenancetechniquesinsparse networks. basedtechniques;itjustmeansthattheyprovidedaworseperformancewiththoseparticularsettings,i.e.1000timeunitsforthetime-basedcriterion,and10%ofthetotal remainingenergyfortheenergy-basedcriterion.MoreinsightsaboutthisaspectareincludedinSection6.8. Figure6.6.2.2plotsthebestperformingmechanismsineachcase.Asinpreviouscases,it seemsthatthetopologymaintenancemechanismbasedontheA3topologyconstruction algorithmhasabetterperformancethantheonesbasedontheCDS-Rule-KandEECDS algorithms,however,theadvantageismarginal.AlthoughA3hasbettermessagecomplexitythanCDS-Rule-KandEECDS,thesmallamountofsensorsandthesmall energythreshold%causethetopologymaintenancealgorithmtocallthetopology constructionalgorithmveryfewtimes,whichmakestheamountofenergyspentbythe threeschemesverysimilar.AmorepronoundcedlifetimeadvantageofA3wouldhad beenseenifthetopologyconstructionalgorithmhadbeenrunmanymoretime. 166

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aA3 bEECDS. cCDS-Rule-K Figure6.8:Networklifetimewithandwithoutdynamicglobaltopologymaintenance usingtheA3,EECDS,andCDS-Rule-Ktopologyconstructionmechanismsindense networks. 167

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Figure6.9:Bestperformingdynamicglobaltopologymaintenancetechniquesindense networks. 6.6.3PerformanceEvaluationofDynamicLocalTopologyMaintenanceTechniques ThedynamiclocaltopologymaintenancetechniquewasalsoimplementedintheAtarraya simulatorandevaluatedusingthesameparametersandscenariosutilizedbefore.Inthe nextsubsectionstheresultsinsparseanddensenetworksarepresentedwherethefollowingtopologymaintenancetechniquesandtriggeringcriteriaareincluded: NoTopologyMaintenance-NoTM: Theinitialreducedtopologyworkspermanentlyuntilthesinkdetectsthatitdoesnothaveanymoreactivenodesinrange. Thisisthesameterminationpolicyfortherestofthealgorithms. DynamicLocalEnergy-andDSR-basedRepair-DLEDSR: Everytimeanode reachesacriticalenergythreshold,thelocaltopologymaintenancealgorithmbased ontheDSRprotocolrepairsthetopology. 168

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6.6.3.1SparseNetworks Figure6.10showsthesimulationresultsofthedynamiclocaltopologymaintenance techniquecomparedwiththecaseofnotopologymaintenanceinsparsenetworksusing theA3,EECDS,andCDS-Rule-Ktopologyconstructionalgorithms.Asitisclearly shown,thedynamiclocaltechniqueenhancesthenetworklifetimeinallcases,meaning that,eveninsparsenetworks,itisworthapplying.Anotherobservationisthatinthis case,thetechniquebasedontheCDS-Rule-Ktopologyconstructionmechanismisthe bestperformingoneSeeFigure6.6.3.1.ThisisbecausetheCDS-Rule-Kalgorithm somehowbuildstreeswithclosebranches,andthelocalprocedureisabletorestorethe connectivityofthebranchwithveryfewnodes,ascomparedwithA3andEECDS.This effectisbetterseenafterthetopologyhasbeenrunforsometime,after15000timeunits inthegures.Atthattime,manynodesstartreachingtheenergythreshold,triggeringthe localproceduremoreandmoreoften.Astimecontinues,thenumberofnodestriggering thelocalprocedureincreasesmakingtheadvantageofCDS-Rule-Kmoreappreciable overtheA3andEECDScounterparts. 6.6.3.2DenseNetworks Thesimulationresultsoftheenergy-andDSR-baseddynamiclocaltechniqueindense networksarepresentedinFigure6.12.Asbefore,theresultsimprovewiththedensity ofthenetwork,asmorepossibilitiesexisttoreconnectthetopologywhenmorenodes areavailable.Asthegureshows,inallcasestheapplicationofthedynamiclocaltopologymaintenancetechniqueimprovesthenetworklifetimecomparedwiththecaseofno topologymaintenance.Further,theperformancealsoimprovesoverthecasewithsparse 169

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aA3 bEECDS. cCDS-Rule-K Figure6.10:Networklifetimewithandwithoutdynamiclocaltopologymaintenance usingtheA3,EECDS,andCDS-Rule-Ktopologyconstructionmechanismsinsparse networks. 170

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Figure6.11:Bestperformingdynamiclocaltopologymaintenancetechniquesinsparse networks. networks,asexpected.Similartotheresultsinsparsenetworks,Figure6.6.3.2showsthat thelocaltechniquebasedontheCDS-Rule-Kalgorithmoutperformstheothertwo.The behavioristhesameonlythatwithmorenodestheperformanceisbetter.TheCDS-RuleKtopologyconstructionalgorithmtsverywellintothisdynamiclocalstrategy. 6.6.4PerformanceEvaluationofHybridGlobalTopologyMaintenanceTechniques UsingthesamenetworkparametersdescribedinTable6.1,andthesameunderlying topologyconstructionmechanismsutilizedintheperformanceevaluationsincludedin sections6.2and6.3,simulationexperimentswerecarriedouttoassessthenetworklifetimeofthehybridglobaltopologymaintenancetechniquejustdescribedinsparseand densenetworks.Thefollowingtopologymaintenancetechniquesandtriggeringcriteria wereincluded: 171

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aA3 bEECDS. cCDS-Rule-K Figure6.12:Networklifetimewithandwithoutdynamiclocaltopologymaintenance usingtheA3,EECDS,andCDS-Rule-Ktopologyconstructionmechanismsindense networks. 172

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Figure6.13:Bestperformingdynamiclocaltopologymaintenancetechniquesindense networks. NoTopologyMaintenance-NoTM: Theinitialreducedtopologyworkspermanentlyuntilthesinkdetectsthatitdoesnothaveanymoreactivenodesinrange. Thisisthesameterminationpolicyfortherestofthealgorithms. HybridGlobalTime-basedTopologyRecreationRotation-DGTTRecRot: Every settimeintervalthetopologymaintenancealgorithmrotatestheactivereduced topologyforoneofthepreplannedones.Ifthenewpre-plannedtopologycannot providetheexpectedservicehasnoconnectionwiththesink,thehybridtopology maintenancealgorithminvokesthetopologyconstructionalgorithmtocreateanew reducedtopologyonthey. HybridGlobalEnergy-basedTopologyRecreationRotation-DGETRecRot: Every timeanodereachesacriticalenergythreshold,thetopologymaintenancealgorithm rotatestheactivereducedtopologyforoneofthepreplannedones.Ifthenewpreplannedtopologycannotprovidetheexpectedservicehasnoconnectionwiththe 173

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sink,thehybridtopologymaintenancealgorithminvokesthetopologyconstruction algorithmtocreateanewreducedtopologyonthey. 6.6.4.1SparseNetworks Asinthecaseofthestaticanddynamictopologymaintenancetechniquespresentedin sections6.2and6.3,theperformanceresultsofthehybridglobaltechniquepresented hereshowsnomajorimprovementcomparedwiththenotopologymaintenanceoption insparsenetworks.Insomecases,thetechniqueincreasesthenetworklifetimeandin somecasesreducesit,butwithsmallmarginsinbothcases,emphasizingtheconclusion reachedbeforewithothertechniquesthatapplyingtopologymaintenanceinsparsenetworkswillnotproducesignicantimprovementsintermsofnetworklifetime. Figure6.6.4.1alsoemphasizespreviousresults.Forexample,itshowsthattheenergybasedhybridtechniquealsooutperformsthetime-basedtechnique.Also,theperformance ofthehybridtechniquebasedontheA3topologyconstructionisconsistentwithprevious results,showingitsadvantagealthoughwithoutimpressivemargins.Finally,Compared withthestaticanddynamiccounterparts,itseemsthatthehybridtechniqueimprovesthe performance,butnotconsiderably.MoreonthisinSection6.7later. 6.6.4.2DenseNetworks Thesameexperimentswereruninamoredensenetwork,onewith100nodes-twicethe numberofnodesutilizedinthesparsescenario.ThesimulationresultsshowninFigure6.16clearlydemonstratethepowerofthistechnique.Inallcasesthehybridglobal topologymaintenancetechniqueoutperformsthenotopologymaintenanceoptionby impressivemargins.Asinpreviouscases,Figure6.6.4.1showsthatthehybridtechnique 174

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aA3 bEECDS. cCDS-Rule-K Figure6.14:Networklifetimewithandwithouthybridglobaltopologymaintenance techniquesusingtheA3,EECDS,andCDS-Rule-Ktopologyconstructionmechanisms insparsenetworks. 175

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Figure6.15:Bestperforminghybridglobaltopologymaintenancetechniquesinsparse networks. withtheA3topologyconstructionalgorithmperformsbetterthanthetechniquewith theEECDSandCDS-Rule-Kalgorithms.Itisclearthat,oncethestaticportionofthe techniqueexhauststheenergyofthepre-plannedtrees,thedynamictechniquestillcan ndnewtrees,andtherefore,runthenetworklonger. 6.7ComparisonofTopologyMaintenanceTechniques Thissectionsummarizesalltheperformanceevaluationresultspresentedthusfarinthis partofthebookinordertoprovidegeneralconclusionsastowhichtechniqueisbetterto useinsparseanddensenetworks.Assuch,thissectionismeanttoanswerquestions,such as: Whatisthebeststatic,dynamicandhybridtechniqueinsparseanddensenetworks? IfIhaveasparseoradensenetwork,whattechniqueshouldIuse? 176

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aA3 bEECDS. cCDS-Rule-K Figure6.16:Networklifetimewithandwithouthybridglobaltopologymaintenance techniquesusingtheA3,EECDS,andCDS-Rule-Ktopologyconstructionmechanisms indensenetworks. 177

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Figure6.17:Bestperforminghybridglobaltopologymaintenancetechniquesindense networks. Whichapproachisbetter,globalorlocal? Whattriggeringcriteriaisbetter,energy-basedortime-based? AllthesequestionscanbeansweredbylookingattheresultspresentedinFigure6.18, whichincludesthebestperformingtechniquesinsparseanddensenetworksusingthe samesimulationparametersandscenariosoutlinedthusfar.Fromthegure,threegeneral conclusionscanbeeasilydrawn.First,consistentwithallresultspresentedsofar,itcan beseenthatregardlessofthenetworkdensity,thescopeofthetechniqueglobalorlocal, andtypeoftechniquestatic,dynamicorhybridtheenergy-basedtechniquesarethe bestperformingones.Second,theglobaltechniqueseitherstatic,dynamic,orhybrid performbetterwiththeA3topologyconstructionalgorithm.Finally,thelocalDSR-based techniquebasedontheCDS-Rule-Ktopologyconstructionalgorithmoutperformsthe globaltechniquesinbothsparseanddensenetworks.Therefore,theenergy-,DSR-and 178

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aBestofallinsparsenetworks. bBestofallindensenetworks. Figure6.18:Bestperformingtopologymaintenancetechniquesinsparseanddense networks. 179

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CDS-Rule-K-baseddynamiclocaltopologymaintenancetechniqueisthebestperforming techniqueinsparseanddensenetworks. Anotherimportantconclusionaboutthebehaviorofthesetechniquesisthatdynamic globaltechniquestendtoofferbetterperformancelongerthanstaticandhybridglobal techniques,butoncetheperformancestartstodecay,itdecreasesfaster.Theperformance ofstaticglobaltechniquesstartstodecaysoonerbutthedecreaseisnotassharp,beingabletolivelongerthandynamicglobaltechniquesoverlongerperiodsoftime.The hybridglobaltechniquesareagoodcompromise.Theyhavethesameperformanceas staticglobaltechniquesduringtheinitialcontinuoustimebuttheirperformanceover timeisconsiderablybetterthanstaticordynamicglobaltechniques,withasmoothernetworklifetimedecay.Finally,theDSR-andCDS-Rule-K-baseddynamiclocaltechnique presentstheworstperformanceatthebeginning,meaningthatnodesstarttodiefaster,but showsthebestperformanceofallovertime. Morespecicconclusionscanbedrawnlookingateachgureindividually.Forexample, fromFigure6.18a,itcanbeseenthat,again,topologymaintenancetechniquesinsparse networksdonotimprovethelifetimeofthenetworkbyanimportantmargincompared withthenotopologymaintenanceoption.Thisisdenitivelynotthecaseindensenetworks,asitcanbeseenfromFigure6.18b,wherethepositiveeffectofthetopology maintenancetechniquesoverthenetworklifetimeisappreciable. Inconclusion,dynamicglobaltechniquesarethebestoptionifacontinuousoperationof theentirenetworkisneededoveraspecicamountoftime,lessthanthetimeatwhich theystarttodiefast.Iftheapplication,ontheotherhand,requiresthenetworktobealive longerevenwithfewernodesandmaybewithsomeareasnotcompletelycovered,then thedynamiclocaltechniqueusingtheCDS-Rule-Ktopologyconstructionmechanism isthebestwaytogo.Agoodcompromiseinthisspectrumofpossibilitiesistheglobal 180

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hybridtechnique,whichprovidesbetterperformancethanthelocaltechniqueatthebeginningworkswithallthenodeslonger,andanintermediateperformanceovertime comparedwiththedynamicglobalandthelocaltechniques. Itisimportanttomentionthatthesegeneralandspecicconclusionsonlyrepresentone pictureoftheentirespectrumofpossiblescenarios.Alltheseconclusionshavebeen drawnfromthesimulationresultsofexperimentsrunwith50and100nodes,anenergy thresholdof10%,atimethresholdof1000timeunits,maximumof3reducedtopologies inthecaseofstatictechniques,theA3,CDS-Rule-K,andEECDStopologyconstruction algorithms,andthelocalDSR-basedtopologymaintenancemechanism.Inthenextsection,theseresultsareextendedbyrunningadditionalexperimentsvaryingtheenergyand timethresholds,andthenetworkdensity. 6.8SensitivityAnalysis Thusfar,allsimulationexperimentshavebeenperformedusing50or100nodestorepresentsparseanddensenetworkscenarios,respectively,andxedenergyandtimethresholds,of10%and1000timeunits,asdenedinTable6.1.Thissectionismeanttoprovidemoreinsightsabouttheperformanceofthetopologymaintenancetechniquesunder considerationwhentheseparametersarevaried.Inwhatfollows,simulationresultsare presentedwhenthetimethresholdisvariedfrom600to1000to5000to10000units;the energythresholdischangedfrom5%to10%to25%to50%oftheremainingenergyin thenode;andthenumberofnodesisvariedfrom50to100to400nodes.Experiments arerunusingstatic,dynamic,andhybridglobaltechniquesusingtheA3algorithmasthe onlytopologyconstructionalgorithm,andtheDSR-baseddynamiclocaltechniqueusing theCDS-Rule-Kalgorithmonly.Also,allexperimentsarerunindensenetworksonly. 181

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Thesedecisionsarebasedonthesuperiorperformanceoftheglobaltechniquesbased ontheA3algorithm,thesuperiorityofthelocaltechniquebasedontheCDS-Rule-K algorithm,andthefactthat,inmostcases,topologymaintenanceisworthapplyingin densenetworksonly. 6.8.1Time-basedAnalysis Figure6.19showsthenetworklifetimeresultsforthestatic,dynamic,andhybridglobal topologymaintenancetechniqueswithtimethresholdsof600,1000,5000,and10000 timeunitsusingtheA3topologyconstructionalgorithm.Thegureprovidesinsightson twofronts.First,itimmediatelytellsabouttheimpactofchangingthetimethresholdin thenetworklifetime.Asitcanbeobserved,inallcases,thenetworklifetimeseemstobe mostlyunaffectedbythetimethreshold.However,theguresclearlyshowtheeffectof thethresholdintheoperationofthenetwork.Forexample,theguresshowthebumpy behaviorofthetechniqueswhenthethresholdissetat10000units.Itisclearthatthe thresholdtimeisbigenoughastoallowmanynodestodiebeforeitexpires,andwhen itexpires,thenewtopologyisabletoincludemoreactivenodesthanthetopologyjust replaced.Ontheotherhand,thiseffectisnotseenwhenasmallthresholdisused,suchas inthecaseofthe600timeunitsthreshold. Second,thegureprovidesanoverallcomparisonbetweenstatic,dynamic,andhybrid globaltechniques.AsitcanbeobservedfromFigure6.20,acompromisebetweenperformanceandsmoothbehaviorisachievedwhenthetimethresholdissetto5000time units.Asitcanbeseen,thebestperformingtechniqueineachcaseistheoneusingthis thresholdof5000timeunits.Atthesametime,althoughthedynamictechniquestill presentssomebumps,itisconsiderablybetterthanthecasewith10000units.Ofthethree 182

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aStatictechnique. bDynamictechnique. cHybridtechnique. Figure6.19:Time-basedsensitivityanalysisofnetworklifetimeforstatic,dynamic,and hybridtopologymaintenancetechniques. 183

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Figure6.20:Bestperformingtechniquesoutoftimesensitivitytests. besttechniques,thegurealsoshowsthatthehybridtechniqueisthemostappropriate, presentingthesameperformanceoftheothertechniquesduringtheinitial15000time unitsbutdecayingslowerasthetimeincreases. Inconclusion,itcanbesaidthat,asexpected,increasingthetimeprovidesbetterperformance,asthetopologyconstructionmechanismneedstoberunfewertimes,butincreasingthetimethresholdtoomuchalsoproducesbumpybehavior.Therefore,agood compromiseistosetthethresholdtoavalueclosetothetimeatwhichthenodesare expectedtostartdying. 6.8.2Energy-basedAnalysis Inthispartsimilarsimulationresultsareprovidedbychangingtheenergythreshold. Figure6.21showsthenetworklifetimeresultsforthestatic,dynamic,andhybridglobal topologymaintenancetechniques,andtheDSR-baseddynamiclocaltopologymainte184

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aStatictechnique. bDynamictechnique. cHybridtechnique. dDSR-baseddynamiclocaltechnique. Figure6.21:Energy-basedsensitivityanalysisofnetworklifetimeforstatic,dynamic,and hybridtopologymaintenancetechniques. nancetechniquewithenergythresholdsof5%,10%,25%,and50%ofthenode'sremainingenergyusingtheA3topologyconstructionalgorithm.Thegureimmediatelyprovidesinsightsabouttheimpactofchangingtheenergythresholdinthenetworklifetime. Asitcanbeobserved,thereisageneraltrend:thenetworklifetimeimproveswiththe reductionoftheenergythreshold.Asmallerthresholdcorrespondstofewerrunsofthe topologyconstructionmechanism,savingmoreenergy. Figure6.22providesanoverallcomparisonbetweenthetechniques.Thegureclearly showsthatinthiscase,thehybridtechniqueisthebestofall,startingitsperformance 185

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Figure6.22:Bestperformingtechniquesoutofenergysensitivitytests. decayalmostatthesametimeastherestofthepolicies,butoutperformingthemallover time.Giventheresultsobtainedintheselasttwosections,itcanbeconcludedthathybrid techniquesarethebestoverall,astheygetthebestofthestaticanddynamictechniques theyaremadeof.Itisimportanttomentionthatthelocaltechniquedoesnotperformas wellastheglobalonesbecauseitisbasedontheA3topologyconstructionalgorithm.As showninFigure6.12c,theinclusionheretheperformanceofthelocaltechniquewith theCDS-Rule-Kalgorithmwouldhaveshownthatitisthebestperformingtechnique. 6.8.3Density-basedAnalysis Finally,experimentswerealsocarriedouttoassesstheperformanceofthestatic,dynamic,andhybridglobaltechniques,andthedynamicDSR-basedlocaltechniquein scenarioswithdifferentnodedensitiesusingtheA3topologyconstructionalgorithm. 186

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aStatictechnique. bDynamictechnique. cHybridtechnique. dDSR-baseddynamiclocaltechnique. Figure6.23:Nodedensity-basedsensitivityanalysisofnetworklifetimeforstatic, dynamic,andhybridtopologymaintenancetechniques. 187

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Figure6.23showsthenetworklifetimeresultsofthetechniquesunderconsideration with50,100,and400nodesusinganenergythresholdof10%andatimethresholdof 1000timeunits.Ageneral,andexpected,trendcanbeeasilyobservedfromthegure: thenetworklifetimeincreaseswiththenetworkdensity.Asmorenodesareaddedinto thenetwork,moredisjointtopologiescanbeformed,andthereforethetotallifetimecan beincreased.Also,morenodesincreasethenetworkwideenergyresources.Another observationconsistentwithpastresults,isthattheenergy-basedtechniquesoutperform theirtime-basedcounterparts.Finally,Figure6.21dshowstheperformanceoftheDSRbasedenergy-baseddynamiclocaltechnique,whichshowsmixedresultscomparedwith theglobaltechniqes,butdenitively,itshowsitsvalueinsomeinstances.Recalthatthis localtechniqueutilizestheA3algorithm,andbetterperformanceresultsareobtainedwith theCDS-Rule-Kalgorithm. AninterestingresultisshowninFigure6.23cwheretheeffectofcombiningstaticand dynamictechniquescanbeclearlyseen.Atthebeginningandduringtherst20000time units,thehybridtechniqueoperatesasthestaticone,asalltopologiesincludedintherotationlistcanactuallycommunicatewiththesinknode,withalltheirnodesparticipating inthetopology.However,after20000timeunits,nodesstarttodieandtheperformance ofthehybridtechniquestartstodecayfollowingtheslopeofthestatictechnique,asup tothispoint,thedynamicpartofthetechniquehasnotbeenactivatedforthersttime. Itisat40000timeunitswhenthedynamictechniquesstartworking,assometopologies inthestaticrotationlisthavenocommunicationwiththesinknodeanymore.Fromthis timeuntilapproximately150000timeunitsnotshownintheguretheperformanceof thehybridtechniqueisfairlystable.Afterthat,mostofthenodesdieandthedynamic techniquecannolongerndmoretopologies. 188

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Figure6.24:Bestperformingtechniquesoutofthedensitysensitivitytests. Comparingtheseresults,itcanbeconcludedthatincreasingthenetworkdensitycan increasethenetworklifetimeconsiderably.Also,amongthesetechniques,thedynamic energy-basedtechniqueoffersthebestperformanceoverallduringafairlylargeamount oftime,afterwhichthehybridtechniquetakesovermaintaininganstillveryacceptable performanceforalmosttwicetheoriginaltime.Figure6.24includesthebestperforming techniquesineachcase,wherethislastconclusioniseasilyobserved. Finally,onelastexperimentwasperformedinordertopresentthetotalbenetsthatapplyingatopologycontrolmechanismbringstothelifetimeofthenetwork.Threecases whereconsidered:whennotopologycontrolisappliednotopologyconstructionor maintenance,whenjusttopologyconstructionisappliedwithnomaintenancepolicy, andwhenacompletetopologycontrolschemeisapplied,includingtopologyconstruction andmaintenance.Figure6.25showsthecomparisonofthenetworklifetime,usingthe A3topologyconstructionprotocolandtheDGETRectopologymaintenanceprotocols, inscenarioswith400nodes.Thelifetimecomparisontookplaceintwomoments:rst, 189

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Figure6.25:Comparisonofnetworklifetimewhenusingtopologyconstructionand maintenance,topologyconstructiononlyandnotopologycontrol. whenthenumberofactivenodesofthereducedtopologiesreacheshalftheinitialsize nodes,and5activenodeswhenthenetworkisalmostdead.Intherstcase,when thenumberofactivenodesis15,theresultsshowshowthelifetimeofthenetworkis extendedin3200%whenusingbothtopologyconstructionandmaintenance,and450% whenusingonlyatopologyconstructionmechanism.Inthesecondcase,whenthenumberofactivenodesis5andthenetworkisalmostdead,theresultsshowsagainof1450% whenusingbothtopologyconstructionandmaintenance,and220%whenusingonly atopologyconstructionmechanism.Thesegainsshowthepoweroftopologycontrol techniquesinwirelesssensornetworksasatoolforextendingthelifetimeofthenetwork. 190

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Chapter7:ConclusionsandFutureWork 7.1Conclusions Topologycontrolisanareathathasseenanincreaseininterestduringthepastdecade, factthatisunmistakenlyshownbytheamountofpublishedpapersandbooksinthearea. Thenatureofthesolutionsprovidedinthisareastartedwiththeoreticalandcentralized approaches,whichwerebasedontraditionalgraphtheorytechniques,andthenevolved intothepresentstagewithalargeselectionoffullydistributedandsimpleprotocolsthat canrunefcientlyinconstraineddevices.Inaddition,thetrendhasgrownfromonlyofferingconnectivityinthenetwork,intoalsoguaranteeingcoverageoftheareaofinterest, withdifferentlevelsofredundancyand,inmanycases,withouttheneedoflocalization informationofthenodesinthenetwork. TheA3familyofsimpleconnectivity-andcoverage-orientedprotocolspresentedinthis dissertationareclearexamplesofthesesolutions.Thebenetsoftheapplicationofthese protocolswasseeninthedifferentperformanceevaluations.Forexample,theA3and A3LiteprotocolsshowedaconsiderableadvantageinmessageandenergyoverheadcomparedtotheothertwodistributedprotocolsEECDSandCDS-Rule-K,whileproducing verysimilarsizedreducedtopologies.Inaddition,theresultsofA3andA3Litewere comparedtothecentralizedMIP-MCDSformulation,anditcouldbeseenthattheaveragedifferencebetweentheoptimalresultsandtheonesproducedwiththeheuristics 191

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reachedupto37%insomescenarios.Oneinterestingaspectoftheresultsshowedisthat theheuristicswereveryclosetotheoptimalsolutionintopologieswithasmallnumber ofnodes,orwhenthenodedegreewasveryhigh.InthecaseofA3CovandA3CovLite, theyofferedbettercoverageratiothantheACOSprotocolandsimilarcoveragetothe StanGAprotocol;however,A3CovandA3CovLiteguaranteeconnectivity. Thebenetsoftopologycontrolareveryclearthroughoutthisdissertationandallthereferencedworkintheliterature.Awirelesssensornetworkcannotaffordnothavingsome kindoftopologycontrolinordertoguaranteetheefcientuseofitsresourcesduringthe timeofactivity.Thiscanbeconcludedfromtheperformanceevaluationofthedifferent topologymaintenanceprotocols.Thedifference,intermsoflifetimeofthenetworksthat didnothaveanymaintenanceprotocolsagainsttheonesthatdid,showstheundeniable benetofhavingamaintenancestrategyinthenetwork. Onetopicthatisexpectedtoreachtheinterestoftheresearchcommunityistheseparationoftheconceptoftopologymaintenancefromthetopologyconstructionprocess, whichsimpliestheanalysis,developmentandimplementationofnewtopologymaintenanceprotocols,andalsotheirpairingwithexistingandnewtopologyconstructionprotocolsinordertondabetterperformance.Theimportanceofthisfactcanbeseeninhow thedifferentmaintenanceapproachesproducedindividualresultsnotonlybasedonthe natureoftheprotocolsbutalsobasedontheparticularpairingoftopologyconstruction andmaintenancethatwereevaluated. Thenewconceptofinterdependenceintopologycontrolmustalsobeacknowledgeby simulationtools,whicharealwaystherststepintheimplementationandtestingprocess ofnewprotocols.ThischaracteristicisoneofthemaincontributionsthatthenewsimulationtoolAtarrayaintroducestothemarketofsimulatorsfortopologycontrolinwireless sensornetworks. 192

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7.2SummaryofContributions Thisdissertationpresentsnewcontributionsintheareaoftopologycontrolforwireless sensornetworks.Thisisasummaryofthedocumentandthecontributions. AnewdenitionofTopologyControlisproposed,basedontheseparationofthe TCprocessintotwoinstances:topologyconstructionandtopologymaintenance. Basedonthisdenition,anewtaxonomyisproposedinordertoclassifytheexistingprotocols.Aspecialdistinctionismadebetweenconnectivity-andcoverageorientedtopologyconstructionprotocolsinthetaxonomy,giventheparticularities oftheprotocolsineachofthesecategories. AnewmathematicalformulationoftheMinimalConnectedDominatingSet,based ontheMixedIntegerProgrammingapproach,thatsolvesinaparallelapproach totheproblemsofdominanceandconnectivityusingamodicationofthemulticommodityapproachcalled"`owoftokens"'.Somecharacteristicsofthissolution arethatitusesalinearnumberofrestrictions,thatitrunsinasingleiterationand thatitdoesnotneedpreprocessing. Twonewconnectivity-orientedtopologyconstructionprotocolsareproposed,based onthehierarchicalapproach:A3andA3Lite.Theseprotocolsgrowatreerooted atthesinknode,createaCDSthatconnectsallthenodesinthenetwork,andthen turnsoffallredundantnodesthatdonotofferconnectivitytoanyoftheirneighbors. Thesimplicityoftheprotocolsisoneofthemainreasonswhytheseprotocolsexcel intheperformanceevaluationcomparedtootherwell-knownprotocolsoftheir samecategory,especiallyintermsofenergyconsumptionandmessageoverhead. 193

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Twonewcoverage-orientedtopologyconstructionprotocolsareproposed,basedon theA3andA3Liteprotocols:A3CovandA3CovLite.Theseprotocolsstartfrom theconnectedreducedtopologyproducedbyitspredecessors,andthenextendthem byaddingnodesthatincreasetheareacoveredbytheactivenetwork.Inaddition, theyimplementasimplepolicythatdeterminesvariablelevelsofcoverage,asa tradeoffparameterbetweencoverageandnumberofactivenodes.The Cov protocolsarecomparedwiththeoreticaloptimalsolutions,andwithtwodistributed protocols,inwhichthe Cov protocolsshowsuperiorityincoverageandconnectivity. Fourtopologymaintenanceprotocolsareimplemented:SGTRot,DGTRec, HGTRecRotandLD-DRS,withthelasttwobeingcompletelynewprotocols.Their performanceistestedinordertoevaluatethejointexecutionoftopologyconstructionandmaintenanceascompleteintegratedtopologycontrolsolutions.Theresults showthatingeneraltheDGTRecprotocoltendstoprovideabetterperformance, maintainingthehighestpossiblenumberofactivenodesuntiltheresourcesare completelydepleted,andthattheHGTRecRotandLD-DSRproducegoodresults dependingonthetopologyconstructionprotocol. AnewsimulationtoolcalledAtarrayahasbeendevelopedfortesting,implementingandteachingtopologycontrolprotocolsinwirelesssensornetworks.Thisisthe rstsimulationtoolthatworksbasedonthedivideddenitionoftopologycontrol. TheappendixofthisdissertationisdedicatedtothedetaileddescriptionofAtarraya,includingthesimulator'sinternalstructure,howtheprotocolsweredesigns andalistoftheconsiderationsforaneffectiveuseofthetool.ThecodeofAtarraya 194

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isavailabletothepublicunderGPLlicensingat http://www.cse.usf.edu/ ~labrador/Atarraya 7.3FutureWork Asexpected,thisdissertationcannotcoverallpossibleinsightsfromalltheareaspresented.Someoftheareasinwhichtherecouldbesomeextensionarethefollowing: AmoredetailedanalysisofthemixedintegerprogrammingsolutionfortheminimumconnecteddominatingsetMCDSproblemisrequiredtominimizeasmuch aspossiblethesizeoftheproblemdenitionandtheexecutiontime.Inaddition,an extensionofthisprobleminordertoconsidercoveragewouldbeverybenecialto theareaofcoverage-orientedtopologyconstruction. ThetestingofthefamilyofA3-basedprotocolsundermorerealisticscenariosthat mayconsiderdifferentcommunication,sensingandenergymodels,heterogeneous andmobilenetworks,anddifferentMACandroutingprotocols.Inaddition,amore detailedanalysisoftheimpactoftheweightsintheselectionmetriccouldprovide moreinsightonhowtocalculatethoseweightsinordertoextendthelifetimeofthe networkevenmore. Thisdissertationonlyconsiderstopologymaintenanceprotocolsthatuseenergyor timeastriggeringcriteria.Theconsiderationofothertriggersandtheirperformance evaluationagainstthecurrentonesispartofalogicalsequencethatwillenrichthis areaofresearch. ThesimulationtoolAtarrayaisstillaprojectunderdevelopment.Fromtheimplementationofmoretopologyconstructionandmaintenanceprotocols,alongwith 195

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sensor-datamanagementandroutingschemes,tothesimulationofenvironmental eventstoevaluatetherealperformanceandaccuracyoftheprotocolstested;these areascouldbeinvestigatedwithrespectiveextensionsinAtarraya.Inaddition,a moreefcientstructuretoallowfastersimulationsisalsooneofthemediumterm goalsafterthisdissertation. 196

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[80]V.FodorandI.Glaropoulos,Onthegainsofdeterministicplacementand coordinatedactivationinsensornetworks,in ProceedingsofIEEEGlobecom 2008,pp.1. [81]B.Wang,K.Chua,andV.Srinivasan,Connectedsensorcoverforareainformation coverageinwirelesssensornetworks, InternationalJournalofCommunication Systems ,vol.21,no.11,pp.1181,2008. [82]K.Yildirim,T.Kalaycir,andA.U gur,Optimizingcoverageinak-coveredand connectedsensornetworkusinggeneticalgorithms,in Proceedingsofthe9th WSEASInternationalConferenceonEvolutionaryComputing ,2008,pp.21. [83]A.Konstantinidis,K.Yang,andQ.Zhang,Anevolutionaryalgorithmtoamultiobjectivedeploymentandpowerassignmentprobleminwirelesssensornetworks, in ProceedingsofIEEEGLOBECOM ,2008,pp.1. [84]F.Ye,G.Zhong,J.Cheng,L.Songwu,andL.Zhang,Peas:Arobustenergy conservingprotocolforlong-livedsensornetworks,in Proceedingsofthe23rd InternationalConferenceonDistributedComputingSystems ,2003,pp.28. [85]Y.Cai,M.Li,W.Shu,andM.Wu,Acos:Anarea-basedcollaborativesleeping protocolforwirelesssensornetworks, AdHoc&SensorWirelessNetworks ,vol.3, no.1,pp.77,2007. [86]S.Zhang,Y.Liu,J.Pu,X.Zeng,andZ.Xiong,Anenhancedcoveragecontrol protocolforwirelesssensornetworks, ProceedingsoftheHawaiiInternational ConferenceonSystemSciences ,pp.1,2009. [87]M.Wueng,S.Hwang,andC.Ho,Akce:Anefcientandaccuratek-coverage eligibilityalgorithminwirelesssensornetworks,in ProceedingsoftheIEEE InternationalSymposiumonModeling,AnalysisandSimulationofComputersand TelecommunicationSystems ,2008,pp.1. [88]H.Bai,X.Chen,B.Li,andD.Han,Alocation-freealgorithmofenergy-efcient connectedcoverageforhighdensitywirelesssensornetworks, DiscreteEvent DynamicSystems ,vol.17,no.1,pp.1,2007. 206

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Appendices 210

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AppendixA:ABriefOverviewofAtarraya Introduction ThemainideabehindthecreationofAtarraya-whichmeans shnet inSpanish-was totestthetopologyconstructionprotocolnamedA3thatwasbeingdevelopedaspart ofthisresearch.Thesoftware,asoriginallyconceptualized,wasverysimple,rigidand tightlycoupledwiththeA3protocol.However,duetothefactthatitwasnecessaryto comparetheperformanceofA3againstotherknowntopologyconstructionmechanisms, thedesignofthetoolwasnotadequate.Therefore,thedecisiontobuildamoregeneric simulator,inwhichothertopologyconstructionalgorithmscouldbepluggedin,andhave asingleplatformwheretoevaluatethemallunderthesameconditions,wasnecessary. Then,theconceptoftopologycontrolwasalsoexpandedtoincludetopologymaintenancealgorithms,andseveralofthesemechanismsweredesignedandincludedaswell. ThenalresultisAtarraya:ageneric,Java-based,event-drivensimulatorfortopology controlalgorithmsinwirelesssensornetworks.Aswithanysimulationtoolbornoutof aresearcheffort,Atarrayaisstillindevelopment;however,initscurrentstate,itisan excellenttoolnotonlyforresearch,todevelopandtestnewtopologycontrolalgorithms, butalsoforteaching.Atarraya'sgraphicaluserinterfaceshowshowtopologycontrolprotocolswork,andhowtheyshapetopologiesduringtheirexecution.Inaddition,Atarraya includesnecessarymechanismstoexperimentwithclassictheoreticalresultsrelatedto topologycontrolinwirelesssensornetworks,suchasthegiantcomponentexperiment, calculationofthecriticaltransmissionrangeCTR,calculationoftheMinimumSpanningTreeofagraph,andothers. InthisappendixthebasicsofAtarrayaarepresentedalongwithitsinternalstructure,so thereaderknowshowtodevelopandpluginnewtopologycontrolalgorithmsandproto211

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AppendixA:continued cols,andabriefguideonhowtousethetool.Allexplanationsanddescriptionsincluded inthisdocumentarerelatedtoAtarraya'sversion1.0,whichistheversionthatwasused torunalltheexperimentsincludedinthebook.Futureversionsandnewfeatureswillbe documentedontheproject'sWebsiteathttp://www.csee.usf.edu/labrador/Atarraya. DescriptionofAtarraya'sInternalStructure InthissectiontheinternalstructureofAtarrayaisdescribed.First,itsmainfunctional componentsandAtarraya'sclasstreearepresented.Then,thestructureoftheprotocolsis describedinmoredetail,includinghowtheycommunicatewiththemainclassandwith otherprotocols,howtoinitializethenodes,andhowtohandleprotocolevents. AbstractDesignandFunctionalComponents Thissectiondescribesthemainfunctionalcomponentsofthesimulatorandhowthey interactamongthemselves.Thefunctionalcomponentsofferthebigpicturenecessary tounderstandthecriticalcomponentsofAtarraya.FigureA.1presentsaglobalviewof theinternalstructureofthesimulator,whichconsistsofthemainsimulatorthread,the nodehandler,andthebatchexecutor.Theelementsofthisstructurearedescribedinthis section. 212

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AppendixA:continued FigureA.1:Atarraya'sfunctionalcomponents. 213

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AppendixA:continued TheMainSimulatorThread-The the_sim Class Thisisthecoreofthesystem.Thesimulatorthread,denedintheclass the_sim ,isin chargeoffetchingthenexteventfromthesimulationeventqueue,andsendingtheevent tothenodehandlerforexecution.AninstanceofthisclassiscreatedbythemethodStartSimulationwheneverasimulationisexecuted.Thisclasscontainstheeventqueue,the simulationclock,thedisplaymanager,thedatabasewiththedataaboutthenodes,andthe simulationagent,whichisinchargeofstoringthesimulationresultsforthereportsinthe respectivelogs. Whenaninstanceofthe the_sim classiscreated,itisnecessarytoaddtheinitialevents tothequeuebeforethethreadisstarted.Therstthingthethreadwilldooncestartedis tocheckifthereareanyeventsintheEventQueue.Ifthethreadisstartedwithoutany events,itwillconsiderthatanerrorhasoccurred,andthesimulationwillbesuspended. Oncethersteventshavebeenloadedintothequeue,thesimulatorthreadcangetstarted. Thethreadstartsaloopthatwillexecuteuntiloneofthethreeterminationconditions istrue:therearenoeventsinthequeue,allthenodeshavereachedthenalstateinthe topologycontrolprotocol,ortheprotocolshavecalledfortheendofthesimulationfor example,thetopologymaintenanceprotocolhasfoundthatthesinkhasnomoreneighbors,sothenetworkisdead.Iftherstconditionoccursandthesimulatorhasnotbeen notiedthattheprotocolsnishedexecution,itmeansthattherewasanerrorduringthe simulation,anditwillbenotiedonthesimulationreport. Intheloop,therstthingthethreaddoesistoverifyiftheeventisvalid.Ifso,theevent willberegisteredifthisoptionwasselectedbytheuser,thesimulationclockwillbe 214

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AppendixA:continued updated,andtheeventwillbesenttothe NodeHandler .There,theeventwillbedelivered totheappropriate EventHandler accordingtotherespectiveprotocoltheeventbelongs to.Oncetheeventisexecuted,thesimulatorwillgobacktotheloopandstartagainthe process.Thesimulatorupdatestheclockwiththeexecutiontimeoftheeventsbasedon thefactthatalltheeventsinthequeuearesortedbytheirprojectedexecutiontime,so thereisnosuchthinglikeatriptothepast. Oncethesimulatorbreakstheloopbyanyofthenalizationconditionsmentionedabove, thethreadgoestothereportconstructionsection,savingalltheeventsandstatistics,as selectedbytheuser.Thissectionalsotakesintoaccountwhetherornotthesimulationis partofabatchexecution,inwhichcaseallthedatafromallpreviousexecutionsiskept untilthelastonenishes.Allthisinformationisstoredindatastructuresthatarestored inthereportlesafterthesimulationisnished.Readingthissectionofthecodewill providetheuserwithinformationaboutalltheoptionsforeachcongurationofreport inbothsingleandbatchsimulationcases.Oncethesimulationandthereportbuilding sectionnish,thethreadendstoo. Inthecurrentversionofthesimulator,justonesimulatorthreadcanrunatatimebecausethereisonlyonedatastructuretostorethetopology,whichislocalizedinthe atarraya_frame class.Individualinstancesofthedatastructurerunningseveralsimulations inparallelwillconsumealltheresourcesoftheJavavirtualmachine,especiallyifthe networktopologiesarebig. 215

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AppendixA:continued TheProtocolManager-The NodeHandler Class Thisclassisinchargeofdeningtheprotocolstobeusedinthesimulationandrouting theeventtotheappropriateprotocoloncereceivedfromthesimulationthread.The NodeHandler classdenesthefourpossibleprotocolsthatanodecanhaverunningduringa simulation:Topologyconstruction,topologymaintenance,sensor-datamanagement,and communication-routingprotocols.Giventhattherearedifferentalgorithmsforeachtype ofprotocol,themainpurposeofthisclassistomakethatselectiontransparenttotherest ofthesimulator,sothatnodetailabouttheselectionisrequiredinordertoexecutethe simulation.Whenasimulationisstarted,thisclasscreatestheinstancesoftheselected protocolsineachofthefourdifferentcategories.Thesimulationthreadsendsthenext eventfromtheeventqueuetothe NodeHandler class.Oncetheeventisreceived,itis routedtotheappropriateprotocolbasedontheprotocolidentierincludedintheevent. TheMultipleOperationThread-The BatchExecutor Class ThemainpurposeoftheBatchExecutorthreadistoperformoperationsthatrequiremultipleexecutions,suchascreatingasetoftopologies,performingalargenumberofsimulations,andtheGiantComponenttest.Sincetheseoperationsarerunonathreadindependentfromthemainone,thegraphicaluserinterfacedoesnotfreezewhilethese operationsarebeingexecuted,whichallowsfortheinteractionbetweentheuserandthe simulatorevenwhilesomeoftheseoperationsarerunninginthebackground.Thisclass isinstantiatedwheneveroneofthementionedoperationsisstarted. 216

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AppendixA:continued TheDisplayManager-The newpanel Class Thedisplaymanager,or newpanel class,istheoneinchargeofthegraphicalrepresentationofthetopologies.TheheartofthisclassistheoverrideofthePaintmethodofthis classthatextendsaPanelclass.Allthepaintingoptionsforthetopologyaredenedin thismethod.Theothermethodsperformminorbutnecessaryactionslikeobtaininginformationabouttheoptions,providingcoordinatesfromthedeploymentarea,etc.Thisclass wasdenedasaprivateclassofthe atarraya_frame classsoitcanhavedirectaccessto thetopologydatastructure. Atarrayaprovidesseveraloptionsfortopologyvisualization,whichcanbeseeninmore detailinthevisualizationoptionsinFigureA.12.Themostrelevantvisualizationoptions arethefollowing: MaxPowerTopology:Thisistheoriginalviewofthetopologywithallnodestransmittingatfullpower,andallthelinksthattheirunitdisksprovide. Singleselectednetworkcongurationortree:Inthisviewtheuserdeneswhich oftheVirtualNetworkInfrastructuresVNIheorshewantstosee.MoreonVNI laterinSectionA.ThedefaultcongurationisBlackinmostprotocols. Allnetworkcongurations:Ifseveralcongurationsaredenedinacertaintopology,thisviewallowstheusertoseeallofthemandappreciatethedifferencesbetweenthem. 217

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AppendixA:continued Activenetworkconguration:Eachnodeisassumedtobeabletomaintainseveral VNIs,butuseonlyoneatatime.Thisviewallowstheusertoseeinreal-timein whichnetworkcongurationsthenodesofthetopologyare. Atarraya'sClassTree InthissectiontheclasstreeofAtarrayaisdescribedandabriefexplanationofthestructureandmissionofthecurrentinternalstructureoftheapplicationisprovided.TheclassesinAtarrayaareorganizedinthreepackages: Atarraya :themainfunctionalelementsarestoredhere,suchasthemainframe,the simulationagent,andthedisplaymanager. Atarraya.element :Thispackagecontainstheclassesthatmodelthedatastructures, likethenode,VNI,routingtable,etc. Atarraya.event :Thispackagecontainstheclassesrelatedtotheprotocolsandthe denitionoftheeventqueue. The Atarraya Package The Atarraya packageisisthemainpackageofthesimulator.Itcontainsthefollowing classes: Main class:Thisisthelauncherofthesimulator.Itinvokesthetitleframeandthe mainframe. 218

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AppendixA:continued atarraya_frame class:Thisisthemainclassofthesimulator.Thisclasscontains thegraphicaluserinterfaceandthesimulatorcore. newpanel privateclass:Thisclassdenestheoperationrelatedtothevisualization panelforthetopologies:painting,selectionofcoordinates,selectionofnodes,grid, etc.Itisaprivateclassofthe atarraya_frame classsothe newpanel classhasdirect accesstothedatastructures. the_sim privateclass:Thisclassdenesthestructureofthethreadthatsimulatesa scenario;inotherwords,thisclassisthesimulationexecutor.Itwasmadeprivate alsotopreservethedirectaccesstothedatastructures. BatchExecutor class:Thisclassisinchargeofexecutingoperationsthatinvolve multiplescenarios,beingthatcreatemultipletopologies,orsimulatemultiplescenarios.Theadvantageofusingaseparateclassisthatitcreatesadifferentthread thatfreezesthemainframewhileexecuting. constants interface:Thisinterfacedenesthestandardvaluesformultiplevariables. Giventhatmanyclassesmustshareasetofstandardvalues,theuseofthe constant interfaceallowsthiswithouthavingtodeneidenticalvariablesoneachclass. FrameLogo class:Initialframewiththelogoofthesimulator. AboutFrame class:FramethatcontainstheAboutusmessage. 219

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AppendixA:continued The Atarraya.element Package Thispackagecontainstheclassesthatdenetheelementsthatwillbeusedinthesimulatorforstoringinformation.Theseclassesare: node class:Thisclassrepresentsalltheinformationaboutasinglenodeandallthe operationsthatcanbeperformedonit. register class:Thisclasscontainstheinformationthatthesimulatorhasaboutthe neighborsofanode.Thereisadifferencebetweentheinformationthatthenode hasaboutitsneighborsandtheinformationthatthesimulatorhasaboutthem.For example,thesimulatorneedstoknowtheexactpositionofeachnode,but maybethenodedoesnothavetheabilitytoknowthepositionofitsneighbors. candidate class:Thisclasscontainstheinformationthatthenodehasaboutitsown neighbors.Thisclasshastwodatastructures:candidatelistandchildrenlist.Both aregeneralusedatastructuresonthenode. NodeNetworkConf class:BasedontheassumptionthateachnodemayhavedifferentVNI,thisclassrepresentseverythingthenodeneedstoknowfromitscurrent network:listofneighbors,listofgateways,sink'saddress,routingtable,etc.A nodecanhaveasmanydifferentVNIasdesired.Bydefault,themaximumnumber ofVNIis5andeverynodeisintheVNI0andwillremainthereuntilsomething elseisdened. 220

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AppendixA:continued NodeSensingConf class:Thisclassissimilartothe NodeNetworkConf class,but appliedtothesensingdevice.Eachnodemayhaveseveralsensingdevicesordifferentcongurations.Thisclasshasnotbeenfullyimplemented. routing_table class:Thisclassdenesthedatastructureandmethodsoftherouting tableofaVNIofanode.Themainstructureisavectorof routing_table_register elements.Examplesoffunctionalitiesofthisclassareobtainingtheappropriate gatewaynodeforsendingapacketthroughthebestroute,addingroutes,storing messagesequencenumbers,etc. routing_table_register class:Thisclassdenestheformatofaregisteroftheroutingtable.Itincludestheaddressofthedestinationnode,theIDofthenexthopand routingmetric,andthevectorforstoringthehistoryofmessagesequencenumbers, whichareimportantforroutingalgorithms. TMStructConfList class:Sometopologymaintenanceprotocolsrequireagreat amountofinformation,especiallythosethatcanrunseveralprocessesinparallel. Thisclassmodelsadatastructurethatimplementsalistoftheindependent TMConfStructure instancesthatanodeishandlingatacertainmomentintime.TheconceptissimilartotheoneoftheVNI,butjustappliestothetopologymaintenance protocol. TMConfStructure class:Thisclassdenestheinformationthatanodehasabouta singletopologymaintenanceprocess,suchastheidentier,thenode'sstateonthe topologymaintenanceprocess,andaroutingtablethatcouldbeusedwhenspecic pathsmustberestored. 221

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AppendixA:continued pair class:Aclassthatdenesapairofintegervalues. trio class:Aclassthatdenesasetofthreeintegervalues. edge class:Aclassthatdenesanedgesource,destination,andweight.Thisclass isusedtocalculatetheMSTofagraph. The Atarraya.event Package Thispackagecontainstheclassesthatdenethestructureoftheevents,theeventqueue, andtheeventhandlersthatwillexecutetheeventsaccordingly.Themainclassesare: event_sim class:Thisclassdenestheinformationofanevent:source,destination, typeofevent,embeddedinformation,conguration,layerthatgeneratedtheevent, etc.Thisclasscontainsalltheinformationthattheeventhandlerrequirestoexecute theeventproperly. eventQueue class:ThisclassdenesthequeueofeventsthatAtarrayausesduring theexecutionofasimulation.Eventsareaddedtothequeueinanorganizedway, basedontheprojectedexecutiontimeoftheevent,sotheeventontheheadofthe queueisalwaystheclosesttothepresenttime. EventHandlerxxx class:Thisisafamilyofclassesthatdenetheprotocols.Each classhastodenesomeinitializationoperationsforthenodes,howtheeventswill affectthestateofthenodes,thedatastructures,othereventsthatgettriggeredas aconsequenceoftheoccurrenceofoneevent,etc.Aclassofthistypeneedstobe designedifanewtopologycontrolalgorithmistobeincludedinthesimulator,or 222

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AppendixA:continued ifanexistingalgorithmistobemodied.Initscurrentversion,Atarrayasupports fourtypesofprotocols:TopologyConstruction,TopologyMaintenance,SensorDataManagement,andCommunication-routingprotocols.Thewaytheseprotocols communicateisbygeneratingeventsofeachother'stype. NodeHandler class:Thisclassdenesadatastructurethatholdstheselectedoptionsforthefourtypesofprotocols.AnynewprotocoladdedtoAtarrayamustbe includedintheexistinglistthatthisclasscontains. ProtocolStructureandDesign-The EventHandler Class ThissectionintroducesthedesignandstructureoftheprotocolsinAtarraya.TheEventHandlerclassistheonethatmodelsthestructureofaprotocolinAtarraya.ThenextsubsectionsdescribethetypesofeventsthataprotocolinAtarrayacanmodel,howstatesare labeled,howeachprotocolcommunicateswiththe atarraya_frame class,howprotocols interactwitheachother,hownodesareinitialized,andhowthesimulatorhandlesevents. SimulationEvents GiventhatAtarrayaisanevent-drivensimulator,everythingthathappensduringasimulationisanevent,soprotocolsmustbedenedintermsofcause-effectwhencertainevent occurs.Eachofthesetypesofeventstriggerssomeinternalactionsinthenodethatmight modifyitsstatus,datastructures,etc.,andcouldalsocausethegenerationofnewevents inthefuture.Themostcommonexamplesofeventsinaprotocolare: 223

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AppendixA:continued SendingMessages Whenanodeintendstosendamessage,itmaybeaddressedtoaspecicnodeunicast oritmaybeintentedforeveryneighborwithinrangebroadcast.Regardless,themethod thatanodeneedstocalloninordertosendamessageisbroadcast.Theparametersare thetimeatwhichthepacketisreceived,thecurrenttime,theidofthesendernode,the idofthereceivernodeifitisaunicastmessage,thetypeofmessage,thepayload,and theVNIcorrespondingtothispackage.Ingeneral,amessageofthiskindisassumedto beofthesametypeasthatoftheprotocolthatcontainsit,whichexplainswhythereisno specicationoftheprotocol'stype.Moredatacanbeincludedinthismessage,likethe rstsenderofthemessageorsource,andthenaldestinationofthepacket,incaseitisa messagethatwilltravelthroughmultiplehops. broadcasttemp_clock+getRandomMAX_TX_DELAY_RANDOM,temp_clock, sender,-1,HELLO,temp_data,temp_vni; Themethodbroadcastisinchargeofgeneratingthereceptioneventsintheneighbors withincommunicationrangeofthesendernode,iftherecipientsandthesendernodeare active.Themethodbroadcastisdenedonthe atarraya_frame class. ReceivingMessages Whenanodereceivesamessage,itcallstheeventdeterminedbythetypeofmessage. Ifthemessageissupposedtobeaunicasttransmission,thenodeveriesiftheidofthe destinationnodematchesitsown.Ifthatisthecaseitcontinueswiththeexecutionofthe 224

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AppendixA:continued algorithm.Ifthereceiverandthedestinationdonotmatch,thenodeignoresthepacket. Now,ifthemessagewasdesignedtobeabroadcasttransmissionorthenodeneedsto snoopinthepacketsnotaddressedtoitself,itcanignorethereceiverdestinationvericationandjustcontinuewiththeexecutionoftheprotocol. caseHELLO: ifreceiver==destination||destination==-1{ ...//Ifthemessagewasaunicastandthereceiverwasthe destinationorthepacketwasabroadcast }else{ ...//Ifthepacketwasaddressedtoanothernodeandthis issnooping } break; ProgrammingaTimeout Sometimesanodeneedstowaitsometimeinordertoperformacertainaction.Thedefinitionofatimeriscrucialforthistypeofoperation.AtimerinAtarrayaisaneventthat anodeprogramsaddressedtoitselfinthefuture.Theparametersareverysimilartothe onesprovidedtothe broadcast method,withthedifferencethatheretheparametersof anewevent,thatwillbeincludeddirectlyinthesimulationqueue,arealsospecied. Sincethisisareectiveevent,thesenderandthereceiverhavethesamevalue.Also,in thedeclarationitisnecessarytospecifythetargetprotocolofthiseventinthevariable type.Intheexample,thenodesenderisprogrammingitselfaneventofthetype PARENT_RECOG_TIME_OUT ,thatwillbeexecutedin TIMEOUT_DELAY timeunits. 225

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AppendixA:continued pushEventnewevent_simtemp_clock+TIMEOUT_DELAY,temp_clock, sender,sender,PARENT_RECOG_TIME_OUT,"",temp_vni,type; InvalidatingaProgrammedEvent Anodeprogramseventsinthefuturewithoutknowingwhatwillreallyhappenbetween thecurrenttimeandthefutureevent.Forexample,anodecanbeprogrammedtosenda messageinthefuture,butforsomereasonitmayalsobeputtosleepbeforeitcansend themessage.Sincethatparticulareventwillnotoccur,ithastobetakenoutfromthe simulationqueue,wheretheyarewaitingtobeexecuted.Atarrayaprovidesthemethods InvalidateAllEvents inordertoguaranteethatanodecancanceleventsthatshouldnot happen.Intheexample,thesendernodeeliminatesalltheeventsofthecurrentprotocol, referenttotheVNI temp_tree fromthecurrenttimeforward. InvalidateAllEventsFromIDFromTimeTOfTypeTysender, temp_clock,type,temp_vni; StateLabels Ingeneral,agoodnumberoftopologyconstructionprotocolsusenodestatestorepresenttheevolutionoftheprotocol.InAtarraya,nodescanbeinanyofthefollowingfour states:Initial,Active,Inactive,andSleepingstates.Thedenitionsofthesefourstates areincludedinthe Node_Handler class.Thevaluesdenedastheparametersareusually denedinthe constants interface,andtheyareallpositiveintegervalues. tc_protocol_handler.setLabelsS_INITIAL_STATE,S_ACTIVE, 226

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AppendixA:continued S_SLEEP,S_SLEEP; GiventhatmosttopologycontrolprotocolsimplementedinAtarrayaarecompletelydistributed,thesinkcannotcalltheendoftheprotocolbecauseithasnoinformationabout thestateofallthenodes.ThatisthereasonwhyAtarrayaknowsthataprotocolhasnishedwhenallthenodeshavereachedthenalstate.Eachtopologycontrolprotocol candenewhichstatesareselectedasthenalstates.Thisisdoneinthemethod CheckIfDesiredFinalStateints thatisdenedinevery EventHadler ,whichisinvokedinthe atarraya_frame classwhenthesimulationagentistryingtoverifyifthetopologycontrol algorithmisnished.Inthefollowingexample,theprotocolisselectingtheactiveandthe inactivestatesasthenalstatesofthenodes. publicbooleanCheckIfDesiredFinalStateints{ ifs==active||s==inactive returntrue; returnfalse;} Atarrayastopswheneverthenodesofthetopologyareinanyoftheselectedstates,no matteriftherearestilleventsinthequeue. Communicationwiththe atarraya_frame Class EachprotocolreceivesareferencetotheinstanceofAtarraya'smainframe,asdenedin the NodeHandler .Thisreferenceallowstheprotocoltohaveaccesstovariablesfromthe mainclass.Inordertoaccessthevariablesfromthesimulator,theprotocolneedstouse themethod father.getVariableintcode ,wheretheparameter code isadenedlabelfor 227

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AppendixA:continued thesetsofvariablesthatcanbeaccessed.Thislistcanbefoundinthe constants interface, andinthe atarraya_frame classwherethe getVariable methodisdened.Forexample, iftheuserwantstoknowhowmanynodesareinthetopologyincludingthesinknodes, thefollowinglinereturnsthisvalue: tam=intfather.getVariableNUMPOINTS Whentheprotocolneedstogetinformationaboutanodeormodifyit,themethodtouse is getNodeintid ,where id istheuniqueidofthenode.Inordertosetnode i intheinitial stateoftheprotocolintheVNI_vniID,thefollowinglinecanbeused: getNodei.setStateinitial,_vniID InteractionwithOtherProtocols Therewillalwaysbesomelevelofcommunicationbetweenprotocols.Forexample, inter-protocolcommunicationisneededtoavoidsituationslikeonenodewantingtosend adatamessagewithouthavingaroutetothesink.GiventhatinAtarrayaeveryeventin thesimulationgoestothesamequeue,itisnecessarytodeterminetowhichprotocolit mustsendtheeventto.Eachtypeofprotocolhasitsownidentierlabel,whichisincludedintheeventdenition.Thisallowsthe Node_Handler tosendtheeventtothe appropriateprotocol. OneofthepremisesofAtarrayaistocreatemodularprotocolsthatcanbeusedinas manycombinationsaspossiblewiththeotherprotocols.Accordingly,protocolsinAtarrayacanonlygenerateeventsinotherprotocols.Forexample,onceanodereachesthe nalstateofitstopologyconstructionalgorithm,itcannotifythetopologymaintenance 228

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AppendixA:continued protocoltostartthemaintenanceprocedure.Mostofthetimestheseinter-protocolevents aremeanttoinitiateorstopcertainactivity,sotheprotocolandhowitworksinternally arecompletelyindependent,buttheotherprotocolscandecidethestartingpoints.The followingexampleillustratesatopologyconstructionprotocolwhenitinvokesthetopologymaintenanceprotocol. pushEventnewevent_simtemp_clock+DELTA_TIME,temp_clock, receiver,receiver,INIT_EVENT,"",temp_tree,TM_PROTOCOL; InitializationofNodesandtheInitialEvents-The init_nodes andthe initial_event Methods The init_nodesintvni methodisusedtosetthenodesreadytostarttheexecutionof thesimulation.Nodesaresettotheirinitialstates,andanypreviouslydenedevents regardingotherprotocolsandallnecessaryvariablesaresettotheirdefaultvalues.This methodisinvokedinthe StartSimulation methodinthe atarraya_frame class,forall nodes,includingthesink.Thefollowingcodeisanexampleofa init_nodes routine,in whicheverynodeissettoitsinitialstate,everystatelabelisdened,anyexistentprogrammedeventinthequeueiscancelled,andtheexecutionofthetopologymaintenance andsensoranddatamanagementprotocolsarereset. publicvoidinit_nodesint_vniID{ tam=intfather.getVariableNUMPOINTS; _clock=father.getVariableCLOCK; temp=0; 229

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AppendixA:continued fori=0;i
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AppendixA:continued topology,makesurethateventsareincludedinthequeueusingthe init_nodes_vniID method. The HandleEvent Method Thismethodisthecoreoftheprotocol,asitdenestheactionstakenbytheprotocol whenaneventoccurs.Theuniqueparameterthatthismethodreceivesistheeventtaken fromtheeventqueue. Theeventsareclassiedbasedonaneventlabel.Eachprotocoldenesasetoflabelsfor alltheeventsthatituses.Theselabelsaredenedinthe constants interface.Therstactiontakenbythe HandleEvent methodistorecoveralltheeldsfromtheeventandstore themintemporaryvariables.Dependingonthenatureoftheprotocol,theclassicationof theeventscanbedoneindifferentways:Label-then-StateorState-then-Label.Intherst case,themostimportantinformationisthelabeloftheevent,whichbecomesthemain classicationfactor.Oncethelabelisfound,thecodeinsidedeterminesifthestateofthe nodeisimportantornotfortheexecutionoftheactionsassociatedwiththeevent.Inthe secondcase,themostimportantinformationisthestateofthenode.Thismethodology isusefulwhentherearenotmanytypesofeventsbuteachtypeisinterpreteddifferently basedonthestateofthenode. Thefollowingcodeshowsthe HandleEvent methodfromtheexampleprotocolpresented inthissection,theSimpleTree. 231

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AppendixA:continued publicvoidHandleEventevent_sime{ intcode=e.getCode; intsender=e.getSender; intsource=e.getSource; intfinal_destination=e.getFinalDestination; intreceiver=e.getReceiver; intdestination=e.getDestination; doubletemp_clock=e.getTime; Stringtemp_data=e.getData; inttemp_vni=e.getTree; switchcode{ caseINIT_NODE: init_nodetemp_vni,receiver; break; caseINIT_EVENT: initial_eventreceiver,temp_vni; break; /* *Thiseventiswhenanodewillstart *sendingHellomessagetoitsneighbors */ caseSEND_HELLO: 232

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AppendixA:continued //Thenodewillcleanthecandidatesfrom //theneighbor'shellosmessages getNodesender.cleanCandidates; getNodesender.setStateS_IN_SEARCH,temp_vni; //SendingHellomessagetoallneighbors broadcasttemp_clock+getRandomMAX_TX_DELAY_RANDOM, temp_clock,sender,-1,RECEIVE_HELLO,temp_data,temp_vni; //Finaltimeoutforevaluatingcandidatesandadoptchildrennodes pushEventnewevent_floattemp_clock+TIMEOUT_DELAY,temp_clock, sender,sender,LISTEN_4_REPLY_TIME_OUT,"",temp_vni,type; break; /* *ThiseventiswhenanodereceivedaHellomessage *fromitsparent */ caseRECEIVE_HELLO: //Ifthenodedoesnothaveaparentinthecurrenttree... if!getNodereceiver.isCoveredtemp_vni{ 233

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AppendixA:continued //Decompressthedatainthemessage temp_data_array=temp_data.split"@"; try{ //Theleveloftheparentiscomminginthedata temp_data_int=Integer.parseInttemp_data_array[0]; //ThesinkaddressofthisVNI temp_data_int2=Integer.parseInttemp_data_array[1]; }catchExceptionex{ex.printStackTrace;} //Changethestateofthenodefromtheinitialstate getNodereceiver.setStateS_VISITED,temp_vni; //Definetheparentinthecurrenttreeandthesinkaddress getNodereceiver.setParenttemp_vni,sender,sender,temp_data_int2; //Definethelevel getNodereceiver.setLeveltemp_data_int+1; //SchedulestheBroadcastoftheReplymessage pushEventnewevent_floattemp_clock+getRandomPROCESSING_DELAY, temp_clock,receiver,receiver,SEND_REPLY,"",temp_vni,type; //IfitisnotaparentafterTIMEOUT_NO_PARENTunits, //itwillgointoS_SLEEPINGmode pushEventnewevent_floattemp_clock+TIMEOUT_NO_PARENT,temp_clock, receiver,receiver,END_TIMEOUT_NO_PARENT,"",temp_vni,type; } 234

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AppendixA:continued break; /* *Thiseventiswhenthetimeoutforlisteningtootherneighbors *finishes,andthenodecansenditsownreplytotheparent. */ caseSEND_REPLY: //Parent'sID temp_ID=getNodesender.getParentIDtemp_vni; //Themetriccanbewhatevertheuserneedsittobe:energy,ID,etc. metric=getNodesender.getMetrictemp_ID; //Youcanusethresholdstolimitresponses... //Forexample,ifenergyislow,donotanswer //y=java.lang.Math.random; y=0; ifmetric>y{ //Determinethemetrictosend temp_data=""+metric; //Broadcastthemessage broadcasttemp_clock+getRandomMAX_TX_DELAY_RANDOM,temp_clock, receiver,temp_ID,RECEIVE_REPLY,temp_data,temp_vni; 235

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AppendixA:continued } break; /* *ThiseventiswhenanodereceivedareplyfromaHellomessage *fromitschildrenorneighbors. */ caseRECEIVE_REPLY: //Iftheparentistheonethatreceivesthismessage ifreceiver==destination{ //Obtainingtheneighboridentifierinthenode temp_ID=getNodereceiver.getNeighborIndexsender; //Obtainingthemetricthatthenodesent try{ metric=Double.parseDoubletemp_data; }catchExceptionex{ex.printStackTrace;} //Includeanewneighborfromwhichthenodeheardahellomessage getNodereceiver.addCandidatenewcandidatetemp_ID,sender,metric; } break; /* 236

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AppendixA:continued *Thiseventiswhenaparentnode'stimeouttoselectchildrenfinished. */ caseLISTEN_4_REPLY_TIME_OUT: i=0; sw=true; temp=0; temp_data=""; //Numberofcandidates temp2=getNodesender.getNumCandidates; iftemp2>0{ //Changingthestateofthenodetobeparent getNodesender.setStateS_PARENT,temp_vni; getNodesender.setParenttemp_vni,true; //InitiatetheTMprotocolonlyontheactive //nodesofthetopology!! ifTM_Selected{ pushEventnewevent_simtemp_clock+DELTA_TIME,temp_clock, receiver,receiver,INIT_EVENT,"",temp_vni,TM_PROTOCOL; } //Initiatethesensorqueryingprotocolonlyontheactive //nodesofthetopology!! ifSD_Selected{ pushEventnewevent_simtemp_clock+DELTA_TIME,temp_clock, 237

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AppendixA:continued receiver,receiver,INIT_EVENT,"",temp_vni,SENSOR_PROTOCOL; } //InitiatetheCOMMprotocolonlyontheactive //nodesofthetopology!! ifCOMM_Selected{ pushEventnewevent_simtemp_clock+DELTA_TIME,temp_clock, receiver,receiver,INIT_EVENT,"",temp_vni,COMM_PROTOCOL; } fori=0;i20{ //Addingthethenewchild getNodesender.addChildgetNodesender. getNeighbortemp_cand.getIndex; //Sendingthepacket broadcasttemp_clock+getRandomMAX_TX_DELAY_RANDOM, temp_clock,sender,temp_cand.getID, ACCEPTANCE_MESSAGE,temp_data,temp_vni; } 238

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AppendixA:continued } } break; /* *Thiseventiswhenanodeisacceptedbythesendernodeand *itgetspermissiontostartitsownbranchofthetree. */ caseACCEPTANCE_MESSAGE: temp=0; ifsender==getNodereceiver.getParentIDtemp_vni&& receiver==destination{ pushEventnewevent_floattemp_clock+getRandomMAX_TX_DELAY_RANDOM, temp_clock,receiver,-1,SEND_HELLO, ""+getNodereceiver.getLevel+"@" +getNodereceiver.getSinkAddresstemp_vni,temp_vni,type; } break; /* *Thiseventiswhenanodedidnotreceived *anACCEPTANCE_MESSAGE. */ 239

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AppendixA:continued caseEND_TIMEOUT_NO_PARENT: if!getNodesender.getStatetemp_vni==S_VISITED{ frame_repaint; getNodesender.setStateS_SLEEPING,temp_vni; } break; } } } SimpleTree:AnExampleofaTopologyConstructionProtocol Inordertoillustratealltheseconcepts,asimpleexampleofatopologycontrolalgorithm follows.Theselectedexampleisahierarchicaltopologyconstructionprotocolbasedon thegrowingatreetechniqueSeeSection2.2.2.1.Theideaistoillustratesomecommon messageexchangesequences,theuseoftimeouts,andhowthemodicationofthestatusofthenodemodiestheexecutionoftheprotocol.Theprotocolworksbasedonthe followingassumptions: Thegrowingatreeprotocolleaveseverynodeactive,exceptthosewithIDnumber lessthan20. Thenodeshavenoinformationabouttheirpositionandhavenolistofneighbors. 240

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AppendixA:continued Everynodestartsinaunvisitedstate. Thesinkistheinitiatoroftheprocess. Theprotocolendswheneverynodeisinactivemodeorinsleepingmode. Theinitialtopologyisconnected. Theprotocol,stepbystep,worksasfollows: Thesinknodeinitiatestheprotocolsendinga Hello message.Itincludesitsaddress andlevelnumberofhopsfromthesink,whichinthecaseofthesinkitisequal to0.Thesendernodeprogramsatimeouttostoplisteningforanswersfromits neighbors. All unvisited nodesonthetransmissionrangeofthesendernodethatreceivedthe Hello messageanswerbackwitha Reply message,setthesenderastheirdefault gateway,andchangetheirstatusto In-Process mode.Thereceivernodesatthe sametimesetatimeoutincasetheydonotreceiveanacknowledgmentfromtheir defaultgatewaythesendernode. Oncethetimeoutofthesenderexpires,thisnodechecksthelistofneighborsthat answeredbackwiththe Reply message.Ifthesendernodedidnotreceiveanyanswerback,itturnsitselfoffandchangesitsstatusintoa Sleeping mode.Ifthe sendernodereceivedatleastoneanswerback,itgoesinto Active modeandsends anunicastmessagetoeachoneoftheminordertoletthemknowtheywereselected.AllneighborsexceptthosewithIDnumberlessthan20willreceivethis unicastmessage. 241

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AppendixA:continued Onceanodereceivestheconrmationmessagefromitsdefaultgateway,itwaitsa randomamountoftimeandsendsitsown Hello messagetodiscovernew unvisited nodes. Ifthetimeoutofanodein In-Process modeexpires,itmeansthatthenodewasnot selected,soitturnsitselfoffandgoesinto Sleeping mode. Oncethenodenishesitsprocessandendsupinan Active mode,itstartsthetopologymaintenance,sensoranddatamanagement,andcommunicationprotocols. Althoughdescribingaprotocolinwordsisusefulforunderstandingitsoperation,theyare morerigorouslydenedbyFiniteStateMachines,especiallyinthosecaseswherenodes changeseveraltimesfromonestatetoanotherduringtheexecutionoftheprotocol,and byatimelineofmessageexchanges.Forthisexampleprotocol,thesediagramsareshown inFigureA.2. Therstpartofthealgorithmisa HELLO-REPLY sequencethatisusedbymanyprotocolsintheneighborhooddiscoveryprocess.Themessagesequenceissimple:onemessageannouncesthepresenceofanode,andasetofnodes,whosesizeisunknown,answerbackwithareplymessage.Giventhattheinitiatorhasnoideaofhowmanynodes arewithinitstransmissionrange,itwaitsforacertainamountoftime.Thistimercanbe staticaxedvalueorarandomvaluedenedontheyordynamicvalueischanged afterthereceptionofanewreplymessage. Thesecondpartoftheprotocolconsistsoftheselectionandnoticationprocesses.Inthis case,thesendernodeselectsthenextgenerationofpossibleactivenodesbasedonapolicyallnodeswithIDlessthan20,andnotiesthemonebyoneusingunicastmessages. 242

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AppendixA:continued aFinitestatemachine. bMessagesequencediagram. FigureA.2:Usefuldiagramstodesignacommunicationprotocol. 243

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AppendixA:continued Thethirdpartistheinitiationoftheotherprotocols.Rememberthattopologyconstructionprotocolsareonlyusedtoreducethesizeoftheinitialtopology,buttheydonotnecessarilytakecareofmaintainingthistopologyduringitsoperation,orsenddatamessages tothesink.Iftheuserisattheearlystagesoftheprotocoldesign,runningexperiments withthetopologyconstructionprotocolonlyisveryconvenient;however,formorecomplexexperimentsthatincludenetworklifetimemeasurementsitisnecessarytostartthe topologymaintenanceprotocols. HowtoUseAtarraya Atarrayaoffersavarietyofoptionsfordesigningandexperimentingwithtopologycontrolalgorithms.Thissectionprovidesanin-depthuserguideonhowtousethesimulation toolandallitsavailableoptions. Therststepistohaveaclearunderstandingofthesimulationscenariostoberun.Here, theuserneedstoknowinadvancewhichprotocolsheorshewantstouse;whetherthe experimentisjustapreliminarytestoranexhaustiveperformanceevaluation;whatisthe natureofthetopologiesthatsheisplanningtouse;whattypeofstatisticsareneeded,and soforth.Inthissection,thesequestionsareansweredinorderforausertocreateandrun successfulsimulationswithAtarraya. SelectionoftheProtocols Atarrayaincludesfourtypesofprotocols:Topologyconstruction,topologymaintenance, sensor-datamanagement,andcommunication-routingprotocols.Atarrayacanbesetto 244

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AppendixA:continued workineitherofthefollowingtwomodesrelatedtotopologycontrol:Topologyconstructiononly,orAllprotocols.Therstmodeisdesignedtotestaspecictopologyconstructionalgorithmandmeasuretheinitialreducedtopologythatthealgorithmproduces.In ordertoselectthismode,theuseronlyneedstoselectatopologyconstructionprotocol. Thesecondmodeisintentedtotestnotonlythereducedtopologybutthelifetimeof thenetwork,basedonthecombinationofalltheprotocols,i.e.topologyconstruction andtopologymaintenance.Inordertoselectthesecondmodetheuserneedstoselect aprotocolineachoftheprotocolcategories,i.e.selectatopologyconstructionanda topologymaintenanceprotocol,otherwiseAtarrayawillnotallowtheusertorunthe experiment. ThetopologyconstructionprotocolsincludedinAtarrayaarebasedonalgorithmspresentedinpublishedpapers.Currently,Atarrayaincludesthealgorithmsevaluatedinthis book,i.e.A3,EECDS,andCDS-Rule-K.Althoughalltypesoftopologyconstruction protocolsmightbeimplemented,suchasthosebasedonchangingthetransmissionrange ofthenodes,hierarchicalprotocols,cluster-basedprotocols,etc.,thecurrentversionof AtarrayaincludesonlythosebasedontheConnectedDominatingSetconcept.Inaddition,andforthesakeofcomparisonwithawirelesssensornetworkwithouttopology control,Atarrayaoffersaprotocolthatdoesnotreducethetopologyatall,calledJustTree.Theonlyservicethatthisprotocolprovidesisthecreationofaforwardingtreeto implementtheconstantgatewayforwardingprotocol. AtarrayaalsoincludesallthetopologymaintenancetechniquesincludedinChapter6of thisbook.Theyaregenericalgorithmsthatworkwithanyofthetopologyconstruction protocols.ThesimplesttopologymaintenanceprotocolincludedinAtarrayaistheNo 245

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AppendixA:continued TopologyMaintenanceprotocol,whichdoesnothingtomaintaintheinitialtopology,but monitorsituntilitdies.TheprotocolisinchargeofinformingAtarrayawhenthisevent happens.InAtarraya,theterminationpolicyisdenedasthemomentatwhichthesink stopsreceivinginformationfromthenodes. The sensor-datamanagementprotocol modelsthebehaviorofthesensors,regardingvariableslikedatatransmissionfrequency,dataaggregationpolicies,etc.Atarrayaprovides asimpleprotocolforsendingandreceivingmessageswithoutdataaggregation.Nodes transmitdatapacketsatpredenedtimes,andforwardeveryreceiveddatapacketbased ontheforwardingpolicyexplainedinthefollowingparagraph. Althoughcommunicationorroutingprotocolsarenotthefocusofthissimulator,some kindofroutingprocedureisnecessarysopacketscanreachthesink.GiventhatthetopologycontrolprotocolsimplementedinAtarrayaaredesignedtoproduceatree-likereducedtopology,thetoolprovidesaverysimpleforwardingalgorithmthatallowspacketstoreachthesinknode:The constantgatewayforwardingprotocol .Inthisprotocol, packetsarealwaysforwardedtoadefaultgatewayunlessthedestinationofthepacketisa directneighbor,inwhichcaseitwillbesentdirectlytothatnode.Inatree-liketopology, thegatewayofanodeissimplyitsparentnode.Inthisfashion,thepacketwillnally reachthesinknode,sinceitistherootofthetree. Atarrayadoesnotincludeanyroutingprotocol,butdenesadatastructurethatmodelsa routingtable.Thisdatastructureallowsuserstodevelopmoreadvancedroutingprotocols thantheonecurrentlyimplemented.Inaddition,theroutingtablecanstorealimited amountofpacketsequencenumberseventshaveaeldforthispurposethatallowthe implementationofotherforwardingalgorithmslikeooding-basedprotocols,orsavethe 246

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AppendixA:continued FigureA.3:Simulationcontrolpanel. lastversionsoftheroutingprotocolinformationpackets,likeroutingtablesonaDistance Vectorprotocol,orthelastneighborhoodinformationinaLink-Stateprotocol. InAtarraya'sgraphicaluserinterface,thepanelnamed Atarraya presentstheavailable protocols.Inaddition,thispanelcontainsthecontrolsforthesimulationagent,thereport congurationoptions,simulationeventsandstatisticspanels,andthebatchsimulations controls.ThispanelisshowninFigureA.3. OtherProtocols Inordertowritethisbook,severalexperimentswereruntovalidateanalyticallyderived equationstoshowspecialeffectsorbehaviorsoftopologycontrolalgorithms.Thissec247

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AppendixA:continued tiondescribesvetoolsincludedinAtarrayathatareverywellsuitedforeducational purposes,astheyallowusersto: CalculatetheCriticalTransmissionRangeCTRbasedontheformulasofPenroseSantiandSanti-Blough. ReproducetheexperimenttoobtaintheGiantComponentgures:GreatestConnectedComponentandRatioofConnectedTopologies. ReproducetheexperimentthatprovesconnectivityoftheCTRformulaofSantiBloughfor2dimensionaldeployments. CalculatetheMinimalSpanningTreeonagivengraphandprovidethesumofthe selectededges. Savetheneighborhoodsofagraphinale. TherstthreetoolswereutilizedinChapter2.Theusercanreproducethoseexperiments withdifferentparametersifsodesired.TheMinimalSpanningTreeofagraphisstilla classicaltoolforgraphanalysis-Prim'salgorithmwasimplemented.Regardingthelast tool,theinformationprovidedbyitcanbeusedtodeneandsolvelinearprogramming optimizationproblemsongraphs,likendingaminimalsetcoverofthegraph.Thepanel thatcontainsallthesetoolsisshowninFigureA.4. EnergyandCommunicationsModel InthedesignofAtarrayasimplicityandfocusonreachingabetterunderstandingofthe behaviorofthetopologycontrolalgorithmswasembraced.Assuch,severalassumptions 248

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AppendixA:continued FigureA.4:Otherprotocolsforeducationalpurposes. 249

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AppendixA:continued weremadetomakethesimulatorsimplerwhilestillgoodenoughforachievingitsmain objective.Theseassumptionsarerelatedtotheenergyandthecommunicationmodels utilizedinthetool. TheenergymodelincludedinAtarrayaisbasedonthefollowingformulas,taken from[55]: E TX = bit = E elect + )]TJ/F42 11.9552 Tf 5.476 -9.69 Td [(E amp )]TJ/F40 11.9552 Tf 5.476 -9.69 Td [(p r 2 A.1 E RX = bit = E elect Inaddition,Atarrayaalsomakesthefollowingassumptions: Duringtheidletime,anodedoesnotspendenergy.Eventhoughthisassumption hasbeenprovenuntruebecausebeingidlemightbeascostlyasreceivingdata, thisisstillanassumptionthatcanbedoneinmostexperiments,sincethemost importantfactoristheoverheadintermsofmessageexchangeanditsassociated cost. Thenodesareassumedtohaveoneradioforgeneralmessagesandasecondradio forcontrolmessages:Themainradioisusedinalloperationswhenthenodeisin activemode,andthesecondonelowpowercheaperradioisusedtosendand receivecontrolpacketstowakeupthemainradio.Onlythemainradiocanbe turnedoff,whichmeansnomessageswillbereceivedandnoenergywillbeused. Thesecondaryradioisassumedtousehalftheenergyofthemainradio. 250

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AppendixA:continued Thesinknodehasainnitesourceofenergy.Ingeneral,thesinknodeisassumed tobepoweredfromanexternalsourceofenergy. ThecommunicationmodelusedinAtarrayaisbasedonthefollowingassumptions: Thecommunicationrangeofthenodesisaperfectsymmetricunitdisk.If d x ; y r x x and y canseeeachother. AconstantbiterrorrateBERisdenedforthewholenetwork.Thisisasimple implementationofanerrormodel.Wheneverapacketisgoingtobesent,arandom numberisgeneratedandcomparedtothemessageerrorratethatdependsonthe sizeofthemessage.Iftherandomnumberisgreater,themessageisreceived, otherwiseitislost.ThedefaultvaluefortheBERis0,whichmeansthereisno packetloss.Nosumofpartiallyreceivedpacketswillbuildacompletepacket. AtarrayaassumesthatthereexistsaDataLinkLayerthatdealswithpacketlosses andretransmissions,butitdoesnotmodelthis.InordertomodelsomeoftheconsequencesoftheoperationsoftheMAClayer,thepacketsaredelayedarandom amountoftimeinordertomodeldelaysoccurringduetoretransmissions,contention,etc.Thevariablethatdenesthemaximumdelayvaluecanbefoundin the constants interface,bythenameof MAX_TX_DELAY_RANDOM .Thedefault valueforthisvariableis0.2timeunits. TypeofExperiments Atarrayaofferstwotypesofexperiments:singletopologybased,thatusesthevisual representationofthetopology,andthebatchexecutionmodethatsimulatesalargeset 251

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AppendixA:continued oftopologies.Thesingletopologybasedtypeisgoodforprotocoldesignanddebugging. Thebatchtypeismadeforfullscaleevaluationandanalysis. Duringtheprotocoldesignphase,itisveryimportanttohavethecapabilitytorunasmall numberofcontrolledtopologiesoneatatimetobeabletocomparetheresultsofseveral runsonaknownscenario.Thisisadebuggingphasewheremanychangesareintroduced intheprotocoluntilitbehavesasintended.Duringthisprocess,avisualrepresentationof thetopologyandtheperformanceofthetopologycontrolalgorithmisveryhelpful. Oncetheprotocolhasreachedastableversionthathasworkedwellinseveralsingle topologies,theprotocolneedsamoreexhaustivetestwithalargernumberoftopologies inordertoanalyzeitsaveragebehavior.Thebatchexecutionmodeallowstheresearcher torunsimulationswithhundredsofrandomtopologies.Inthiscase,thevisualrepresentationofthetopologiesisnotnecessary;actually,itwouldslowdownthesimulation process. Inthesingletopologymode,thetopologyisloadedusingthe LoadTopology iteminthe File menutab,orthe DeploymentOptions tab,whichisgeneratedbytheuserthegenerationoftopologieswillbeexplainedinthefollowingsection.Inthebatchexecution mode,severaltopologiesareloadedfromlesselectedbytheuser.Thebatchexecution controlsarelocatedinthe Atarraya panel,asshowninFigureA.3. Inordertoincreasetherandomizationofthesimulationprocess,Atarrayaintroduces somenoiseonsomecommonprocessesinthenetwork,likemessagetransmissiondelay, soeachinstanceofasimulation,evenworkingonthesametopology,wouldproduce differentoutcomes.Atarrayaallowsmultiplereplicasofeachtopology,whichisuseful 252

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AppendixA:continued toobtaintheaverageresultsandthevariabilityofasingletopologythatshowsthecondenceofthealgorithm. StructureofaTopology AtopologyinAtarrayaiscomposedoffourbasicelements:Deploymentarea,regular nodes,sinknodes,andvirtualnetworkinfrastructuresorVNI.Thedeploymentareaisan abstractconcept,whichisusefulforvisualizationpurposes.Itisarectangleinwhichthe userdeploysthenodesofthenetwork.Inordertodenethedeploymentarea,theuser needstodeneitswidthandheight. Thesetofregularnodesisusuallythebiggestsetofelementsinthetopology.Theyare inchargeofmonitoringtheenvironmentalvariableorvariableofinterest,sendingthis informationtothesinkandroutingpackets.Aswithanywirelesssensordevices,regular nodesareverylimitedintermsofresources. Thesinknodesarespecialnodesthat,inmostscenarios,areincludedtoreceivetheinformationfromallactivenodesinthenetwork.Theyserveasbridgesbetweenthewireless sensornetworkandanytypeofexternalnetworkusedtotransportthesenseddatatoits naldestinationsomewhereelseintheInternet.Insomecasestheyarealsoincharge ofinitiating,executing,and/orcontrollingthetopologyconstructionandmaintenance protocols,routingprotocols,etc. Despitethefactthatinreallifethehardwarecongurationofthesinknodesisdifferent comparedtoaregularwirelesssensordevice,Atarrayausesthesamedatastructureto modelbothnodes,withthemaindifferencethatsinknodesareconsideredtohavean unlimitedamountofenergy. 253

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AppendixA:continued OnecontributionofAtarrayaistheintroductionoftheconceptof VirtualNetworkInfrastructuresVNI .Thisideaisanabstractionusedtoallowoverlayingtopologiesover thesamesetofnodes.Imaginehavingseveralsinknodesontheinitialtopology,andthat eachonebuildsareducedtopologyrootedatitself.Usingthisabstractionnotonlysink nodescanrotate,butalsocompletetopologies.Thisapproachwasusedtoimplementthe staticglobaltopologymaintenancetechniquesdenedinSection6.2.Theinitialideawas toletthenetworkoperateinthesamewaythelightsinaChristmastreerotate:acertain numberofsubsetstaketurnsorshiftstobeactiveduringacertainamountoftime,andgo tosleepuntilthenextturn. AtarrayaidentiesthedifferentVNIswithnumbersfrom0to6,andvisuallywithcolors: Black,Red,Blue,Green,Orange,Pink,andYellow.Eachnodeisassumedtohavea separateddatastructureforeachVNI,sotheinformationofeachoneisindependent fromeachother.RegularnodeshavenoafliationwithaparticularVNI,whileeach sinknodeisassociatedwithaVNItowhichitservesasasinknode.Allsinknodesare assumedtoberegularnodesbytheVNI,thatarenotassociatedwiththem,keepingtheir characteristicofunlimitedenergy. Thefollowinglistcontainsalltheavailableoptionstodenethenetworktopology: SinkorNoSink:Eventhoughmostwirelesssensornetworkscontainoneormore sinknodes,Atarrayaallowstheusertodeneawirelesssensornetworkwithout sinks. OneormultiplesinksinasingleVNI:Atarrayaallowstodeneasinglenetwork withasinglesinkormultiplesinks.FigureA.5ashowsthisrstcase,whichfacilitatesthedesignbecausethereisonlyoneactiveelementinchargeoforganizing 254

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AppendixA:continued theprotocols.Nonetheless,Atarrayaalsoallowsfornetworkdesignswithmultiplessinksinasinglenetwork,asshowninFigureA.5b.Includingmanysinks distributedintheareaofdeploymentcanbeagoodideatoreducetheaveragepath length;however,havingmultiplesinkscanalsocausenetworkpartitions,especially iftheirstructuresaredisjoint. OneVNIormultipleVNIs:HavingmultipleVNIsisthewayinwhichthestatic globaltopologymaintenancetechniqueswereimplemented,wherethereareseveral subsetsoftopologiesandonesink. StructureoftheNodes Intermsofthenodes,Atarrayacanmanagehomogeneousnetworks,inwhichallnodes havethesamecharacteristics,andheterogeneousnetworks,wherethereisatleastone nodethatisdifferentfromtheothers. Whencreatingatopology,thesimulatorworksbasedonsubsetsofhomogeneousnodes. Eachsetdenesafamilyofnodesthatsharethesamecharacteristics.Forexample,the usercandeneasetofweaknodeswithlowtransmissionrangeandlowenergy,anda setofpowerfulnodeswithhightransmissionrangeandhigherenergy.Atarrayaalso allowsfordifferentrandomdistributionsforthelocationandenergyofeachgroupof nodes,thatwillallowtheusertocreatedenserzonesinthetopology,orzoneswithnodes thathavelessenergy. Thedatastructurethatmodelsthesefamiliesofnodesiscalled CreationWords .These creationwordsarecreatedbasedonthevaluesdenedonthe DeploymentOptions panel 255

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AppendixA:continued aSingleVNI,singlesink. bSingleVNI,multiplesinks. FigureA.5:DifferenttopologydesignsgeneratedbyAtarraya. 256

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AppendixA:continued FigureA.6:Deploymentdenitionpanel. inthesimulatorFigureA.6.Theusercancreateasmanycreationwordsasdesired: thesefamiliescanmodelfromasinglenodetothecompletesetofregularnodes.Inthe paneltherearetwolistboxeswherethecreationwordsarestoreduntilthetopologyis created:Theregularnodeslisttopandthesinkcreationwordsbottom.Therearethree buttonsforaddinganewcreationword,removingaselectedcreationword,andclearing bothlistboxes. Theparametersthatcanbedenedinahomogeneousfamilyofnodesare: Numberofnodes. Communicationradius. Sensingradius. 257

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AppendixA:continued Sizeoftheareaofdeployment. Positiondistribution: Uniform,withcenterin x ; y andthelimitsdenedbythedeploymentarea parameters. Normalwithcenterin x ; y ,requiringmeanandstandarddeviationofthe location. GridH-V:coverthedeploymentareawithagridwherenodesareconnected ofitshorizontalandverticaladjacentnodesinthegrid.Numberofnodesis notaparameterforthisoption.Distancebetweenthenodesisthecommunicationradius, comm radius GridH-V-D:coverthedeploymentareawithagridwherenodesareconnected ofitshorizontal,verticalanddiagonaladjacentnodesinthegrid.Thenumber ofnodesisnotaparameterforthisoptioneither.Thedistancebetweenthe nodesis comm radius p 2. Constantpositionat x ; y Centerofarea,basedonthesizeofthedeploymentareaparameters. Manual:pressthebuttonandclickonthepaneltoselectthethepositionofthe node,asmanytimesasdenedonthenumberofnodesofthesubset. Energydistribution: Constantvalue. Normal,requiringmeanandstandarddeviationoftheenergyfunction. 258

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AppendixA:continued Poisson,requiringlambdaoftheenergydistribution. Uniform,requiringmaximumoftheenergyfunction. Inter-querytime:Frequencyofqueryingthesensorforreadings.Thisparameteris validonlywhenasensor-dataprotocolisselected. Inthecaseofthesinknodeset,twoextraparametersmustbedened: Sink?:selectthecheckboxifyouwantthenodesinthesettobeincludedassink nodes. VNISelection:selecttheVNIidentierassociatedtothesinksoftheset. Atarrayaallowstheuseofametricforcomparingnodescanbeseeninagoodnumberof protocols.Examplesofmetrics,asseenintheprotocolsinpreviouschapters,areusually relatedtoenergy,distance,IDofthenodeorevenarandomnumber.Atarrayaallows theusertodeneitsownmetricbasedonitspreference.Inaddition,itallowstheuseof twometrics:aprimaryandsecondarymetric.Whenusing2metrics,therearedifferent optionsofhowtousethemetrics: Metric1OnlyThismodeisusedifonlyonemetricisneededontheprotocol. Metric2Only Metric1Primary:thevalueswillbegroupedinblocksbyMetric1,andsortedinternallyoneachblockbyMetric2. Metric2Primary:thevalueswillbegroupedinblocksbyMetric2,andsortedinternallyoneachblockbyMetric1. 259

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AppendixA:continued Linearcombinationofmetrics:Thenodecanobtainthelinearcombinationofthe 2metrics,providingtherespectiveweightstotheprimaryandsecondarymetrics. Thedefaultvaluesare0.5forbothweights,soaregularaveragewillbeobtained. Wp Metric 1 + Ws Metric 2 Wp + Ws Wp:weightofprimarymetric Ws:weightofsecondarymetric Atarrayaalsoincludessomeotherspecialpurposevariables,asfollows: Inter-querytime:Timeperiodbetweenreadingthesensorandtransmittingthedata packettothesinknode. Inter-resettime:Timeperiodbetweenthetime-triggeredtopologymaintenance protocols. Energythreshold:Energypercentagedifferentialusedtoinvokeenergy-triggered topologymaintenanceprotocols.Everytimetheenergyofanodecrossesthisenergythresholdvalue,sincethelastinvocationofthetopologymaintenanceprotocol,thenodewillinvoketheprotocolagain.Forexample,ifthebatteryisfully chargedandtheenergythresholdissetto0.10,thenodewillinvoketheprotocolfor thersttimewhen90%ofitsenergyisconsumed. Alltheseoptionscanbefoundinthe DeploymentOptions tab,underthetabsnamed Main Parameters and OtherParameters .TheDeploymentOptionsandDeployment'sother optionspanelsareshowninFiguresA.6andA.7. 260

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AppendixA:continued FigureA.7:Otherparametersfordeploymentdenition. 261

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AppendixA:continued SimulationResults Atarrayaoffersthreetypesofresultlogsthatcanbeobtainedfromasetofexperiments: Generalstatistics,networklifetime,andthesimulationeventLogs.The generalstatistics log canregisterthestateofseveralvariablesinaperiodicalmanner,orprovidejustone snapshotofthenetworkattheendofthesimulation.Themostusuallyconsultedvariables are: Simulationclock. Numberofnodes. Numberofsinknodes. Numberofactivenodes. Numberofdeadnodes. Averagenodedegree. Averagelevelofnodesiflevelisusedbytheprotocol. Numberofmessagessentandreceived. Numberofdatamessagesreceivedbythesink. Energyonthetree,energyspent,etc. Areaofcommunicationcoverage. 262

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AppendixA:continued Thesevaluesarestoredinatextlewhereeachindividualrowcontainsasnapshotof thevariablesofthenetworkinthemomentatwhichdatawascollected.Ifaexperiment includesmorethanonetopology,theusercandecideifthedataisgoingbestoredindividuallyperexecution,orifalltheresultsaregoingtobesummarizedinasinglele. Theusualformatinwhichdataispresentedisincommaseparatedvalues.csv,which isreadablebymostdataanalysisprograms,likeExcel,Matlab,etc.However,iftheuser doesnotwanttheresultstobesavedinles,the Report panelhasatextareathatholds thestatisticsgeneratedbytheexperimentsincsvformat.Ifjustonetopologyissimulated,theusercanusethe Stats textareainthe Atarraya panel,whichpresentstheresults inplaintextformat.FigureA.8showsoneexampleofthesimulationresultsgeneratedby Atarraya. The networklifetimelog registersthestatusoftheactivetopology.Thislogstoresinformationeverytimethetopologymaintenanceprotocolisinvoked,orwhenanodedies. Thisspeciclogcannotbestoredinindividuallesperexecution;itisstoredinasummarizedformatincsvformat. Theinformationstoredinthenetworklifetimelogbyasingletopologyisrepresentedin fourrows.Therstrowregistersthemomentinwhichtheinformationofthenetwork wascalculated.Thesecondrowrepresentsthenumberofactivenodesthatcanstillreach thesinknode-thosethatstillcanprovideinformationtothesink.Thisvalueisimportant becauseifthesinkgetsisolated,nomatterhowmanyactivenodesremain,allofthem areuselessbecausetheinformationtheyproducegetslost.Inthecaseofhavingmore thatoneVNIs,theprogramworkswiththeactiveVNIinthenodes.Thethirdrowshows theratiobetweenthenumberofactivenodesthatcanreachthesinkvaluefoundonthe 263

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AppendixA:continued FigureA.8:ExampleofstatisticsgeneratedbyAtarraya. 264

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AppendixA:continued FigureA.9:Reportpanel. secondrowandthemaximumnumberofactivenodes.Thisvalueisthepercentageof activenodesthatarestillaliveandconnectedtothesink.Finally,thefourthrowcontains thepercentageofcoveredareabytheactivenodesinthesecondrow.Thisinformation canbeveryusefulinordertocompareefciencybetweenprotocols,intermsofnumber ofactivenodesandrealcoveredarea. Atarrayaoffersawaytosummarizethislogbycalculatingtheaveragenumberofactive nodesforthecompletesetofexecutionsthatarestoredinasinglele.Theideaisto createasinglelifetimefunctionthatrepresentstheaveragenumberofactivenodesand wrapsalltheindividuallifetimes.Atarrayacreatesadiscretetimeline,inwhichthesize ofeachcellisbasedontheparameterTimestep.Eachcellcontainstheglobalaverage ofallexperimentsduringthatspecicamountoftime.The Report panelpresentsthe controlsforthisoperation,asshowninFigureA.9. 265

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AppendixA:continued FigureA.10:Nodestatisticspanel. The simulationeventlog registersalltheeventsgeneratedbythesimulatorduringthe executionofasingletopology.Thecompletesetofeventsallowstheusertodebugthe protocolbyseeingthesequenceofoperationsexecuted.Thisinformationisonlyavailable inindividuallespertopology. Atarrayanotonlyoffersstatisticsfromthecompletesimulationpointofview,butfrom theindividualnodeperspective.Itisalwaysveryusefultoknowthestatusofthenodes atanygivenpointintimetocheckifthealgorithmsareworkingasdesired.Thisinformationcanbefoundinthe NodeStats panel,asshowninFigureA.10.Inordertogetthe informationofanode,theusercandoitintwoways:draggingthemousepointertothe desirednodeandclickingoverit,ortypingtheidnumberofthenodeinthetexteldand pressthebuttonGenerateStats.Oncethenodeisselected,thepointinthetopologyturns orangeandincreasesinsize. 266

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AppendixA:continued FigureA.11:Mainwindowdescription. Atarrayaalsoallowsforthevisualrepresentationofthereducedtopology.ThemainwindowofAtarrayaisdividedintwoenvironments:Thedeploymentvisualizationarealeft andthecontrolarearight,asshowninFigureA.11.Oneofthepanelsinthecontrolarea containsthevisualizationoptions:changingviewfromMaxPowergraphtothereduced topologyAtarrayamode;showingtheactivenodesParentmode,communicationand sensingcoverageareas,andnodeid's;drawingagridoverthedeploymentthearea,etc. ThecombinationofsomeoftheseoptionsareshowninFigureA.12,whereontheleft sideofthegurethedeploymentvisualizationareawiththedifferentpresentationoptions canbeseen. 267

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AppendixA:continued FigureA.12:Visualizationcontrolpanel. 268

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AppendixA:continued FutureofAtarraya Atarrayaisaveryusefultoolfortestingtopologycontrolalgorithms,butitisstillfar fromreachingitsfullpotential.Thereisalotofroomforfutureimprovements.Forexample,transmissionrangecontroltopologyconstructionprotocols,localtopologymaintenanceprotocols,dataaggregationalgorithms,routingandforwardingprotocols,3D scenarios,etc.couldbeincluded.Morecomplexandrealisticsensingandcommunication modelsanddatalinklayerprotocolscouldbeincorporatedaswell. ItishopedthatmakingAtarrayafreelyavailabletheresearchcommunitywillcontribute toitsexpansion.MaintainingAtarraya'sWebsitewiththemostrecentversionsofthe tool,itsupgradesandfeatures,forthebenetoftheentirecommunityandtheresearch areaisamajorcommitment.Pleasecontacttheauthorswithyourownupgrades,suggestions,corrections,etc.ThemainAtarrayaWebsiteisat http://www.cse.usf.edu/ ~labrador/Atarraya 269

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AbouttheAuthor PedroWightmanreceivedhisB.Sc.inSystemsEngineeringfromtheUniversidaddel Norte,inBarranquilla,Colombia,in2004.HereceivedhisM.Sc.inComputerScience fromtheUniversityofSouthFloridain2007,whereheisaPh.D.candidateinthesame department.PedroworkedasanadjunctinstructorattheUniversidaddelNorteduring 2004and2005.In2005hewasselectedtoparticipateintheNationalProgramofYoung ResearchersinColombia,sponsoredbytheColombianInstituteofScienceandTechnology,Colciencias.In2005,hewasselectedbytheUniversidaddelNortetoparticipatein theTeachingFormationProgramwhichgavehimtheopportunitytostarthisdoctorate. Hisresearchinterestsareinthedevelopmentofenergyefcienttopologyconstruction andtopologymaintenanceprotocolsforwirelesssensornetworks.Heisamemberof theIEEECommunicationSociety,andco-founderofCommNet,theCommunication NetworksGroupatUSF.


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Topology control in wireless sensor networks
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ABSTRACT: Wireless Sensor Networks (WSN) offer a flexible low-cost solution to the problem of event monitoring, especially in places with limited accessibility or that represent danger to humans. WSNs are made of resource-constrained wireless devices, which require energy efficient mechanisms, algorithms and protocols. One of these mechanisms is Topology Control (TC) composed of two mechanisms, Topology Construction and Topology Maintenance. This dissertation expands the knowledge of TC in many ways. First, it introduces a comprehensive taxonomy for topology construction and maintenance algorithms for the first time. Second, it includes four new topology construction protocols: A3, A3Lite, A3Cov and A3LiteCov. These protocols reduce the number of active nodes by building a Connected Dominating Set (CDS) and then turning off unnecessary nodes. The A3 and A3-Lite protocols guarantee a connected reduced structure in a very energy efficient manner. The A3Cov and A3LiteCov protocols are extensions of their predecessors that increase the sensing coverage of the network. All these protocols are distributed -they do not require localization information, and present low message and computational complexity. Third, this dissertation also includes and evaluates the performance of four topology maintenance protocols: Recreation (DGTRec), Rotation (SGTRot), Rotation and Recreation (HGTRotRec), and Dynamic Local-DSR (DLDSR). Finally, an event-driven simulation tool named Atarraya was developed for teaching, researching and evaluating topology control protocols, which fills a need in the area of topology control that other simulators cannot. Atarraya was used to implement all the topology construction and maintenance cited, and to evaluate their performance. The results show that A3Lite produces a similar number of active nodes when compared to A3, while spending less energy due to its lower message complexity. A3Cov and A3CovLite show better or similar coverage than the other distributed protocols discussed here, while preserving the connectivity and energy efficiency from A3 and A3Lite. In terms of network lifetime, depending on the scenarios, it is shown that there can be a substantial increase in the network lifetime of 450% when a topology construction method is applied, and of 3200% when both topology construction and maintenance are applied, compared to the case where no topology control is used.
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