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PAGE 1 Freeway Exit Ramp Traffic Flow Research Based on Computer Simulation by Xu Wang A Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Civil and Environmental Engineering College of Engineering University of South Florida Major Professor: Jian John Lu, Ph.D. Manjriker Gunaratne, Ph.D. Huaguo Zhou, Ph.D. George Yanev, Ph.D. Pan Liu, Ph.D. Date of Approval: December 7, 2007 Keywords: Speed, Lane change, Corsim, ANOVA,Tukey Copyright 2008, Xu Wang PAGE 2 ii Acknowledgements This dissertation was made possible by the help of many people. Firstly, I would like to thank my main advisor Dr. Jian John Lu for his dedicated help, advice, inspiration, encouragement and criticism throughout my study. I also express my appreciation to the members of my committee, Dr. Manjriker Gunartne, Huaguo Zhou, George Yanev and Pan Liu. Without their knowledge and assistance this study would not have been successful. I further express my appreciation to my fellow researchers at the transportation research lab for their help and assistance. Zhenyu Wang, Hongyun Chen, Bin Cao, Tao Pan, and Xiaodong Wang. Special thanks to Linjun Lu for his enlighten discussions and suggestions. Finally, I would thank my family for their encouragement and support during my time of study. My wife sacrificed too much for my career and success. PAGE 3 i Table of Contents List of Tables................................................................................................................. .v List of Figures................................................................................................................ xi Abstract....................................................................................................................... ..xv Chapter 1 Introduction....................................................................................................1 1.1. Background..........................................................................................................1 1.2. Problem Statement...............................................................................................3 1.3. Research Objectives and Expected Results.........................................................4 1.4. Significance of This Research.............................................................................5 1.5. Methodology........................................................................................................5 1.6. Organization of This Paper..................................................................................6 Chapter 2 Literature Review...........................................................................................8 2.1. General.................................................................................................................8 2.2. Design Standards.................................................................................................8 2.2.1. OneLane Taper Type Exit....................................................................8 2.2.2. OneLane Parallel Type Exit.................................................................9 2.2.3. TwoLane Exits...................................................................................10 2.3. Operation and Safety..........................................................................................11 2.4. Simulation..........................................................................................................14 2.5. Other Issues........................................................................................................23 2.6. Summary............................................................................................................26 Chapter 3 Factors Affect Ramp Design........................................................................28 3.1. Introduction........................................................................................................28 3.2. Influencing Factors at Ramp Designs................................................................28 3.3. Limitation of Factors in Traffic Simulation.......................................................30 3.4. Internal Factors in CORSIM..............................................................................31 3.5. Sensitivity Study of Internet Factors..................................................................32 3.6. External Factors in CORSIM.............................................................................34 3.7. Selection of Factors for Analysis.......................................................................35 3.7.1. Number of Lanes of Mainline.............................................................37 3.7.2. Number of Lanes of Exit Ramp..........................................................37 3.7.3. Free Flow Speed..................................................................................38 3.7.4. Freeway Grade....................................................................................38 3.7.5. Truck Percentage.................................................................................39 3.7.6. Restriction to Lane Usage of Truck....................................................40 3.7.7. Location of Exit Sign..........................................................................40 PAGE 4 ii 3.8. Summary............................................................................................................41 Chapter 4 Data Collection.............................................................................................43 4.1. Introduction........................................................................................................43 4.2. Input File Production.........................................................................................43 4.3. Affecting Factors in Input Files.........................................................................44 4.4. Freeway Exit Ramp Configuration....................................................................46 4.5. Entry Volume for CORSIM Simulation............................................................48 4.6. Number of Simulation Runs..............................................................................49 4.7. Data Collection..................................................................................................51 4.8. ANOVA & Tukey..............................................................................................52 4.8.1. Assumptions........................................................................................52 4.8.2. Hypotheses..........................................................................................53 4.8.3. Grand Mean........................................................................................53 4.8.4. Total Variation....................................................................................53 4.8.5. Between Group Variations..................................................................54 4.8.6. Within Group Variations.....................................................................54 4.8.7. F Test Statistic.....................................................................................55 4.8.8. Summary Table...................................................................................55 4.8.9. Tukey Test..........................................................................................56 4.9. Summary............................................................................................................56 Chapter 5 Capacity Comparisons..................................................................................58 5.1. Introduction........................................................................................................58 5.2. Mean Discharging Volume Comparisons..........................................................59 5.2.1. Before Functional Area at Low Entry Volume...................................59 5.2.2. Within Functional Area at Low Entry Volume..................................60 5.2.3. After Functional Area at Low Entry Volume.....................................62 5.2.4. Before Functional Area at Medi um Entry Volume............................63 5.2.5. Within Functional Area at Medium Entry Volume............................64 5.2.6. After Functional Area at Medium Entry Volume...............................66 5.2.7. Before Functional Area at High Entry Volume..................................67 5.2.8. Within Functional Area at High Entry Volume..................................69 5.2.9. After Functional Area at High Entry Volume....................................70 5.3. Summary............................................................................................................71 Chapter 6 Traffic Speed Comparisons..........................................................................74 6.1. Introduction........................................................................................................74 6.2. Mean Speed Comparisons..................................................................................75 6.2.1. Before Functional Area at Low Entry Volume..................................75 6.2.2. Within Functional Area at Low Entry Volume..................................76 6.2.3. After Functional Area at Low Entry Volume.....................................77 6.2.4. Before Functional Area at Medium Entry Volume............................78 6.2.5. Within Functional Area at Medium Entry Volume............................79 6.2.6. After Functional Area at Medium Entry Volume..............................81 6.2.7. Before Functional Area at High Entry Volume..................................82 PAGE 5 iii 6.2.8. Within Functional Area at High Entry Volume.................................84 6.2.9. After Functional Area at High Entry Volume....................................85 6.3. Summary............................................................................................................87 Chapter 7 Lane Change Comparisons...........................................................................89 7.1. Introduction........................................................................................................89 7.2. Total Lane Change Number Comparisons.........................................................90 7.2.1. Before Functional Area at Low Entry Volume..................................90 7.2.2. Within Functional Area at Low Entry Volume..................................91 7.2.3. After Functional Area at Low Entry Volume....................................93 7.2.4. Before Functional Area at Medi um Entry Volume............................94 7.2.5. Within Functional Area at Medium Entry Volume............................95 7.2.6. After Functional Area at Medium Entry Volume..............................97 7.2.7. Before Functional Area at High Entry Volume.................................98 7.2.8. Within Functional Area at High Entry Volume.................................99 7.2.9. After Functional Area at High Entry Volume..................................101 7.3. Summary..........................................................................................................102 Chapter 8 Sensitivity Analysis....................................................................................105 8.1. Entry Volume...................................................................................................106 8.1.1. Entry Volume Sensitivity before Functional Area...........................106 8.1.2. Entry Volume Sensitivity within Functional Area...........................108 8.1.3. Entry Volume Sensitivity after Functional Area..............................109 8.1.4. Entry Volume Sensitivity Sum up....................................................110 8.2. Free Flow Speed..............................................................................................111 8.2.1. Free Flow Speed Sensitivity before Functional Area......................111 8.2.2. Free Flow Speed Sensitivity within Functional Area......................112 8.2.3. Free Flow Speed Sensitivity after Functional Area.........................114 8.2.4. Free Flow Speed Sensitivity Sum up...............................................115 8.3. Freeway Grade.................................................................................................116 8.3.1. Freeway Grade Sensitivity before Functional Area.........................116 8.3.2. Freeway Grade Sensitivity within Functional Area.........................117 8.3.3. Freeway Grade Sensitivity after Functional Area............................119 8.3.4. Freeway Grade Sensitivity Sum up..................................................121 8.4. Truck Percentage.............................................................................................121 8.4.1. Freeway Truck Percentage Sensitivity before Functional Area......121 8.4.2. Freeway Truck Percentage Sensitivity within Functional Area......122 8.4.3. Freeway Truck Percentage Sensitivity after Functional Area.........124 8.4.4. Freeway Truck Percentage Sensitivity Sum up...............................125 8.5. Restrictions to Truck........................................................................................125 8.5.1. Restrictions to Truck sensitivity before Functional area.................126 8.5.2. Restrictions to Truck Sensitivity within Functional Area................127 8.5.3. Restrictions to Truck Sensitivity after Functional Area..................128 8.5.4. Restrictions to Truck Sensitivity Sum up........................................130 8.6. Location of Exit Sign.......................................................................................130 PAGE 6 iv 8.6.1. Location of Exit Sign Sensitivity before Functional Area...............130 8.6.2. Location of Exit Sign Sensitivity within Functional Area...............132 8.6.3. Location of Exit Sign Sensitivity after Functional Area.................133 8.6.4. Location of Exit Sign Sensitivity Sum up.......................................135 Chapter 9 Summary, Conclusions and Recommendations.........................................141 9.1. Summary..........................................................................................................141 9.2. Conclusions......................................................................................................143 9.2.1. Volume Discharge Rate..................................................................143 9.2.2. Operational Speed...........................................................................144 9.2.3. Total Lane Change Number............................................................144 9.2.4. Sensitivity Analysis... ................ ................ ................ .............. ........145 9.3. Recommendations...........................................................................................146 9.3.1. Simulation Software........................................................................147 9.3.2. Exit Ramp.......................................................................................147 References...................................................................................................................14 9 About the Author . .......End Page PAGE 7 v List of Tables Table 1 Recommended Parameter Values........................................................................31 Table 2 CORSIM Capacity and HCS Capacity................................................................33 Table 3 Auxiliary Lane Length at Different FFS .............................................................36 Table 4 Selected Factors for CORSIM Simulation..........................................................41 Table 5 Record Type of Selected Variables.....................................................................45 Table 6 Notations of Files Name in the Research...........................................................46 Table 7 Three Scenarios for Exit Ramp Comparison.......................................................49 Table 8 One Way ANOVA..............................................................................................55 Table 9 Auxiliary Lane Length of Exit Ramps................................................................59 Table 10 Mean Discharging Volume at LEV before FA.................................................60 Table 11 ANOVA Results of Mean Discharging Volume at LEV before FA.................60 Table 12 Mean Discharging Volume at LEV within FA................................................61 Table 13 ANOVA Results of Mean Discharging Volume at LEV within FA.................61 Table 14 Tukey Results of Mean Discharging Volume at LEV within FA.....................61 Table 15 Mean Discharging Volume at LEV after FA....................................................62 Table 16 ANOVA Results of Mean Volume at LEV after FA........................................63 Table 17 Mean Discharging Volume at MEV before FA................................................63 Table 18 ANOVA Results of Mean Dischargin g Volume at MEV before FA................64 Table 19 Mean Volume at MEV within FA.....................................................................64 Table 20 ANOVA Results of Mean Volume at MEV within FA...................................65 Table 21 Tukey Results of Mean Volume at MEV within FA........................................65 Table 22 Mean Discharging Volume at MEV after FA...................................................66 Table 23 ANOVA Results of Mean Discharging Volume at MEV after FA...................66 Table 24 Mean Volume at HEV before FA.....................................................................67 PAGE 8 vi Table 25 ANOVA Results of Mean Volume at HEV before FA.....................................68 Table 26 Tukey Results of Mean Volume at HEV before FA.........................................68 Table 27 Mean Discharging Volume at HEV within FA.................................................69 Table 28 ANOVA Results of Mean Discharging Volume at HEV within FA................69 Table 29 Tukey Results of Mean Discharging Volume at HEV within FA.....................69 Table 30 Mean Volume at HEV after FA........................................................................70 Table 31 ANOVA Results of Mean Volume at HEV after FA........................................71 Table 32 ANOVA Findings for Discharging Volume.....................................................71 Table 33 Tukey Findings for Discharging Volume..........................................................72 Table 34 Mean Speed at LEV before FA.........................................................................75 Table 35 ANOVA Results of Mean Speed at LEV before FA........................................76 Table 36 Mean Speed within Functional Area at LEV within FA...................................76 Table 37 ANOVA Results of Mean Speed at LEV within FA........................................76 Table 38 Mean Speed at LEV after FA...........................................................................77 Table 39 ANOVA Results of Mean Speed at LEV after FA...........................................78 Table 40 Mean Speed at MEV before FA........................................................................78 Table 41 ANOVA Results of Mean Speed at MEV before FA......................................79 Table 42 Mean Speed at MEV within FA........................................................................80 Table 43 ANOVA Results of Mean Entry Volume at MEV within FA..........................80 Table 44 Tukey Results of Mean Speed at MEV within FA............................................80 Table 45 Mean Speed at MEV after FA...........................................................................81 Table 46 ANOVA Results of Mean Speed at MEV after FA..........................................81 Table 47 Mean Speed at HEV before FA.........................................................................82 Table 48 ANOVA Results of Mean Speed at HEV before FA........................................82 Table 49 Tukey Results of Mean Speed at HEV before FA............................................82 Table 50 Mean Speed at HEV within FA.........................................................................84 Table 51 ANOVA Results of Mean Speed at HEV within FA........................................84 Table 52 Tukey Results of Mean Speed at HEV within FA............................................84 Table 53 Mean Speed at HEV after FA...........................................................................86 PAGE 9 vii Table 54 ANOVA Results of Mean Speed at HEV after FA...........................................86 Table 55 Tukey Results of Mean Speed at HEV after FA...............................................86 Table 56 ANOVA Findings for Speed.............................................................................87 Table 57 Tukey Findings for Speed.................................................................................87 Table 58 Mean Lane Change Number at LEV before FA...............................................90 Table 59 ANOVA Results of Lane Change Number at LEV before FA.........................91 Table 60 Mean Lane Change Number at LEV within FA...............................................92 Table 61 ANOVA Results of Lane Change Number at LEV within FA.........................92 Table 62 Tukey Results of Lane Change Number at LEV within FA.............................92 Table 63 Mean Lane Change Number at LEV after FA..................................................93 Table 64 ANOVA Results of Lane Change Number at LEV after FA............................93 Table 65 Tukey Results of Lane Change Number at LEV after FA................................93 Table 66 Mean Lane Change Number at MEV before FA..............................................95 Table 67 ANOVA Results of Lane Change Number at MEV before FA........................95 Table 68 Mean Lane Change Number at MEV within FA..............................................95 Table 69 ANOVA Results of Lane Change Number at MEV within FA........................96 Table 70 Tukey Results of Lane Change Number at MEV within FA............................96 Table 71 Mean Lane Change Number at MEV after FA.................................................97 Table 72 ANOVA Results of Mean Lane Change Number at MEV after FA.................97 Table 73 Mean Lane Change Number at HEV before FA...............................................98 Table 74 ANOVA Results of Mean Lane Change Number at HEV before FA..............98 Table 75 Tukey Results of Lane Change Number at HEV before FA.............................98 Table 76 Mean Lane Change Number at HEV within FA...............................................99 Table 77 ANOVA Results of Lane Change Number at HEV within FA.......................100 Table 78 Tukey Results of Lane Change Number at HEV within FA...........................100 Table 79 Mean Lane Change Number at HEV after FA................................................101 Table 80 ANOVA Results of Mean Lane Change Number at HEV after FA...............101 Table 81 Tukey Results of Mean Lane Change Number at HEV after FA....................101 Table 82 ANOVA Findings for Lane Change Number.................................................104 PAGE 10 viii Table 83 Tukey Findings for Lane Change Number......................................................104 Table 84 Entry Volume Sensitivity on Running Speed before FA................................106 Table 85 Entry Volume Sensitivity on Total Lane Change Number before FA............106 Table 86 Entry Volume Sensitivity on Running Speed within FA................................108 Table 87 Entry Volume Sensitivity on Total Lane Change Number within FA............108 Table 88 Entry Volume Sensitivity on Running Speed after FA...................................109 Table 89 Entry Volume Sensitivity on Total La ne Change Number after FA...............109 Table 90 Free Flow Speed Sensitivity on Link Volume before FA...............................111 Table 91 Free Flow Speed Sensitivity on Total Lane Change Number before FA........111 Table 92 Tukey Results of Free Flow Speed on Total Lane Change Number before FA 111 Table 93 Free Flow Speed Sensitivity on Link Volume within FA...............................112 Table 94 Free Flow Speed Sensitivity on Lane Change Number within FA.................113 Table 95 Free Flow Speed Sensitivity Tukey Analysis.................................................113 Table 96 Free Flow Speed Sensitivity on Link Volume after FA..................................114 Table 97 Free Flow Speed Sensitivity on Lane Change Number after FA....................114 Table 98 Tukey Results of Free Flow Speed on Lane Change Number after FA..........114 Table 99 Freeway Grad e Sensitivity on Running Speed befo re FA.............. .......... ......116 Table 100 Tukey Results on Grade Sensitivity on Running Speed before FA..............116 Table 101 Freeway Grade Sensitivity on Lane Change Number before FA..................116 Table 102 Tukey Results of Grade on Lane Ch ange Number before FA......................116 Table 103 Freeway Grade Sensitivity on Running Speed within FA............................118 Table 104 Tukey Results of Grade Sensitivity on Running Speed within FA...............118 Table 105 Freeway Grade Sensitivity on Lane Change Number within FA..................118 Table 106 Tukey Results of Grade on Lane Change Number within FA......................118 Table 107 Freeway Grade Sensitivity on Running Speed after FA...............................119 Table 108 Tukey Results of Grade Sensitivity on Running Speed after FA..................119 Table 109 Freeway Grade Sensitivity on Lane Change Number after FA.....................120 Table 110 Tukey Results of Grade Sensitivity on Lane Change Number after FA.......120 PAGE 11 ix Table 111 Truck Percentage Sensitivity on Running Speed before FA.........................121 Table 112 Truck Percentage Sensitivity on Lane Change Number before FA..............121 Table 113 Tukey Results of Truck Percentage on Lane Change Number before FA....122 Table 114 Truck Percentage Sensitivity on Running Speed within FA.........................123 Table 115 Truck Percentage Sensitivity on Lane Change Number within FA..............123 Table 116 Tukey Results of Truck Percentage on Lane Change Number within FA....123 Table 117 Truck Percentage Sensitivity on Running Speed after FA............................124 Table 118 Truck Percentage on Lane Change Number after FA...................................124 Table 119 Tukey Results of Truck Percentage on Lane Change Number after FA.......124 Table 120 Restrictions to Truck Sensitivity on Running Speed before FA...................126 Table 121 Restrictions to Truck Sensitivity on Lane Change Number before FA........127 Table 122 Restrictions to Truck Sensitivity on Running Speed within FA...................127 Table 123 Restrictions to Truck Sensitivity on Lane Change Number within FA........127 Table 124 Restrictions to Truck Sensitivity on Running Speed after FA......................129 Table 125 Restrictions to Truck Sensitivity on Lane Change Number after FA...........129 Table 126 Location of Exit Sign Sensitivity on Running Speed before FA..................131 Table 127 Location of Exit Sign Sensitivity on Lane Change Number before FA........131 Table 128 Location of Exit Sign Sensitivity on Running Speed within FA..................132 Table 129 Location of Exit Sign Sensitivity on Lane Change Number within FA........132 Table 130 Location of Exit Sign Sensitivity on Running Speed after FA.....................133 Table 131 Location of Exit Sign Sensitivity on Lane Change Number after FA...........134 Table 132 LRM for Speed of Tapered OneLane Exit before FA.................................136 Table 133 ANOVA of Speed Modeling of Ta pered OneLane Exit before FA...........136 Table 134 Coefficients of Speed Modeling of Tapered OneLane Exit before FA.......136 Table 135 LRM for Lane Change Number before FA...................................................137 Table 136 ANOVA of Lane Change Number Modeling Number before FA................137 Table 137 Coefficients of Lane Change Number Modeling before FA.........................137 Table 138 LRM for Speed within FA.............................................................................137 Table 139 ANOVA of Running Speed Modeling within FA.........................................137 PAGE 12 x Table 140 Coefficients of Speed Modeling within FA..................................................138 Table 141 LRM for Lane Change Number within FA...................................................138 Table 142 ANOVA of Lane Change Number Modeling within FA..............................138 Table 143 Coefficients of Lane Change Number Modeling within FA.........................138 Table 144 LRM for Speed after FA...............................................................................139 Table 145 ANOVA of Speed Modeling after FA..........................................................139 Table 146 Coefficients of Speed Modeling after FA.....................................................139 Table 147 LRM for Lane Change Number after FA......................................................140 Table 148 ANOVA of Lane Change Number Modeling after FA.................................140 Table 149 Coefficients of Lane Change Number Modeling after FA............................140 PAGE 13 xi List of Figures Figure 1 Taper Type OneLane Exit Terminal..................................................................9 Figure 2 Parallel Type OneLane Exit Terminal..............................................................10 Figure 3 Taper Type TwoLane Exit Terminal................................................................10 Figure 4 Parallel Type TwoLane Exit Terminal.............................................................11 Figure 5 The Effect of Access Controlled Frontage on Volume.....................................13 Figure 6 NonFreeFlow Loop and FreeFlow Loop.......................................................14 Figure 7 Auxiliary Lanes Terminat ed with One Lane Exit Ramp ................... ........... .....14 Figure 8 Auxiliary Lanes Terminated with Two Lane Exit Ramp........ ................ ..........15 Figure 9 Auxiliary Lanes Terminated with Down stream Taper............ ................ ..........15 Figure 10 Analysis of Ramp Weaving Section................................................................16 Figure 11 A Constraint Operation of a Ramp Weaving Section......................................17 Figure 12 A Multiple Weaving Area with Flow Distribution..........................................17 Figure 13 Analysis of a Major Weaving Area.................................................................18 Figure 14 Black down Arrow...........................................................................................24 Figure 15 Black Right down Arrow.................................................................................24 Figure 16 Black Right up Arrow......................................................................................25 Figure 17 Ideal Paths of Motorists before Exit Ramp......................................................25 Figure 18 Unnecessary Lane Changes before Exit Ramp................................................26 Figure 19 Truck Percentage Distributions.......................................................................39 Figure 20 Tapered OneLane Exit Ramp.........................................................................47 Figure 21 Tapered TwoLane Exit Ramp........................................................................47 Figure 22 Parallel OneLane Exit Ramp..........................................................................48 Figure 23 Parallel TwoLane Exit Ramp.........................................................................48 Figure 24 Mean Volume Comparisons at LEV before FA..............................................60 PAGE 14 xii Figure 25 Mean Volume Comparisons at LEV within FA..............................................61 Figure 26 Mean Volume Comparisons at LEV after FA.................................................63 Figure 27 Mean Volume Comparisons at MEV be fore FA.............................................64 Figure 28 Mean Volume Comparisons at MEV within FA.............................................66 Figure 29 Mean Volume Comparisons at MEV after FA................................................67 Figure 30 Mean Volume Comparisons at HEV before FA..............................................68 Figure 31 Mean Volume Comparisons at HEV within FA..............................................70 Figure 32 Mean Volume Comparisons at HEV after FA.................................................71 Figure 33 Mean Speed Comparisons at LEV before FA.................................................76 Figure 34 Mean Speed Comparisons at LEV with in FA.................................................77 Figure 35 Mean Speed Comparisons at LEV after FA....................................................78 Figure 36 Mean Speed Comparisons at MEV before FA................................................79 Figure 37 Mean Speed Comparisons at MEV with in FA................................................80 Figure 38 Mean Speed Comparisons at MEV after FA...................................................81 Figure 39 Mean Speed Comparisons at HEV before FA.................................................83 Figure 40 Mean Speed Comparisons at HEV within FA.................................................85 Figure 41 Mean Speed Comparisons at HEV after FA....................................................86 Figure 42 Mean Lane Change Comparisons at LEV before FA......................................91 Figure 43 Mean Lane Change Comparisons at LEV within FA......................................93 Figure 44 Mean Lane Change Comparisons at LEV after FA.........................................94 Figure 45 Mean Lane Change Comparisons at MEV before FA.....................................95 Figure 46 Mean Lane Change Comparison at MEV within FA......................................96 Figure 47 Mean Lane Change Comparisons at MEV after FA........................................97 Figure 48 Mean Lane Change Comparisons at HEV before FA.....................................99 Figure 49 Lane Change Comparisons at HEV within FA..............................................100 Figure 50 Mean Lane Change Comparisons at HEV after FA......................................102 Figure 51 Entry Volume Sensitivity on Running Speed before FA...............................107 Figure 52 Entry Volume Sensitivity on Total Lane Change Number before FA..........107 Figure 53 Entry Volume Sensitivity on Running Speed within FA...............................108 PAGE 15 xiii Figure 54 Entry Volume Sensitivity on Tota l Lane Change Number within FA.........109 Figure 55 Entry Volume Sensitivity on Running Speed after FA.................................110 Figure 56 Entry Volume Sensitivity on Total Lane Change Number after FA.............110 Figure 57 Free Flow Speed Sensitivity on Link Volume before FA.............................112 Figure 58 Free Flow Speed Sensitivity on Total Lane Change Number before FA......112 Figure 59 Free Flow Speed Sensitivity on Link Volume within FA.............................113 Figure 60 Free Flow Speed Sensitivity on Lane Change Number within FA...............113 Figure 61 Free Flow Speed Sensitivity on Link Volume after FA................................115 Figure 62 Free Flow Speed Sensitivity on Lane Change Number after FA..................115 Figure 63 Freeway Grade Sensitivity on Runni ng Speed before FA.............................117 Figure 64 Freeway Grade Sensitivity on Lane Change Number before FA..................117 Figure 65 Freeway Grade Sensitivity on Runni ng Speed within FA.............................118 Figure 66 Freeway Grade Sensitivity on Lane Change Number within FA..................119 Figure 67 Freeway Grade Sensitivity on Speed after FA..............................................120 Figure 68 Freeway Grade Sensitivity on Lane Change Number after FA.....................120 Figure 69 Truck Percentage Sensitivity on Ru nning Speed before FA.........................122 Figure 70 Truck Percentage Sensitivity on La ne Change Number before FA..............122 Figure 71 Truck Percentage Sensitivity on Running Speed within FA.........................123 Figure 72 Truck Percentage Sensitivity on La ne Change Number within FA..............124 Figure 73 Truck Percentage Sensitivity on Speed after FA...........................................125 Figure 74 Truck Percentage Sensitivity on La ne Change Number after FA.................125 Figure 75 Restrictions to Truck Sensitivity on Running Speed.....................................126 Figure 76 Restrictions to Truck Sensitivity on Lane Change Number before FA.........127 Figure 77 Restrictions to Truck Sensitivity on Running Speed within FA....................128 Figure 78 Restrictions to Truck Sensitivity on Lane Change Number within FA.........128 Figure 79 Restrictions to Truck Sensitivity on Running Speed after FA......................129 Figure 80 Restrictions to Truck Sensitivity on Lane Change Number after FA............129 Figure 81 Location of Exit Sign Sensitivity on Running Speed before FA...................131 Figure 82 Location of Exit Sign Sensitivity on Lane Change Number before FA........131 PAGE 16 xiv Figure 83 Location of Exit Sign Sensitivity on Running Speed within FA...................132 Figure 84 Location of Exit Sign Sensitivity on Lane Change Number within FA........133 Figure 85 Location of Exit Sign Sensitivity on Running Speed after FA......................134 Figure 86 Location of Exit Sign Sensitivity on Lane Change Number after FA...........134 PAGE 17 xv Freeway Exit Ramp Traffic Flow Research Based on Computer Simulation Xu Wang ABSTRACT Interstate highways are one of the most important components of the transportation infrastructure in America. Freeway ramps play an important role in the whole interstate transportation system. This paper researches the traffic flow characteristics of four typical exit ramps in USA, which are tapered onelane exit, tapered twolane exit, parallel onelane exit and parallel twolane exit. Computer simulation software, such as CORSIM and HCS are applied as the main tools in this research. ANOVA and Tukey are used for statistical purpose. It compares the maximum capacity, average running speed and the total lane change number of those four exit ramps. It is found that no matter in terms of traffic discharging rate or total lane charging number; the tape red twolane exit has the best operational performance. Tapered onelane exit ramp has the least capacity. Parallel onelane exit and parallel twolane exit have very limited traffic operational difference in terms of capacity and running speed. It is recommended that parallel twolane exit ramp should not be designed along th e freeway if the right of way along arterial road is enough. It is observed from the simulation data that the grade of freeway, truck percentage, restricted to the truck use of certain lane(s) and the location of exit sign have significant impact on the running speed and total lane change number. An uphill can decrease the PAGE 18 xvi running speed dramatically while more truck brings more lane change, causing safety concerns. It is found that when trucks are restricted to the right two most lane, there will be less lane change number comparing with trucks are not restricted. Location of exit sign operates well at the distance between 4000 ft to 5000 ft. does have a significant impact on the operational speed and total lane change number before, within or after functional area of an exit, based on the data analysis of simulation runs. PAGE 19 1 Chapter 1 Introduction 1.1. Background Interstate freeways are one of the most important components of the transportation infrastructure in America. Freeway ramps are the main connection facilities between freeway and arterial road in the whole interstate transportation system. The rapid growth of transportation in many States, such as Florida, has caused and is causing queues and delays on freeway mainline as well as on ramps. The freeway offramp, or exit ramp, serving as the discharging tool from freeway mainline to local arterial road, is observed to be the bottleneck and heavy crash spot of the freeway system. The queuing vehicles along the exit ramps sometimes even spill back onto the freeway mainline. Spillback of traffic flow along the freeway may neither creates safety issues where highspeed traffic on the freeway suddenly comes upon stop but also creates operational and environmental problems, such as decreased running speed, more oil consumptions and heavy air pollution. Different freeway exit ramps may have different safety concerns and operational performance in dealing with the increasing traffic volume and congestions based on some researches. In order to better understand the traffic flow characteristics of different ramp types, a research is necessary to investigate the traffic features and queue discharging ability of each ramp type. Exit ramp terminals are classified as either single lane or multilane, according to the number of lanes on the ramp at the terminal and as either a tapered or parallel type, according to the configuration of the speed change lane. Typically, there are four main types of exit ramp based on the combination of exit lane number and exit lane PAGE 20 2 configurations: tapered onelane exit, tapere d twolane exit, parallel onelane exit and parallel twolane exit. General, onelane exit can deal with low exiting volume; twolane exit can deal with relatively higher exiting volume. Tapered type gives motorists an optional on exiting or continuing while parallel type gives motorists no choice but have to leaving. The tapered type has been found to operate smoothly on relatively heavy volume freeway because there are less unnecessary lane change maneuver needed. The parallel type has higher crash rate caused by more lane change maneuver but it can offer a storage area for exiting vehicles when something happened at local arterial road access point, making the queuing vehicles spillback to the ramp terminals. Many studies and researches have tried to study the traffic operation and safety characteristics of different exit ramp terminals. The past researches for exit ramp can be categorized into two groups. One is to collect the field traffic and crash data, classifying the crash data as crash number, crash rate and crash type, then attributing the different classifications to each exit ramp, evaluating the safety performance of different ramp by their crash index. Another group is to analyze the traffic flow characteristics of different ramp types by field data or computer simulation, trying to get the capacity, density, running speed and LOS (Level of Service) of researched exit types under certain traffic and geometry conditions. To be compared with freeway mainline traffic flow characteristics, the traffic flow features along the exit ramp are much more complicated. Apart from the conventional factors, such as the volume and free flow speed, etc, the traffic flow along the exit ramp has its own particular variables impacting its characteristics, such as the percentage of exiting traffic volume, the location of exit sign to the terminal gore area, the restriction to truck usage of certain lane, etc. Furthermore, some factors along the exit ramp are easy to identify, such as the ramp posted speed, other factors are very difficult to be measured, such as how many PAGE 21 3 motorists are familiar with the ramp type, the percentage of drivers yielding the rightofway to lanechanging vehicles attempting to merge ahead, etc. The traffic flow characteristics along the freeway exit ramp are far from sufficient research, what is the traffic flow features of these four types of exit ramp, what is the traffic flow features along the different segments of a particular exit ramp, and what is the difference of traffic operational performance about these four types of exit ramp needs more researches. 1.2. Problem Statement Although some research effects have been fulfilled on the traffic flow research of certain exit ramps, it is still far from being specialized study. The research results obtained from one study may not be applicable to other locations. The engineering problems associated with exit ramp studies can be sorted out into two aspects: One is the diversity of field scenarios; e ach exit ramp site for data collection has difference geometry features, such as the free way curvature, freeway configuration, slope, ramp terminal outer edge alignment, etc, also, each exit ramp site has different traffic and user conditions, such as the fleet information, the familiarity of drivers to that area, the percentage of aggressive drives, etc. the combination of geometry features, user difference and traffic characteristics make each exit ramp unique. A lot of approximations and assumptions must be done to draw a conclusion or conclusions. The results based on approximations are normally with less creditability and comparability. Further more, the data collected from field allows less or no adjustment for certain variables to evaluate the sensitivity of a certain variable. The collected data are uncontinuous variables for most cases. Another aspect is the huge budget and time associated with the field data collection. Although certain geometry data of exit ramp can be collected by aviation photograph, the traffic data can only be gathered at exit ramp area at certain time periods. PAGE 22 4 Some exit ramp configurations can offer desirable traffic and geometry conditions for observers, but some can not. Also, the difficulty to collect field data is the complexity of traffic flow features along a certain exit ramp Significant factors impact the traffic flow characteristics at exit ramp, which make it hard and costly to collect all of the related data. More, the interactions of some variables are very complicated; the value of a variable may change correspondingly to another factor or factors. For instance, the lane distribution (the percentage of total vehicles occupy a certain lane) has direct relation with the restriction to truck usage and reserved carpool lane or lanes. Based on the mentioned engineering problems associated with exit ramp study, it is realistic to research the traffic flow charact eristics by computer simulation. It would be easily and economical to collect all the necessary traffic data. More critical, the researcher can manipulate some factors at will. 1.3. Research Objectives and Expected Results The primary objective of this research is to explore the traffic flow characteristics of these four types of exit ramp by the mean s of computer simulation. The interaction of traffic flow factors, such as the free flow speed and some external factors, such as the location of exit sign, will be addressed in details as well. The expect results may contain the following aspects: 1) In terms of the number of exit ramp, what is the difference between tapered type and parallel type of exit ramp? Or more clearly, when the exit ramp is onelane, what is the good for taper type and what is the good for parallel type? When the exit ramp is twolane, what is the advantage of taper type and what is the advantage of parallel type? 2) In terms of exit type, what is the differ ence between onelane exit and twolane exit ramp? Besides for the traffic volume, any other factors influence the design of exit ramp lane number? In another word, for tapered type exit ramp, what is the PAGE 23 5 good for onelane and what is the good for twolane? For parallel type exit ramp, what is the advantage of onelane and what is the advantage of twolane exit ramp? 3) What is the sensitivity of design elements, such as the freeway grade, truck percentage, the location of exit sign on the design of exit types? 1.4. Significance of This Research This research is very impo rtant to the currently increasing exacerbated traffic conditions. The contributions of this research may be applied to the following fields: One is to make necessary complementaritie s to the traffic flow theories in terms of microscope speed characteristics, microscope flow characteristics, capacity analysis and queuing analysis; The other is to offer reference for th e evaluation of existing exit ramps. The third is to support alternatives for new ramp planning and design. 1.5. Methodology In this study, considerable amount of data are needed for traffic flow analysis, it is unpractical to collect all the necessary data from the field to represent the essential combinations of different traffic characteristics and geometric features. TSISCORSIM software and VBA (Visual Basic Application) programs were used to develop and generate most of the input data and ou tput MOEs (Measure of Effectiveness). Statistics software SPSS 13.0 (Statistical Package for the Social Sciences) and windows excel application were used as well to develop the linear regression models for analyzing the traffic flow characteristics, to analyze the variance of four types of exit ramp in terms of upstream and downstream of exit ramp functional area. Although from the mascoscope point of vi ew, it is common sense that twolane exit ramp has higher capacity than onelane exit ramp, the microscope index, such as the spacemean speed, speed deduction rate and total lane change number happened within a typical area are still obscure for these four types of exit ramp. This dissertation uses PAGE 24 6 discharging volume rate, running speed and total lane change number as the main MOEs, trying to reveal the different microscope traffic flow features of these four types of exit ramp before, within and after the functional area. 1.6. Organization of This Paper The dissertation presents literature review at chapter two, followed by the factor selection and data collection experiment design in Traffic Software Integrated System 6.0. Traffic volume discharging comparing, speed generated comparing and total lane change comparing before, within and after the ramp functional area were performed using ANOVA and Tukey analysis. Entry volume, free flow speed, truck percentage, restriction to truck at main line, grade and location of exit ramp guiding sign were tested for sensitivity analysis. Finally, conclusions, implications of findings, and recommendations for further research were summarized. Chapter two contained various digests fr om the current literatures, with an emphasis on design criteria on the geometric fe atures of exit ramp; In addition, some applications of CORSIM simulation in tra ffic engineering were presented as well. Chapter three selected the related factors for CORSIM simulation for this research. Although many factors do have impact to the capacity and traffic operational characteristics on the different exit ramp choice, the selected factors were limited by the availability of the software and the resear ch time. In the study, seven factors were selected to input to CORSIM simulation after careful consideration. Chapter four designed a data collection process in CORSIM, entry Volume, free flow speed, number of Simulation runs and some other default value changed to generate desired data. Along the procedure, the required traffic data could be obtained. The methodology used for ANOVA and Tukey are explained in detail in this chapter also. Chapter five illustrated the traffic discharging volume based on the traffic data collected from the CORSIM simulation. The tr affic discharging volume is compared for three different segments along the freeway for four different exit ramps. The three PAGE 25 7 segments are before the functional area, within the functional area and after functional area. Chapter six analyzed the speed patterns at different exit ramp based on the traffic data collected from the CORSIM simulation. It used the same procedures as for the traffic discharging volume. Chapter seven presented the total lane changing number at different exit ramp based on simulation runs. It also has the same methodology as traffic discharging volume and speed analysis. Chapter eight offered the sensitivity analys is of entry traffic volume, free flow speed, freeway grade, truck percentage, restrictions to lane usage of truck and location of exit sign. It provided four linear regression models for different exit ramp types too. Finally, Chapter nine presented a final discussion, summary of the findings and recommendations for further researches. PAGE 26 8 Chapter 2 Literature Review 2.1. General Extensive work was conducted to search current rules, design manuals, like AASHTO Green book, standards and regulations, state of practice in Florida and United States. In addition, past research and studies related to the safety and operation issues related to freeway exit ramp were also searched and reviewed. General, this chapter can be divided into three parts: the first is the design aspects of exit ramp types, the second are the safety and operational issues about the freeway exit ramp, the third part is the simulation issues 2.2. Design Standards At A Policy on Geometric Design of Highways and Streets, published by American Association of State Highway and Transportation Officials, 2004, chapter 10, Grade Separations and Interchanges, page 849, there is a segment address the design issues of singlelane free flow exit terminals. The following is the digest from the green book. 2.2.1. OneLane Taper Type Exit The taper type exit fits the direct path preferred by most drivers, permitting them to follow an easy path within the diverging area. The tapertype exit terminal beginning with an outer edge alignment break usually provides a clear indication of the point of departure from the through lane and has general been found to operate smoothly on highvolume freeways. The divergence angle is usually between 2 and 5 degrees. Studies of this type of terminal show that most vehicles leave the through lane at relatively high speed, thereby reducing the potential for rearend collisions as a result of PAGE 27 9 deceleration on the through lane. The speed change can be achieved off the traveled way as the exiting vehicle moves along the taper onto the ramp proper. Figure 1 shows a typical design for a taper type exit. Figure 1 Taper Type OneLane Exit Terminal The taper type exit terminal design can be used advantageously in developing the desired long, narrow, triangular emergency maneuver area just upstream from the exit nose located at a proper oddest from both the through lane and separate ramp lane. The taper configuration also works well in the lengthwidth superelevation adjustments to obtain a ramp cross slope different from that of the through lane. 2.2.2. OneLane Parallel Type Exit A parallel type exit terminal usually begins with a taper, followed by an added lane that is parallel to the traveled way. A typical paralleltype exit termin al is shown in figure 2. This type of terminal provides an inviting exit area, because the foreshortened view of the taper and the added lane width are very apparent. Paralleltype exits operate best when drivers choose to exit the through lane sufficiently in advance of the exit nose to permit deceleration to occur on the added lane and allow them to follow a path similar to that encouraged by a taper design. Drivers who do not exit the through lane sufficiently in advance of the exit nose will likely utilize a more abrupt reversecurve maneuver, which is somewhat unnatural and can sometimes result in the driver slowing in the through lane. PAGE 28 10 In locations where both the mainline and ra mp carry high volumes of traffic, the deceleration lane provided by the paralleltype exit provides storage for vehicles that would otherwise undesirably queue up on the through lane or on a shoulder, if available. Figure 2 Parallel Type OneLane Exit Terminal 2.2.3. TwoLane Exits Where the traffic volume leaving the freeway at an exit terminal exceeds the design capacity of a single lane, a twolane exit terminal should be provided. To satisfy lanebalance needs and not to reduce the basic number of through lanes, it is usually appropriate to add an auxiliary lane upstream form the exit. A distance of approximately 1500ft is recommended to develop the full capacity of a twolane exit. Typical designs for twolane exit terminals are shown in figure 3 and figure 4, figure 3 is tapered type design, whereas figure 4 is the parallel design. Figure 3 Taper Type TwoLane Exit Terminal PAGE 29 11 In cases where the basic number of lanes is to be reduced beyond a twolane exit, the basic number of lanes should be carried beyond the exit before the outer lane is dropped. This design provides a recovery area for any through vehicles that remain in the lane. Figure 4 Parallel Type TwoLane Exit Terminal With the parallel type of twolane exit, as shown is figure 4, the operation is different from the taper type in that traffic in the outer through lane of the freeway must change lanes in order to exit. In fact, an exiting motorist is required to move two lanes to the right in order to use the right lane of th e ramp. Thus, considerable lane changing is needed in order for the exit to operate efficiently. This entire operation takes place over a substantial length of highway, which is dependent in part on the total traffic volume on the freeway and especially on the volume using the exit ramp. The total length from the beginning of the first taper to the point wh ere the ramp traveled way departs from the righthand through lane of the freeway should range from 2500 ft for turning volumes of 1500vph or less upward to 3500 ft for turning volumes of 3000vph. 2.3. Operation and Safety At the sponsor of The U.S. Department of Transportation (DOT) and Federal Highway Administration (FHWA), TurnerFairb anks Highway Research Center finished a technical report called statistical model of accidents on interchange ramps and speed change lanes. The objective of their research was to develop statistical models for PAGE 30 12 defining the relationship between traffic accidents and highway geometric design elements and traffic volumes for interchange ramps and speedchange lanes. The data base used to develop their models consisted of data for interchange ramps and speedchange lanes in the State of Washington and was obtained from the FHWA Highway Safety Information System. Additional geometric design features were obtained from the review of interchange diagrams. Data on other geometric design features, such as the ramp grades and horizontal curvature, were collected for a sample of ramps from aerial photographs and other existing highway agency files. The statistical modeling approaches used in their research included Poisson and negative binomial regression. Regression models to determine relationships between accidents and the geometric design and traffic volume characteristics of ramps were difficult to develop because the observed accident frequencies for most ramps and speedchange lanes are very low. The regression models developed, based on the negative binomial distribution, explained between 10 and 42 percent of the variability in the accident data, with the negative binomial distribution providing a poor to moderate fit to the data. However, most of that variability was explained by ramp Annual Average Daily Traffic (AADT). Other variables found to be significant in some models included mainline freeway AADT, area type (rural/urban ), ramp type (on/off), ramp configuration, and combined length of ramp and speedchange lane. The best models obtained for predicting accident frequencies were those obtained when modeling the combined accident frequency for an entire ramp, together with its adjacent speedchange lanes. These models provided a better fit than separate models for ramps and speedchange lanes. Models developed to predict total accidents generally performed slightly better than did models to predict fatal and injury accidents. I Kristine Williams, Huaguo Zhou, from CUTR of USF Waddah Farah, and from FDOT research the Benefits/Costs of Access Control Near Interchanges, the concluded that The benefits of acquiring additional LA ROW (Limited Access Right of Way) near an interchange in advance of development far exceed the cost. The minimum length of PAGE 31 13 LA ROW is 600 feet, the desirable length of LA ROW is1320 feet. Figure 5 is cut from their research results.II 1400 1500 1600 1700 1800 1900 2000 2100 200400600800100012001400 Length of Access Controlled Frontage (feet)Volume (Off Ramp or Cross Street) Figure 5 The Effect of Access Controlled Frontage on Volume Joe Bared, Greg L. Giering and Davey L. Warren researched the relationship between safety and acceleration, deceleration la ne lengths, a statistical model of accidents was developed to estimate accident frequencies for entire ramps as a function of speed change lane length among other variables. According to the accident model developed in their study, the longer speed change lane shows the less accident frequency. III Dominique Load and James A. Bonneson studied the ramp design configurations, they use a predictive model which was already developed with sufficient data, in their paper, 44 ramps are selected and used in the calibration process. The results show that the exit ramp are more dangerous than entrance ramp and the nonfreeflow ramp experience twice as many accidents as other types of ramps. The following are the figures cut from their paper explain freeflow ramp and nonfreeflow ramp.IV PAGE 32 14 Figure 6 NonFreeFlow Loop and FreeFlow Loop 2.4. Simulation Ralph A.Batenhorst, Jeff G.Gerken researches the operational characteristic of terminating freeway auxiliary lanes with one lane exit and two lane exits. They summarized the findings of a case study on the operational analysis of weaving areas created by auxiliary lanes between two successive interchanges. For auxiliary lanes less than 1,500 feet in length, AASHTO lane balance principles permit the termination of the auxiliary lane with a onelane exit ramp. Fo r auxiliary lanes greater than 1,500 feet in length, the lane balance principles require that the auxiliary lane be dropped with a twolane exit ramp or tapered into the through roadway downstream of a onelane exit ramp. Figure 7 Auxiliary Lanes Terminated with One Lane Exit Ramp The three illustrations, which are figure 6, figure 7 and figure 8 are the typically three scenarios the paper applied. PAGE 33 15 Figure 8 Auxiliary Lanes Terminated with Two Lane Exit Ramp Figure 9 Auxiliary Lanes Terminated with Downstream Taper The operational analyses of the case study were conducted as part of a Major Investment Study (MIS) in Dallas, Texas. As part of the study, auxiliary lanes were recommended at various locations along two major freeway corridors. At twenty of these locations, additional analyses were conducted to compare the qualityofservice provided by a onelane exit ramp versus a twolane exit ramp. The range of traffic and geometric conditions among the twenty sites varied. The analyses were conducted using three software packages: the Highway Capacity Software (HCS), CORSIM and Simtraffic. The findings of the case study suggest that a onelane exit ramp may provide the best traffic operations regardless of weaving length. The experience gained from the case study is presented to aid practitioners in the design of safe and efficient freeway facilities and to aid researchers in current and future efforts to define and understand the operational effects of geometric design.V A master student called Suresh Ramachandran from the Virginia Polytechnic Institute finished his master thesis which focused on the simulation comparing of PAGE 34 16 CORSIM and HCS. Normally, weaving exist at the ramp function area, for onramp function area, the upstream vehicle weave and make lane change before the physical gore to avoid the impact from the incoming vehicle of the ramp, the incoming vehicle weave and make lane change trying merge into the main traffic stream. For offramp area, the upstream vehicle weave and make lane chan ge, preparing to exit or avoid the exiting vehicle; after the physical gore area, vehicles may weave and make lane change again to back to normal traffic flow. He compared the traditional way, which is HCS, with the new simulation method, which is CORSIM; by identify the different results in the same inputs. He set 4 different scenarios; each scenario has different geometric design and traffic volume. By running HCS and CORSIM respectively, he compared the results derived from each scenario. The following figure 9, 10, 11, and 12 are the four illustrations. Figure 10 Analysis of Ramp Weaving Section PAGE 35 17 Figure 11 A Constraint Operation of a Ramp Weaving Section He concluded that CORSIM are not sensitive to various geometric factors such as length of the acceleration lane, deceleration lane etc. While higher volume estimates are produced by CORSIM, it also produces lower density and higher speed estimates than the 94HCM. Figure 12 A Multiple Weaving Area with Flow Distribution He also recommends that the anticipatory warning sign distance should be controlled by the user. In the current version of CORSIM, this distance is set as 1500 ft from the end of the onramp, and this value cannot be changed. PAGE 36 18 Figure 13 Analysis of a Major Weaving Area More than one warning sign should be posted for a vehicle in the mainline indicating an off ramp destination. In the pr esent case, the simulation software allows for one warning sign only .This is not true in real life scenario. Variation of desired freeflow speed ov er different time periods should be possible. In a real situation desired freeflow speed may vary for different time periods. In the current version of CORS IM, desired freeflow speed is fixed for all time periods. Different types of weaving configurations like Type A or Type B or Type C etc. should be considered while designing a weaving model. Because FRESIM cannot simulate two freeway systems connecting each other directly, the simulation software supports only a Type A configuration. Some existing weaving situations like two freeway merging or two freeway diverging cannot be modeled using CORSIM. In the current software only a ramp and freeway are allowed to merge. The logic use for modeling the behavior of driver yielding to lane changes should be modified. The logic behind this state is if there is a vehicle trying to change lanes, the cooperative driver code of its putative follower in the adjacent lane will be checked. For a cooperative driver a risk value of 8 ft/sec is assigned while a value of 10 ft/sec is assigned to a noncooperative driver. However in the current version of the program logic assigns this code to the vehicle trying to change lanes rather than to the follower. PAGE 37 19 OD based output should be generated. In the current version of CORSIM origin destination study can be conducted. In order to test the validity of OD logic a user has to view the graphics. However a user cannot obtain an OD volume for each node. Lots of assumptions need to be done in order to make a comparison analysis between CORSIM and HCM. The variation of random seed number to generate traffic flow conditions did not have effect on the model. This shows that there is a discrepancy in the generation of traffic using random seed numbers. VI Kay Fitzpatrick, Marcus A. Brewer, and Steven Venglar from Texas Transportation Institute research the roadway design issues and the managed lane ramp by plenty of literature review; they found that of the 23 states that had all or part of their design manuals online, 12 had some material available concerning the design of ramps. As part of this research project, members of the research team visited the New Jersey Turnpike. Simulation was used to obtain an appreciation of the effects on corridor operations when several pairs of ramps are modeled. Speed was the primary measure of effectiveness used to evaluate the effects of different ramp spacing, volume levels, and weaving percentages. The research found that a direct connect ramp between a generator and the managed lane facility should be considered when 400veh/hr is anticipated to access the managed lanes. If a more conservative approach to preserving freeway performance is desired, then a direct connect ramp should be considered at 275veh/hr, which reflects the value when the lowest speeds on the simulated corridor for the scenarios examined were at 45 mph or less. VII Mark D.Middleton and Scott A. Cooner from Texas transportation institute evaluated the simulation model performance for congested freeway operations, they focused on three aspects: speedflow relationships for uncongested and congested conditions on freeway; freeway simulation model and freeway simulation model applications. In order to have a good basis for comparison, they selected three simulation PAGE 38 20 models from many simulation software based on some criteria, the three models are FREQ, INTEGRATION and CORSIM. Three sites were selected for comparison by run three different models respectively. They found that the models all performed relatively well for uncongested conditions; however, the performance became sporadic and mostly unreliable for congested conditions. It app ears that the models function better when allowed to begin simulation prior to the onset of congestion. Having data upstream and downstream of a freeway bottleneck (each of the three sites in their project had congestion caused by geometric bottlenecks) or for a location of recurrent congestion helps the models perform better. It is apparent that people drive differently in congested versus uncongested conditions. None of the models tested allowed the user to dynamically change key model parameters (e.g., headway, lane changing, and driver behavior) to account for this driving difference. The CORSIM simulation model was found the most robust in terms of input and output capabilities among the three models The TRAFVU animation program is an invaluable source of informatio n to the user when attempting to determine if the model is performing as expected and for verifying that the network is coded properly. The limitation that was most frustrating was that capacity is not an input or output variable. This distinction made the model ha rd to calibrate because the user never knows capacity. Capacity could not be adjusted on a linkbylink basis as with the others. Nevertheless, The calibration of CORSIM was most easily done by modifying parameters such as carfollowing sensitivity, lane changing, driver aggressiveness, etc., which are all very important in evaluating operations in a congested environment. They think the CORSIM program had the best overall performance in this project and shows promise for future application for the operational evaluation of congested freeway facilities. CORSIM has dramatically improved in the past several years and is continuing to be refined and updated under the direction of the Federal Highway Administration. PAGE 39 21 They recommend that CORSIM be used at locations that are fairly simple geometrically, such as single freewaytofreeway direct connection ramps. The proper and effective calibration of CORSIM for a congested site requires that the users have good and extensive volume and travel time data, as well as origin and destination data. The user must collect data over a time period that begins prior to the onset of congestion and ends after the congest ion has dissipated. Also, the data collection effort must extend over an area that covers the length of the traffic queues formed by the congestion. If the user cannot provide existing data or project future conditions, then the calibration and results of the CORSIM m odel cannot be expected to be reliable.VIII Panos D. Prevedouros, Ph.D. researched the data gathering for freeway simulation using unintrusive sensors and satellite telemetry; it provides a summary of data needs and field data collection technologies used in the simulation of traffic on freeways. Sensor test results, and successful deployments of traffic sensor data retrieval via satellite communication for use in simulation, archival or planning applications are presented. Regardless of the type of freeway simula tion model used (micro or macrosimulation model), the data needed fall into two majo r categories: essential data for running the model and desirable data for calibrating th e model. Essential data include: Freeway volumes on several screen lines; Volumes are required for all freeway onramps and off ramps. Data on freeway segment lengths, number of lanes and other alignment details such as curves, uphill/downhill sections and shoulder availability and width are needed. Vehicle classification denotes the mix of traffic in terms of light duty. Desirable data may include the following: Freeway speed measurements at specific sections which can be compared with model outputs. On ramp survey of motorists destinations or complete origindestination data are desirable when freeway scenarios are planned that include modifications to the freeway that affect demand (i.e., ramp closures, ramp metering, ramp or mainline widening, etc.) Other data that was available for our specific study and are likely to be beneficial for similar largescale freeway studies: Compar isons of data from more than one source PAGE 40 22 to determine volume count accuracy. Helicopter observations during congested periods offered valuable, nearly simultaneous insights on freeway operations and queuing areas. Historical data throughout the 1990s showed trends in volume growth, reduction or stability on onramps and freeway crosssections. Traffic accident reports are invaluable for removing data from days or periods affected by accidents or other nonrecurring events. He conclude that the major data needed for freeway traffic simulation are traffic volumes from all freeway entry and exit points and average speeds at selected crosssections for the calibration of the models. These data can be collected with intrusive (onor underpavement) sensors or with unintrusive (overhead mounted) sensors. Several sensors were tested in various conditions and configurations. Data collection with fiberoptic (Flexsense) and piezoelectric (RoadTrax BL) sensors can be accurate but their deployment is dangerous for the field crew and expensive in the long term because of the rapid deterioration of the onpavement components, particularly so for the fiberoptic sensor tested. Pneumatic tubes tend to provid e unreliable data if the traffic is not freeflowing. Tests of unintrusive detectors including the acoustic (SAS1) and microwave (RTMS XI) revealed that these two sensors have a combination of positive attributes such as being reasonably accurate, fairly easy to deploy and relatively inexpensive to acquire. Offset and height requirements as well as the presence of medians on the highway may create deployment and detection problems, which may be solved by increasing the number of deployed sensors (one sensor for each direction of traffic in sidefired operation or one sensor per lane in overlane operation.) Onsite visits for data retrieval are expensive and demanding in terms of staff needs. In addition, onsite da ta retrieval can be hampered by weather and other adverse conditions. Data collection from field stations via satellite modems and digital pagers (Traflnfo/Orbcomm service) was tested. It was found to be convenient, economical and reliable in most cases.IX PAGE 41 23 Li Zhang, Peter Holm, and James Colyar published a report identifying and accessing key weatherrelated parameters and their impacts on traffic operations using simulation. The object of their report were to identify how weather events affect traffic operations, to assess the sensitivity of weatherrelated traffic parameters in the CORSIM model, and to develop guidelines for using the CORSIM model to account for the affects of adverse weather conditions on traffic operations. Their interesting result of the sensitivity analysis was that a number of parameters tested (19 total) had little or no impact on the MOEs. The majority of these were lane changing parameters.X 2.5. Other Issues Apart from traffic safety and operational aspect of freeway exit ramp, there are some other issues related to the design of exit ramp, such as pavement marking or guiding sign. Richard A. Retting, Hugh W. McGee, and Charles M. Farmer checked the Influence of pavement markings on urban freeway exitramp traffic speeds; they think Motor vehicle crashes on curved roadway sections occur more frequently and tend to be more severe than those on straight sections. Speed is a significant factor in many crashes that occur on curves. The effects on traffic speeds of special pavement markings intended to reduce speeds on freeway exit ramps with horizontal curves were examined. An experimental pavement marking pattern was employed that narrowed the lane width of both the curve and a portion of the ta ngent section leading into the curve by use of a gradual inward taper of existing edgeline or exit gore pavement markings or both. Traffic speeds were analyzed before and after installation of the pavement markings at four experimental ramps in New York and Vi rginia. Results indicated that the markings were generally effective in reducing speeds of passenger vehicles and large trucks. The markings were associated with significant reductions in the percentages of passenger vehicles and large trucks exceeding posted exitramp advisory speeds. XI Bijan Behzadi, from FDOT, researched th e guiding signing for multilane freeway exits with an optional lane. He found Although previous editions of the MUTCD have PAGE 42 24 covered the signing requirements for multilane exits with an option lane ,there is a tremendous lack of uniformity in sign design for this application throughout the United States, from state to state, and even within individual states, a wide variety of sign designs are in use. Below are some of the instances. Figure 14 Black down Arrow Figure 15 Black Right down Arrow PAGE 43 25 Figure 16 Black Right up Arrow Figure 17 Ideal Paths of Motorists before Exit Ramp PAGE 44 26 Figure 18 Unnecessary Lane Changes before Exit Ramp Traffic exit guiding design, should carry at least four concepts, according to Bijan, the first is the concept that a vehicle in the option lane is able to either exit the freeway or continue on the mainline, the second concept is a vehicle in the option lane does not have to change lanes to the left to continue on the mainline, the third concept is a vehicle in the option lane does not have to change lanes to the right in order to exit; and the fourth provision of identifying information about each destination (mainline and exit), such as street name, route number, or destination name. Bijan compared different types and loca tions of guiding sign, the MOE (Measure of Effectiveness) are the number of ideal path and how many unnecessary lane change. Check the figure 17 and 18. XII 2.6. Summary Apparently, a lot of issues related to the traffic performance of freeway exit ramp, from traffic conditions to geometry conditions, from safety performance to operational concern, guiding sign, pavement marking, etc. To address the operational issues of PAGE 45 27 freeway exit ramp, Simulation, despite its limitation and shortcomings, seemed is an effective method to compare, analysis the diff erent aspects of freeway traffic operations. PAGE 46 28 Chapter 3 Factors Affect Ramp Design 3.1. Introduction Numerous factors affect traffic flow characteristics at freeway exit ramps. From the mathematics or statistics point of view, so me factor has several levels while others are continuous variable. For instance, traffic volume is a continuous variable while the grade has several levels from down grade to up grade. It is difficult, sometimes even impossible, to collect all the related traffic data to analyze traffic flow characteristics at exit ramps in field sites. The traditional research method could only collect a portion of field traffic data which is limited by the field sites, weather condition and research budget. Because of these reasons, it would be advantageous to co llect traffic data from traffic simulations, especially for the purpose of design. It is relatively easy and economy to collect traffic data from traffic simulations. In addition, th e factors and their levels can be selected according to the requirement of the research, which may be impossible in real exit ramp sites. 3.2. Influencing Factors at Ramp Designs There are lots of factors affecting the traffic capacity and traffic flow characteristics at exit ramps. Some factors may be easy to measure, such as the grade, sign location and truck percentage in upstream of exit ramps. But some factors are impossible or difficult to accurately measure, such as the driv er psychology, perception reaction time, carfollowing sensitivity etc. According to the literature review at last chapter, the factors that may affect the traffic capacity and flow characteristics at exit ramp are identified as follows: PAGE 47 29 1) Lane number of freeway main line; 2) Lane number of exit ramp; 3) Lane width; 4) Auxiliary Lane length; 5) Curvature of main line and exit ramp; 6) Percentage of heavy vehicles in the traffic stream; 7) Lane use restriction to heavy trucks; 8) Exit ramp guiding sign location; 9) Additional guiding sign location; 10) Posted speed limit; 11) Free flow speed; 12) Grade of freeway and ramp; 13) Traffic volume at freeway way; 14) Traffic volume at exit ramp; 15) Lane distribution; 16) Driver Population; 17) Light Condition (Day versus Night) ; 18) Weather Conditions; 19) Pavement condition; 20) Enforcement condition; 21) Land use intensity; 22) Exit ramp downstream traffic conditions, such as traffic control type, etc. 23) Exit ramp upstream traffic conditions, such as the distance of an onramp, etc. PAGE 48 30 Although all these factors may affect the tr affic condition and capa city of exit ramp, the impact intensity are different, some factors such as the freeway grade and entry volume have significant impact while other factors have limited effect to the capacity of exit ramp, such as the pavement condition according to some research. It is reasonable to limit the research factors in traffic simulation experimental design and still have a reliable result. 3.3. Limitation of Factors in Traffic Simulation From the above chapter, it was obvious that many factors influence exit ramp capacity and traffic flow characteristics. However, because the capacity analysis of exit ramp in this study was performed by traffic simulation software, CORSIM 6.0, the selected factors were greatly limited by the availability of related factors in the software. For example, the weather condition and police presence were two important factors affecting traffic flow characteristics at exit ramps, but in this study the two factors could not be addressed because the CORSIM software could not provide the two factors for traffic simulation runs. In fa ct, although there were many factors affecting the traffic performance of exit ramps, only a part of the factors can be selected to analyze the traffic flow characteristics at exit ramps because of the limitation of the factors provided by CORSIM software. Before selecting of related factors, it wa s necessary to analyze the factors which directly affected the capacity and traffic flow characteristics and the factors which could potentially affect traffic flow characteristic s through other factors at exit ramps. The factors were categorized into two types: one was internal factor, such as vehicle type, driver behavior, etc., and the other was external factor. The internal factor means the factors that were directly related to traffic flow characteristics compared with the external factors, which affected the traffic flow characteristics indirectly, such as number of lanes, grade etc. The following sections discussed the inte rnal and external factors in CORSIM software one by one. The level of different factors is presented also. PAGE 49 31 3.4. Internal Factors in CORSIM According to CORSIM 6.0, some factors could be listed as internal factors which were directly related to traffic flow charact eristics. The following was the list of these factors in GUI (Graphical User Interface) in Traffic Network Editor (TRAFED): 1) Random seeds 2) Vehicle types 3) Acceleration table 4) Environmental table 5) Vehicle entry headway 6) Driver behavior 7) Friction coefficient 8) Freeflow speed percentage 9) Miscellaneous (e.g., Minimum separation fo r generation of vehicles, HOVs) 10) Lane change parameters 11) Lane distribution Table 1 Recommended Parameter Values Description Default Values Altered Values Record Type Maneuver Time (Sec) 3 1 70 Sensitivity factor for car following (sec) 1 1 68 Driver Yielding Percentage 20% 20% 70 Lag To accelerate (sec) 0.3 0.3 69 Lag to Decelerate (sec) 0.3 0.1 69 Minimum Vehicle Separation (sec) 0.2 0.2 70 Desired Free Flow Speed (mph) 65 65 20 Offramp Warning Sign Distance (ft) 2500 5400 20 Mean Startup delay (sec) 1 1 20 % of Vehicles in each lane Average 20, 40, 40 50 PAGE 50 32 CORSIM has default values for the above pa rameters; however, so me researches for the purpose of operational analysis and calibration would change the default values at some special scenarios. Table 1 is the recommended values for CORSIM 4.1 by a research. However, most default values were still used in this st udy. There were three reasons to use the default values of the software in the study. The first reason was that there were no field data available to the analyses, and the study was not aimed to represent any real freeway segment or project. The second was that, in fact, the default values of the parameters presented the most probable situation in the freeway. The third reason was that, the recommended value by the previous study was run only once, one run do not have enough creditabilit y to change the default value. 3.5. Sensitivity Study of Internet Factors In order to test the performance of CORS IM software with default parameters, a small experiment was designed to obtain the freeway capacity from CORSIM simulation with default parameters. If the capacity value was close to recommended values by HCM, it means that the default value in CORSIM software was reasonable. Then it was also acceptable to use default values in the study. This paper according to a similar research finished by Kangyu Zhu, FSU, and a 1200feet freeway segment with two lanes was designed in CORSIM with all default values except the Vehicle Entry Headway. The default value of Vehicle Entry Headway was Uniform Distribution Type. In the experiment, the value was changed to Normal Distribution Type. The experiment was designed to measure the capacity of freeway. So the entry volume of the freeway segment would be close to the capacity of the freeway. According to the traffic flow theory (Adolf D. May, 1990), Under heavyflow conditions, almost all vehicles are interacting, and if an observer stood as a point on the roadway, the time headways would be almost constant. The normal distribution was a mathematical distribution that could be used when either the time headways were all constant or when drivers attempted to drive at constant time headway but driver errors caused the time headways to vary about the intended constant time headway. It was PAGE 51 33 reasonable to use Normal Headway Distribution instead of Uniform Distribution in the capacity research in freeways. The experiment design by Kangyu Zhu from UFXIII uses three levels of free flow speed, 70, 65, 60 mph, and 10 different levels of the entry volume, from 2000 to 2450 vphpl with every incremental step of 50 vphpl. 22 vehicle detectors were deployed along the segment with one in every 100 feet in every lane. The detectors collected the traffic flow characteristics in the segment, including flow rate, speed and time headway. Because of the stochastic simulation, there would be stochastic errors in every time of simulation run. Thirty times of simulation were run for every situation to reduce the stochastic errors. The flow rate was the average value of results from thirty times of simulation runs. When the entry volume was less than the freeway capacity, almost all the volume in each segment was similar. But when the entry volume was much greater than the freeway capacity, there would be a queue in the freeway. So, although the entry volume was high, the volumes in the segments were limited by the freeway capacity. Table 2 CORSIM Capacity and HCS Capacity FFS=70 mph FFS=65 mph FFS=60 mph Segment Capacity from CORSIM Capacity from HCS Capacity from CORSIM Capacity from HCS Capacity from CORSIM Capacity from HCS 1 2228 2400 2222 2350 2219 2300 2 2228 2400 2222 2350 2219 2300 3 2229 2400 2222 2350 2220 2300 4 2228 2400 2222 2350 2220 2300 5 2229 2400 2222 2350 2220 2300 6 2228 2400 2222 2350 2220 2300 7 2228 2400 2222 2350 2220 2300 8 2228 2400 2223 2350 2220 2300 9 2228 2400 2222 2350 2220 2300 10 2228 2400 2223 2350 2220 2300 11 2228 2400 2223 2350 2220 2300 Max. Deviation 0.072% 0.054% 0.035% PAGE 52 34 If the maximum average volumes in each segment were regarded as the capacity of each section, the capacity from the simulation could be compared with the recommended capacity from HCM (2000) as table 2. From table 2, it was shown that the capacity from the CORSIM simulation approximates the capacity recommended by HCM. The maximum deviation was less than 8%. Therefore, it is reasonable that the default parameters in CORSIM could be used to analyze the capacity in freeways. 3.6. External Factors in CORSIM The external factors mean the factors that affect the traffic flow characteristics indirectly by affecting internal factors. For example, freeway grade was an important factor in calculating the capacity and speed in freeways. The grade would first affect the carfollowing sensitivity and driver psychology which, in turn, would directly affect the capacity and speed in the freeway. Hence influence the exit ramp. Most of the research in traffic flow characteristics of freeway exit ramp dealt with external factors. Compared with the internal factors, the external factors were easier to measure. Through the review of past research, the following factors were considered as the potential external factors affecting the traffic flow characteristics in freeway exit ramps. 1) Heavy Vehicles 2) Driver Population 3) Light Condition (e.g., Day versus Night) 4) Exit Ramp Configuration 5) Weather Conditions 6) Presence of Police 7) Auxiliary Lane Length 8) Exit Ramp Sign Location PAGE 53 35 9) Exit Ramp Sign Number 10) Freeway Grade 11) Exit Ramp grade 12) Other Factors, such as downstream traffic control type, etc. Although all the external factors above potentially affect the traffic flow characteristics, just like the internal factors as well, not all of them could be studied in the study. The first concern was the limited parameters provided by the CORSIM software. The traffic simulation could only select some major factors and express the effect of the factors in mathematical or statistical formulas. The selection of factors was limited by the simulation software itself. The second concern was the limitation of computer capability. Actually, not all of the factors in the simulatio n software could be used in the analysis. It would be impossible to apply every single factor for simulation runs. 3.7. Selection of Factors for Analysis According to the analysis above, although numerous internal and external factors influenced traffic operation in freeway exit ramps, only a part of these factors could be selected to analyze traffic flow characteristics at exit ramps based on computer simulation. After careful consideration, the following factors were selected in the study. 1) Number of lanes of main line 2) Number of lanes of exit ramp 3) Freeway Entry Volume 4) Free flow speed at freeway 5) Freeway grade 6) Truck percentage 7) Restrictions on the lane usage for trucks 8) Location of warning sign PAGE 54 36 Here, two parameters must be clarified, which are the length of auxiliary and free flow speed at ramp curve. Although both of them been studied at other projects, they are not included in this paper. Th e reasons are two: for the length of auxiliary length, firstly, some previous study indicated that CORSIM are not sensitivity to the length of auxiliary, secondly, the design of auxiliary lane leng th has been addressed pretty well in the AASHTO Green book, based on different free flow speed on freeway and exit ramp and traffic volume, the auxiliary length are offered at page 851. For the issue of free flow speed at exit curve, although it is important also, it can not be considered as a factor in this paper, firstly, this paper focus on the capacity of freeway main lane, the capacity of ramp curve are deemed as infinite, how much is the free flow speed at exit curve makes no difference to the whole analysis, it mainly impact the capacity of ramp curve; secondly, there is a transaction segment between freeway node and exit curve node required by CORSIM which is used for statistic purpose only. From freeway node to transaction node are deemed as freeway segment too, the free flow speed is the same as free flow speed at freeway. Table 3 is the copy from page 851 of AASHTO Green Book. Table 3 Auxiliary Lane Length at Different FFS Deceleration Length, L(ft) for design speed of exit curve, VN (mph) 15 20 25 30 35 40 45 50 For average running speed on exit curve, Va(mph) Highway Design Speed V Speed Reached Va 0 14 18 22 26 30 36 40 44 30 28 235 200 170 140 / / / / / 35 32 280 250 210 185 150 / / / / 40 36 320 295 265 235 185 155 / / / 45 40 385 350 325 295 250 220 / / / 50 44 435 405 385 355 315 285 225 175 / 55 48 480 455 440 410 380 350 285 235 / 60 52 530 500 480 460 430 405 350 300 240 65 55 570 540 520 500 470 440 390 340 280 70 58 615 590 570 550 520 490 440 390 340 75 61 660 635 620 600 575 535 490 440 390 1) V: Design speed of highway (mph) PAGE 55 37 2) Va : Average running speed on highway (mph) 3) VN : Design speed of exit curve 4) Va : Average running speed on exit curve (mph) The following sections would analyze the ma in factors chosen in the study one by one. After the analyses of the factors, the le vels of each factor we re presented according to the real world experiences and the past research. 3.7.1. Number of Lanes of Mainline Exit ramp capacity and speed might be affe cted by number of lanes of main line. Normally, at two lane freeway, the traffic volume is low and the speed is also not too fast. At three or more lane freeway, the traffic volume is relatively high and the speed is comparatively faster due to the past research. It is common sense that more freeway lanes will cause more lane change maneuver. This paper will focus on threelane main line freeway. For the main line with more than threelane or less than threela ne, due to the time limitation and another reason related to truck restriction, (which will be mentioned later) this paper omits the research of other than threelane freeway. For short, the la ne number of mainline is not a variable. 3.7.2. Number of Lanes of Exit Ramp This paper will focus on the number of lane s of exit ramp when it split from main line, here the auxiliary lane along the center line of freeway mainline and the ramp curve lane after leaving the physical nose are different. For tapered onelane exit, there are no auxiliary, one lane after the physical nose; for the tapered twolane exit, there are one auxiliary lane along the center line and twolane after the physical nose, for parallel onelane exit, there are one auxiliary lane along th e centerline and one lane after physical nose, for parallel twolane exit, there are two auxiliary lane (although the length may different) along the centerline and twolane after the physical nose. Check the figure 1, 2, 3 and 4 at chapter one for details. PAGE 56 38 The lane number after the physical nose, may keep unchanged till it reaches the downstream intersection, or it may split into more lanes to accommodate the traffic volume. Hence the traffic capacity is different for different curve lane numbers. But this is not the concern of this dissertation. In this dissertation, the capacity of curve lane is assumed to be infinite for the purpose of eliminating the influence of curve lane numbers. 3.7.3. Free Flow Speed Free flow speed is different from posted speed. The definition of free flow speed (FFS) in HCM (2000) was: the mean sp eed of passenger cars that could be accommodated under low to moderate flow rates on a uniform freeway segment under prevailing roadway and traffic conditions. Mo reover, in HCM (2000) FFS in freeway was divided into five categories: 75 mph, 70 mph, 65 mph, 60 mph, and 55 mph. However, the past research at freeway rarely considered FFS as an important factor to analyze traffic flow characteristics because of th e limitation of available traffic data. Speed limit was the maximum speed that vehicles were permitted to drive in particular freeway segments. Compared with free flow speed, speed limit was much easy to observe. Almost all of the freeway segments had particular speed limit. Some researchers think that it was reasonable that free flow speed was five mph greater than the speed limit. In CORSIM Software the input freeway speed was free flow speed instead of the speed limit in freeways. In this case, we can take the advantage of computer simulation, the maximum free flow speed provided in CORSIM software was 70 mph. the normal post speed in State freeway is 55mph, and the input speed in simulation is set from 55mph to 70 mph with the step of 5mph. that is 70mph, 65mph, 60mph and 55mph. 3.7.4. Freeway Grade Freeway grade is believed to have significant effect on the traffic operation. It seems reasonable that freeway grade would affect the capacity and speed because of the presence of grades would exacerbate any flow constriction that would otherwise exist, particularly in the presence of heavy vehicles. PAGE 57 39 Freeway grade is necessary for sensitivity analysis in this study, since the computer constraints, five levels of freeway grade were selected: 6, 3, 0, +3, and +6. Heavy vehicle occupy more space on the roadway than passenger cars. Moreover, heavy vehicles accelerate and decelerate slowly and their presence makes other drivers more apprehensive, and they need more operation time to shift lane in freeway. These factors reduce the overall capacity of the freeway ramp. In fact, in most of research on capacity and speed in freeway, including HCM, no matter which years edition, truck percentage is listed among the most important factors. 3.7.5. Truck Percentage Figure 19 Truck Percentage Distributions Figure 19 showed that the truck percentage in about 80% of freeway was less than 15%. The maximum truck percentage could reach 33% although this phenomenon happens rarely. In the paper, truck percentage is categorized into five levels: 4%, 8%, and 12%, 16%, 20%. More than 20% are not considered in this paper. Figure 19 is the copy from Kangyuan Zhous research. PAGE 58 40 3.7.6. Restriction to Lane Usage of Truck Many state freeways have certain restrictions to the lane usage for the heavy vehicle, typically the heavy vehicles are restricted to the right two or three lanes, and the left lane is for faster passing vehicles only. Whether the truck is restricted to a certain lane(s) or not has impact on the capacity and operational characteristics in the exit ramp functional area. Heavy vehicle occupy more space on the roadway than passenger cars. Moreover, heavy vehicles accelerate and decelerate slowly and their presence makes other drivers more apprehensive, if the trucks keep in the right lanes of a freeway, it will make the inner vehicles harder to shift lane to outer lane, especially when the traffic volume is high; if the trucks are not restricted to any lane, when approaching the exit ramp functional area, the truck at inner lane must make at least one lane change maneuver, for threelane main line, the truck must make at least twice lane change maneuvers. It is common sense that truck need more time/or headway space to fulfill a lane change maneuver. When the traffic volume is too high, the truck sometime will be forced to make a lane change, cause potential traffic accident and turbulence. This issue has not been researched by literature review. This is the reason why the research scope was limited to threelane main line only, for twolane freeway; there are no restrictions to the truck utilization of any special lane. 3.7.7. Location of Exit Sign Location of exit sign is an important factor in analyzing the traffic flow characteristics at exit ramps. Generally, from the location of exit sign, traffic flow will be disturbed by lane changing vehicles. Certainly, the effect of location of exit sign depends on how many drivers familiar with the exit type of freewa y terminal, if the exit ramp are used for commute drivers, many drivers may shift lane in advance of th e exit sign; if the exit ramp are used for tourists, the drivers may only make any necessa ry lane change after visualizing the exit sign. Further more, when the traffic demand exceeds the capacity of exit ramp, queues may develop backward and pass the advance exit signs, often surprising approaching PAGE 59 41 traffic and increasing the accident potential. Also, smooth and orderly merging operations may be lost as some drivers remain in the i nner lane attempting to squeeze into the outer lane at the head of queue while other drivers try to prevent drivers in the middle lane from passing them by straddling the centerline or traveling slowly in tandem with another vehicle in the middle lane. These maneuvers tend to reduce the capacity of the merging operation and increase the accident potential and road rage among drivers. CORSIM software provides the default value of location of exit sign. It is 2500 feet upstream of the physical nose of the exit ramp. In the thesis, the location of exit sign is set into 8 levels: 1500ft, 2000ft, 2500ft, 30 00ft, 3500ft, 4000ft, 4500ft, and 5000ft. before the physical nose area. 3.8. Summary The study divided the factors affecting traffic flow characteristics in exit ramps into two types of factors. One was internal factor, which directly affect traffic flow characteristic itself. The other was external factor, which affect traffic flow characteristic through internal factors. Internal factor and external factor both affected the capacity and speed at freeway exit ramp. This chapter presented the internal and external factors which might be considered as the most important to capacity and speed at freeway exit ramps. Table 4 Selected Factors for CORSIM Simulation Factor Level Variable Type Internal Factor Vehicle Headway Distribution Normal Distribution External Factor Number of Lanes of Main Line 3 Classification Constant Number of lanes of Exit Ramp 1, 2 Classification Variable Free Flow Speed in Freeway 70, 65, 60, 55 (mph) Continuous Variable Freeway Grade 6, 3, 0,+3, +6 Continuous Variable Truck Percentage 4, 8, 12, 16, 20 Continuous Variable Restriction to Lane Usage of Truck 0, 1 Classification Variable Location of Exit Sign 1500ft to 5000ft Continuous Variable PAGE 60 42 Because of the limitation of filed traffic data available to the research and the research was also not intent to some particular projects, the values in most of the internal factors were default provided by CORSIM software except for vehicle headway distribution. The study conducted a sensitivity analysis of the default internal factors to exit ramp capacity. The simulation results showed that the capacity from simulation approximated to the value from HCM. The maximum deviation was about 7.2%. It showed that the capacity analyses were reasonable with default value in CORSIM simulation. According to the past research on freeway exit ramps, some potential internal and external factors were selected to analyze traffic flow characteristics at exit ramps in the study. Because of the computer capability a nd calculation time constraint, some minor factors were omitted, and the levels of every selected factor were discrete, not continuous. Table 4 showed the levels and factors selected in the study. PAGE 61 43 Chapter 4 Data Collection 4.1. Introduction The objective of the study was to compare the traffic operational characteristics of tapered onelane exit ramp, tapered twolane exit ramp, parallel onelane exit ramp and parallel twolane exit ramp, hoping to find a general rule on what kind of exit ramp should be chosen under certain conditions. It analyzes the relationship of traffic capacity and speed with related influencing factors at freeway exit ramps using CORSIM simulation. Seven influencing factors had been identified to having effect on the traffic discharging, speed and total lane change number at freeway exit ramps. In this chapter, the seven factors were further evaluated, and an experiment design was outlined to carry out the research study. A 7500 feet freeway exit ramp was setup for the traffic simulation based on the methodology offered by Advanced CORSIM Training Manual. Simulation runs and entry volumes were identified according to mean and standard deviation of the capacity in the most adverse scenarios. Total simulation runs of 64,800 were required to perform the study. With so many simulation runs, it would not be possible to produce input files and analyze the output results from the simulation if every step was done by hand. Computer codes have been developed to deal with most of the data collection. Most of the codes were developed with Visual Basic Application in Microsoft Word and Microsoft Excel. 4.2. Input File Production In TSIS 6.0 there were two tools that could produce CORSIM input files for simulation. One was Traffic Network Edit or known as TRAFED. TRAFED tool would produce *.tno file for CORSIM simulation. The other was Text Editor, which would PAGE 62 44 produce *.trf file for traffic simulation. The files produced by the two tools could be translated each other by the tool Translator in TSIS. TRAFED was used to create models of traffic networks using a pointandclick, graphical user interface. It was designed to support users of the Federal Highway Administration's (FHWA's) CORSIM microscopic traffic simulator. TRAFED stored data in an objectoriented manner rather than using the recordoriented structure of CORSIM TRF file format. Because of TRAFED graphica l user interface, it was much easier to understand the input file compared with the Text Editor. However, because of the input file produced using pointandclick method in TRAFED, it could only produce one input file at a time. If there were many input files to produce, the user had to produce and save the files one by one. Text Editor was another tool to edit CORSIM input (TRF) files for simulation. The TSIS Text Editor used Microsoft's rich edit control to provide a generic text editor that operated similar to Microsoft's Notepad app lication. In addition to the standard text editing capabilities, this editor supported a feature that made the editing of CORSIM input TRF files easier. Specific ally, the Text Editor displayed record type information in the TShell Output View and allowed you to quickly identify individual fields in the TRF file text. Making use of record type information and having the similar function to Microsofts Notepad, it was possible to pr oduce many input files simultaneously with Visual Basic Application (VBA) editor in Microsoft Word. Because a lot of input files were needed in the TSIS software for simulation, it would take a long time to produce the input files if TRAFED tool was used in the process. Therefore, Text Editor Tool was selected instead to produce the input files. With the aid of code developed in VBA using Visual Basic Editor in Microsoft Word, huge numbers of input files were produc ed for the simulation. 4.3. Affecting Factors in Input Files A total of seven factors were selected to analyze the effect on the traffic volume, speed and total lane change number of freeway exit ramps. Because Text Editor was used PAGE 63 45 to produce input the file, it was necessary to introduce Record Type information (RT) to understand the input files. CORSIM structured its data into records and entries. Each record contained one or more entries. The titles associated with e ach record could be found in the CORSIM Reference Manual. The GUI components consisted of dialogs, pages, fields, and graphical displays. Each dialog could contain pages, fields, and graphical displays. Each page could contain fields and graphical displays. A tab inside the dialog window designated a page. A field could be an edit box, radio button, check box, drop down edit box, or buttons. A graphical display could be any graphical picture in a dialog that could be manipulated by the users. When Text Editor was used to produce the input file, the variable should be linked w ith the specific Record Type number. Table 5 illustrated the Record Type number of the selected factors in the Text Editor. Table 5 Record Type of Selected Variables Variable GUI Dialog Name GUI Page Name RTColumns In the Record Type Number of lanes Freeway Link Lanes 19 20 Free flow speed Freeway Link General 20 2122 Grade Freeway Link General 20 2910 Truck Percentage Entry Properties N/A 50 1316 Location of Exit Sign Freeway Link Incidents 20 2933 Volume Entry Entry Properties N/A 50 912 Off Ramp Freeway Turn N/A 25 2124 It must be indicated herein that the number of exit ramp lanes are not included. Because four different tno file will be built which corresponding to the tapered onelane exit (TO), tapered twolane exit (TT), parallel onelane exit (PO), and parallel twolane exit(PT), in another word, the number of exit lanes are not a changeable variable in this table. Also, the number of lanes listed here are for illustrations only, its not changeable. Fixed on threelane only. Changing the values of these variables according to the selected levels would produce different scenarios for input files. Using the program in Visual Basic Application PAGE 64 46 in Microsoft Word, all the input files associated with the selected factors would be produced. All the input files could be input to CORS IM software for simulation simultaneously. In TSIS there was a Multiple Run Many Case function, whic h was useful when batch processing a large number of CORSIM cases. For each run of each case, the script in TSIS applied different random number seeds. Because CORSIM was a Monte Carlo type simulation, multiple runs with different ra ndom number seeds were required to achieve valid average values for the measures of effectiveness produced by the simulation model. Because of the huge number of input files and work zone scenarios, it was necessary to develop an effective notati on for designing different scenarios. The following notation was selected to depict different scenarios: AB_CD_EF_GHIJ_K_LMNO_P Description for the above notations was summarized in Table 6. Table 6 Notations of Files Name in the Research Notation Description Level AB Free Flow Speed in Freeway, mph 70, 65, 60, 55 (mph) CD Freeway Grade, % 6, 3, 0, 3, 6 EF Truck Percentage, % 4, 8, 12,16,20 GH IJ Location of Exit Sign, feet 0500 to 5000 with 500 step K Restriction to Truck No=0, Yes=1 LMNO Entry Volume, vph 12002400 vphpl PQ Off Ramp Percentage % 10, 12, 15 R The Order of Simulation Time 15 4.4. Freeway Exit Ramp Configuration Four different 7500 feet freeway section was designed with a 2500 feet link length for the traffic speed and total lane change number analyses. The four different freeway section are corresponding to TO, TT, PO and PT respectively. The free flow speed in normal freeway was set from 55 mph to 70 mph with 5 mph step. The designed freeway exit could be divided into 3 freeway segments. The first segment was normal freeway PAGE 65 47 with 2500 feet length. The second segment was exit ramp functional area with 2500 ft length too, the auxiliary lane was expected to happened so mewhere within this 2500 ft. The third segment was freeway with 2500 feet downstream of the exit node, the purpose of this link is to compare the traffic characteristics of these four exit ramp after vehicles pass the exit node. The design of the work zo ne configuration was illu strated in Figure 20 to 23. 2500ft2500ft2500ft Figure 20 Tapered OneLane Exit Ramp 2500ft 2500ft 2500ft 1500ft Figure 21 Tapered TwoLane Exit Ramp PAGE 66 481500ft 2500ft 2500ft 2500ft Figure 22 Parallel OneLane Exit Ramp 300ft 1800ft 2500ft2500ft2500ft Figure 23 Parallel TwoLane Exit Ramp 4.5. Entry Volume for CORSIM Simulation This paper does not try to find the capacity of different exit ramp types, actually, it can be done by HCS with ease, however, Th e TSIS CORSIM software could not provide the capacity of freeway, it simulated the movement of the individual vehicle according to car following theory and merging theory et c. So when TSIS simulation was used to analyze the capacity, it had to input several levels of entry volumes, and then compare the traffic operational characteristics of the four different exit ramp types. It is obvious that PAGE 67 49 more reliable conclusions can be drawn if the entryvolume levels vary from smaller than the capacity to greater than th e capacity of exit ramps. Three different scenarios was picked to simulate the traffic volume which was believed from low, medium to high, which also was believed smaller than the capacity, close to the capacity and greater than the capacity. The grade is set to the same for all scenarios. Table 7 Three Scenarios for Exit Ramp Comparison Factors Scenario 1 Scenario 2 Scenario 3 Free Flow Speed in Freeway 70 mph 60 mph 55 mph Grade 0 0 0 Truck Percentage 4% 8% 12% Location of Exit Sign 5000ft 2500ft 1000ft Restricted 0 0 0 Entry Volume 1500vphpl 2000vphpl 2500vphpl Off Ramp Percentage 10% 12% 15% 4.6. Number of Simulation Runs The simulation run was a sensitive topic in traffic simulation. Because the TSIS simulation was stochastic, the results from different simulations were not the same. It is very dangerous to use one run result as the final result, just as to judge the face value of a dice by cast it once. To reduce the stochastic errors and get the relative stable results, it is very necessary to run simulation many times instead of only on e time. But when the simulation times were increased, the time to simulate the scenarios and analyze the data was also increased. So it was preferred to find particular simulation times, which not only satisfied the precision of the results but also did not increase the simulation time greatly. Based on the theory of probability and statistics, the equation below could be used to estimate the required number of runs to provide an estimate of the mean with a specified confidence interval and an error range. PAGE 68 50 Where, n ) Required number of simulation runs ) Sample standard deviation 2 / aZ) The threshold value for 100(1) percentile confidence interval E ) the allowed error range Based on the experiences, the scenarios with expected maximum standard deviation appeared when extreme levels of each factor are selected. Therefore, the extreme Scenario was selected to evaluate the maximum simulation runs. It was 55_6_20_0500_1_2500. The scenario 55_6_20_0500_1_ was run with entry volume from 1200 to 2400 vphpl for 5 times. The standard deviations of the flow rates along the freeway were 100. Assume the allowed error range was 5%. Maximum standard deviation at the exit ramp: =100 =1.96, when Capacity = 2314 vphpl E=2314*5%=116 vphpl Using Equation 1, the required nu mber of simulation runs was, 85 2 ] 116 100 96 1 [ ] [2 2 2 / E z na Hence, for the comparison of the four exit type, a simulation run with 3 times was sufficient for 5% allowed error range with 95% confidence level. Considering that the PAGE 69 51 standard deviation in some scenarios would be greater than the values listed above, a simulation run with 5 times was used in the study. 4.7. Data Collection Because of the huge number of data files, it was not feasible to analyze the data files step by step by hand. In the study some computer codes were developed for data analyses and CORSIM input files production. Almost all of the actions in the data collection, including deleting files and moving files, were done automatically by the codes in Microsoft Word and Microsoft Excel. The general procedure of data collection in the study was as follows. According to the selected levels of th e factors, the codes in Microsoft Word produced the input files for CORSIM simulation. The file names were in the notation of AB_CD_EF_GHIJ_K_LMNO_PQ_R The corresponding level number was 4_5_5_8_2_7_3_5. So the total number of files was 168000 5 3 7 2 8 5 5 4 files. At the same time, the Batch file was created, which contained the path and name of the files to be processed. In CORSIM 6.0, Select MultiRun Many Cases function and input the random number file and the batch file. Simultaneously, the run number of 5 was input. Then the CORSIM would begin to simulate the work zone performances. After the simulation was finished, the TSIS software would produce 168000 CORSIM output files. The traffic volume, speed and total lane change data can be read respectively from all the Excel files. 8 seconds are needed to obtain the traffic volume and speed value from the above steps, according to the computer speed of generally current personal computer. So the total time needed in the simulation and data analyses was about PAGE 70 52 hours 373 3600 8 168000 Notice this is the running time needed fo r one exit type, the main line threelane have four types of exit ramp, the total base map is 4, and the total time needed is days hours 62 1492 373 4 Actually, the separate four exit ramp VBA files can be run at four different computers, which cut the time to 15.5 days. 4.8. ANOVA & Tukey Traffic discharging volume, as well as the traffic speed and the total lane change number are used as the main MOEs for the purpose of comparisons. Traffic discharging volume has direct relation with the traffic capacity; traffic speed has direct relation with the capacity and LOS; the total lane change number has direct relation with safety issues. Actually, The MOEs are different at each run time interval for the same exit ramp type as well as for the different exit ramp, in order to test if the difference for the same exit ramp are acceptable and the difference for different ramp exit types are statistically significant, ANOVA and Tukey are used for the purpose of comparisons. ANOVA and Tukey method are very powerful statistical soluti ons to data analysis and data mining. The following subchapter explains the ANOVA and Tukey test in details. ANOVA is the short for analysis of variance, A OneWay Analysis of Variance is a way to test the equality of three or more means at one time by using variances. It should meet the following criteria: 4.8.1. Assumptions The populations from which the samples we re obtained must be normally or approximately normally distributed. The samples must be independent. The variances of the populations must be equal. PAGE 71 53 The MOEs of this paper meet the assumptions, traffic running speed; discharging volume and total lane change number are distributed normally. And the variances of all the MOEs are equal and independent. 4.8.2. Hypotheses The null hypothesis will be that all population means are equal; the alternative hypothesis is that at least one means is different. In our case, for example, the average number of lane change may equal for all the fo ur exit ramp types or at least one pair is different. In the following, lower case letters apply to the individual samples and capital letters apply to the entire set collectively. That is, n is one of many sample sizes, but N is the total sample size. 4.8.3. Grand Mean The grand mean of a set of samples is the to tal of all the data values divided by the total sample size. This requires that you have all of the sample data available to you, which is usually the case, but not always. It tu rns out that all that is necessary to find perform a oneway analysis of variance are the number of samples, the sample means, the sample variances, and the sample sizes. N x XGM Another way to find the grand mean is to find the weighted average of the sample means. The weight applied is the sample size. 4.8.4. Total Variation The total variation (not variance) is comprised the sum of the squares of the differences of each mean with the grand mean. PAGE 72 54 2) ( ) (GMX x T SS There is the between group variation and the within group variation. The whole idea behind the analysis of variance is to compare the ratio of between group variance to within group variance. If the variance caused by the interaction be tween the samples is much larger when compared to the variance that appears within each group, then it is because the means aren't the same. 4.8.5. Between Group Variations The variations due to the interaction between the samples are denoted SS (B) for Sum of Squares Between groups. If the sample means are close to each other (and therefore the Grand Mean) this will be small. There are k samples invo lved with one data value for each sample (the sample mean), so there are k1 degrees of freedom. 2) ( ) (GMX x n B SS The variance due to the interaction between the samples is denoted MS(B) for Mean Square Between groups. This is the between group variation divided by its degrees of freedom. It is also denoted by2 bS. 4.8.6. Within Group Variations The variation due to differences within in dividual samples, denoted SS(W) for Sum of Squares Within groups. Each sample is considered independently, no interaction between samples is involved. The degrees of freedom are equal to the sum of the individual degrees of freedom for each sample. Since each sample has degrees of freedom equal to one less than their sample sizes, and there are k samples, the total degrees of freedom is k less than the total sample size: df = N k. 2) ( S df W SS The variance due to the differences within individual samples is denoted MS (W) for Mean Square Within groups. This is the within group variation divided by its degrees of PAGE 73 55 freedom. It is also denoted by2wS. It is the weighted average of the variances (weighted with the degrees of freedom, df in short). 4.8.7. F Test Statistic Recall that an F variable is the ratio of two independent chisquare variables divided by their respective degrees of freedom. Also recall that the F test statistic is the ratio of two sample variances, well, it turns out that's exactly what we have here. The F test statistic is found by dividing the between gr oup variance by the within group variance. The degrees of freedom for the numerator are the degrees of freedom for the between group (k1) and the degrees of freedom for the denominator are the degrees of freedom for the within group (Nk). 2 2 w bS S F 4.8.8. Summary Table To sum up, the details for oneway ANOVA are shown at table 8. Table 8 One Way ANOVA SS df MS F Between SS(B) k1 SS(B)/(k1) MS(B)/ MS(W) Within SS(W) Nk SS(W)/ (Nk) N/A Total SS(W) + SS(B) N1 N/A N/A The decision will be to reject the null hypothesis if the test statistic from the table is greater than the F critical value with k1 numerator and Nk denominator degrees of freedom. If the decision is to reject the null, then at least one of the means is different. However, the ANOVA does not tell you where the difference lies. In our research, for instance, if the ANOVA table tells that the tra ffic volume are statistic ally different within the functional area of the four types of exit ramp, it does not indicate which pair are different, maybe only one pair, or all pairs ar e different. For this, another test, the Tukey test is needed. PAGE 74 56 4.8.9. Tukey Test When the decision from the OneWay Analysis of Variance is to reject the null hypothesis, it means that at least one of the me ans isn't the same as the other means. What needed is a way to figure out where the differences lie, not just that there is a difference. This is where the Tukey tests come into play It will analyze pairs of means to see if there is a difference much like the difference of two means covered at ANOVA. Both tests are set up to test if pairs of means are different. The formulas refer to mean i and mean j. The values of i and j vary and the total number of tests will be equal to a combination of k objects, 2 at a time C(k,2), where k is the number of samples. j ii H j H : :1 0 The Tukey test is only usable when the sa mple sizes are the same. This research is applicable to this standard. The Critical Value is looked up in a table. It is a table in the Bluman text. There are actually several different tables, one for each level of significance. The number of samples, k, is used as an index along the top, and the degrees of freedom for the within group variance, v = Nk, are used as an index along the left side. The test statistic is found by dividing the difference between the means by the square root of the ratio of the within group variation and the sample size. Reject the null hypothesis if the absolute valu e of the test statistic is greater than the critical value (just like the linear correlation coefficient critical values). 4.9. Summary This chapter introduced the experiment design for the research in details. The study designed a 7500 feet freeway exit ramp divided into three parts: before functional area, within functional area and after functiona l area. This chapter also discussed the simulation runs and entry volume for the experiment. PAGE 75 57 The total simulation runs were 168000 times. And it took about 16 days on CORSIM simulation and computer data analyses. The final results of the simulation and data analyses were the traffic volume, space mean speed and total lane change number for each exit type scenario. This chapter also introduces the methodology that the whole dissertation will use to analysis discharging volume, speed and total lane change number. PAGE 76 58 Chapter 5 Capacity Comparisons 5.1. Introduction The previous chapters introduced the factors affecting the design in freeway exit ramps and the exit ramp experiment design in CORSIM. This chapter mainly compares the difference of four exit ramp types by the traffic discharging volume, speed and total lane change number based on the traffic simulation data from CORSIM. Because there is no output factor in CORSIM called capacity, the maximum volume discharging rate are used to substitute the capacity. Actually, the HCS analysis can give the capacity of these four different exit ramps based on main lane number and exit ramp number. It seemed that the capacity of different exit ramp has direct relation with free fl ow speed. The auxiliary lane length, the percentage of exit volume has no impact on the main lane and ramp capacity. The HCS analysis will be discussed on the sensitivity chapter, which is at chapter eight. Different from previous study which focus mainly on the functional area of exit ramp, this paper compares the traffic operatio nal characteristics before, within and after the functional area of exit ramp. The 7500 feet length freeway was divided into three parts for comparison, the first 2500 feet length was believed before the functional area of exit ramp, motorist were assumed to drive similar to a long freeway segment without the influence of onramp and exit ramp; the second 2500 feet length was believed within the functional area of exit ramp, actually, the start of auxiliary lane occurs within this segment, the traffic turbulence is believed to happen mostly within this area, traffic volume at different lane, traffic speed and total lane change maneuver is deemed at giant derivation; the third 2500 feet length was believed the exiting vehicle cleared from the freeway mainline (although in some cases, th e exiting vehicles are forced to drive along PAGE 77 59 the freeway mainline because the headway space at the auxiliary lane are too short to make a safe lane change, in another word, they missed their destination), the remaining vehicles will speed up to recover the lost time caused by queuing, avoiding and/or unnecessary lane changing. 5.2. Mean Discharging Volume Comparisons The designed three scenarios are corresponding to traffic volume less than capacity, close to capacity and greater than capacity respectively. All three scenarios are run 5 times for the four exit ramp types. The auxiliary lane length is not a variable according to the previous description, the length of auxiliary are set followed by the standard of AASHTO Green book, for the purpose of comparable, the length of auxiliary are not changed with the free flow speed. Table 9 Auxiliary Lane Length of Exit Ramps Auxiliary Lane Length TO TT PO PT First Auxiliary Lane N/A 1500 ft 1500 ft 1500 ft Second Auxiliary Lane N/A N/A N/A 300 ft Because the simulation results was analyzed by SPSS, the abbreviations for tapered onelane, tapered twolane, parallel onelane, and parallel twolane., were coded into 1, 2, 3, and 4 respectively. FA is the abbreviations of functional area appeared in tables and figures. 5.2.1. Before Functional Area at Low Entry Volume The simulation run results before functional area are list at table 10, the ANOVA analysis are list at table 11. Since F test shows insignificant, Tukey analysis is unnecessary. The LEV is the abbreviation for low entry volume, the MEV is the abbreviation for medium entry volume, and the HEV is the abbreviation for high entry volume in this paper. It can be concluded that before functional area of an exit ramp, when the entry volume of freeway is lower than the capacity, there were no statistical difference of PAGE 78 60 traffic discharging volume generated at threelane freeway for different exit types although it does show the difference in the volume (discharging rate). Table 10 Mean Discharging Volume at LEV before FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 1510.1 102.8 26.5 1453.2 1567.1 1386.4 1677.1 2 15 1510.0 88.8 22.9 1460.8 1559.2 1391.0 1668.7 3 15 1509.9 85.8 22.2 1462.4 1557.5 1407.4 1637.8 4 15 1511.9 96.6 24.9 1458.4 1565.4 1366.3 1661.0 Total 60 1510.5 91.3 11.8 1486.9 1534.1 1366.3 1677.1 Table 11 ANOVA Results of Mean Discharging Volume at LEV before FA Sum of Squares df Mean Square F Sig. Between Groups 40.3 3 13.4 .002 1.000 Within Groups 492091.2 56 8787.3 Total 492131.5 59 1508 1509 1510 1511 1512 1513 TOTTPOPT Ramp TypeVolume Figure 24 Mean Volume Comparisons at LEV before FA 5.2.2. Within Functional Area at Low Entry Volume The simulation run results within functional area at scenario 1 are list at table 12, the ANOVA analysis are list at table 13. Since F test shows significant, Tukey analysis is necessary and list at table 14. PAGE 79 61Table 12 Mean Discharging Volume at LEV within FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 1495.5 135.6 35.0 1420.4 1570.5 1323.9 1741.7 2 15 1441.8 70.7 18.2 1402.6 1480.9 1311.8 1525.5 3 15 1404.5 42.5 11.0 1380.9 1428.0 1335.9 1468.7 4 15 1390.0 63.8 16.5 1354.7 1425.3 1302.3 1532.4 Total 60 1433.0 92.9 12.0 1408.9 1456.9 1302.3 1741.7 Table 13 ANOVA Results of Mean Discharging Volume at LEV within FA Sum of Squares df Mean Square F Sig. Between Groups 99588.9 3 33196.3 4.541 .006 Within Groups 409399.4 56 7310.7 Total 508988.3 59 Table 14 Tukey Results of Mean Discharging Volume at LEV within FA Sig.. TO TT PO PT TO N/A .324 .026 .007 TT .324 N/A .632 .355 PO .026 .632 N/A .967 PT .007 .355 .967 N/A 1300 1350 1400 1450 1500 1550 TOTTPOPT Ramp TypeVolume Figure 25 Mean Volume Comparisons at LEV within FA Figure 25 is the illustration of mean volume comparison. It can be concluded that within functional area of exit ramp, when the entry volume of freeway is lower than the capacity, there are two pairs of exit ramp are statistically significant in traffic volume generated, which are TOPO and TOPT. Tapered onelane exit has more traffic volume than parallel exit type, no ma tter onelane or twolane. It reasonable because there is no PAGE 80 62 auxiliary lane at tapered onelane exit while parallel exit type has one or two auxiliary lane, the main line bears less traffic volume as a consequence. PO and PT have less density along the mainline, which is 6.1% and 7.1% lower respectively to compare with TO. 5.2.3. After Functional Area at Low Entry Volume The simulation run results after functional area are list at table 15, the ANOVA analysis are list at table 16. Since F test shows insignificant, Tukey analysis is unnecessary. Figure 26 is the illustration of mean volume comparison. It can be concluded that after functional area of exit ramp, the traffic vo lume at these four types of exit ramp are statistically insignificant. In another word, af ter the turbulences at the functional area and the leaving of exiting vehicle, the traffic at freeway mainline back to normal in terms of traffic discharging volume. To sum up, at low entry volume, Tapered onelane exit has more traffic volume than parallel exit type, no matter on elane or twolane exit ramp. It is reasonable because there is no auxiliary lane at tapered onelane exit while parallel exit type has one or two auxiliary lanes, the main line bears le ss traffic volume as a consequence. Table 15 Mean Discharging Volume at LEV after FA 95% ConfidenceInterval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 1347.9 117.5 30.3 1282.8 1413.0 1193.9 1530.2 2 15 1350.9 90.4 23.3 1300.8 1401.0 1224.7 1471.0 3 15 1347.0 76.8 19.8 1304.5 1389.6 1253.8 1490.6 4 15 1347.5 82.2 21.2 1302.0 1393.0 1223.7 1509.6 Total 60 1348.4 90.7 11.7 1324.9 1371.8 1193.9 1530.2 PAGE 81 63Table 16 ANOVA Results of Mean Volume at LEV after FA Sum of Squares df Mean Square F Sig. Between Groups 138.8 3 46.2 .005 .999 Within Groups 484979.3 56 8660.3 Total 485118.2 59 1345 1346 1347 1348 1349 1350 1351 1352 TOTTPOPT Ramp TypeVolume Figure 26 Mean Volume Comparisons at LEV after FA The traffic performance between tapered twolane exit and parallel exit are insignificant, in another word, at low entry volume, parallel type exit ramp are no better than tapered twolane exit ramp even they have extra lane along the freeway. 5.2.4. Before Functional Area at Medium Entry Volume The simulation run results before functional area at scenario 2, the volume close to the freeway capacity, are list at table 17, the ANOVA analysis are list at table 18. Since F test shows insignificant, Tukey analysis is unnecessary. Table 17 Mean Discharging Volume at MEV before FA Std. Std. 95% Confidence Interval for Mean Ramp Type N Mean Deviation Error Lower Bound Upper Bound Minimum Maximum 1 15 2013.3 24.7 6.4 1999.6 2026.9 1967.7 2058.4 2 15 2013.7 33.2 8.6 1995.3 2032.1 1949.5 2062.7 3 15 2014.27 25.6 6.6 2000.1 2028.4 1976.8 2056.8 4 15 2015.2 28.2 7.3 1999.6 2030.8 1960.3 2071.9 Total 60 2014.1 27.4 3.5 2007.0 2021.2 1949.5 2071.9 PAGE 82 64Table 18 ANOVA Results of Mean Discharging Volume at MEV before FA Sum of Squares df Mean Square F Sig. Between Groups 30.6 3 10.2 .013 .998 Within Groups 44262.7 56 790.4 Total 44293.3 59 Figure 27 is the illustration of mean volume comparison. It can be concluded that before functional area of an exit ramp, when the entry volume of freeway is close to the capacity, there were no significant difference of traffic discharging volume generated at threelane freeway for different exit types. This phenomenon is very similar to scenario 1. 2012 2013 2014 2015 2016 TOTTPOPT Ramp TypeVolume Figure 27 Mean Volume Comparisons at MEV before FA 5.2.5. Within Functional Area at Medium Entry Volume Table 19 Mean Volume at MEV within FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 1995.4 166.7 43.0 1903.1 2087.8 1779.7 2237.1 2 15 1917.2 89.1 23.0 1867.8 1966.6 1726.2 2034.7 3 15 1858.7 38.0 9.8 1837.7 1879.8 1792.0 1928.7 4 15 1828. 2 71.0 18.4 1788.9 1867.5 1690.2 1952.5 Total 60 1899.9 119.0 15.4 1869.1 1930.6 1690.2 2237.2 PAGE 83 65Table 20 ANOVA Results of Mean Volume at MEV within FA Sum of Squares df Mean Square F Sig. Between Groups 244017.8 3 81339.3 7.702 .000 Within Groups 591385.2 56 10560.4 Total 835403.1 59 The simulation run results within functional area at scenario 2, the volume close to the freeway capacity, are list at table 19, the ANOVA analysis are list at table 20. Since F test shows significant, Tukey analysis is necessary. Table 21 Tukey Results of Mean Volume at MEV within FA SI. TO TT PO PT TO N/A .171 .003 .000 TT .171 N/A .410 .094 PO .003 .410 N/A .848 PT .000 .094 .848 N/A Figure 28 is the illustration of mean volume comparison. It can be concluded that within the functional area of an exit ramp, when the entry volume of freeway is close to the capacity, there were significant difference of traffic volume generated at threelane freeway for different exit types. The exit ramp pairs are TOPO and TOPT, which is tapered onelane exit with parallel onelane exit, tapered onelane exit with parallel twolane exit. Tapered onelane exit has more traffic volume than parallel exit type, no matter onelane or twolane, the difference are 6.9% an d 8.4% respectively. Its still the same as that at the scenario 1. It is reasonable because there is no auxiliary lane at tapered onelane exit while parallel exit type has one or two auxiliary lanes, the main line bears less traffic volume as a consequence. It a little strange that tapered onelane exit ramp has insignificant difference with tapered twolane exit. But tapered twolane exit ramp still has the same traffic performance in terms of traffic discharging volume. PAGE 84 66 1700 1750 1800 1850 1900 1950 2000 2050 TOTTPOPT Ramp TypeVolume Figure 28 Mean Volume Comparisons at MEV within FA 5.2.6. After Functional Area at Medium Entry Volume The simulation run results after functional area at scenario 2, the volume close to the freeway capacity, are list at table 22, the ANOVA analysis are list at table 23. Since F test shows insignificant, Tukey analysis is unnecessary. Table 22 Mean Discharging Volume at MEV after FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 1756.6 134.8 34.8 1682.0 1831.2 1540.6 1914.0 2 15 1764.3 88.5 22.8 1715.3 1813.4 1617.7 1895.2 3 15 1759.5 59.7 15.4 1726.4 1792.6 1669.2 1860.3 4 15 1747.7 72.9 18.8 1707.4 1788.1 1662.8 1888.8 Total 60 1757.0 91.2 11.8 1733.5 1780.6 1540.6 1914.0 Table 23 ANOVA Results of Mean Discharging Volume at MEV after FA Sum of Squares df Mean Square F Sig. Between Groups 2189.3 3 729.8 .084 .969 Within Groups 488520.4 56 8723.6 Total 490709.8 59 PAGE 85 67 1735 1740 1745 1750 1755 1760 1765 1770 TOTTPOPT Ramp TypeVolume Figure 29 Mean Volume Comparisons at MEV after FA Figure 29 is the illustration of mean volume comparison. It can be concluded that after functional area of an exit ramp, when the entry volume of freeway is close to the capacity, there were no significant difference of traffic volume generated at threelane freeway for different exit types. Thats the same thing as scenario 1. To sum up for the scenario 2, the difference between four types of exit ramp is mainly focused within the functional area, tapered onelane exit has to bear more through traffic while the traffic performance of tapered twolane has limited difference with parallel exit type. For parallel on elane or parallel twolane exit, the traffic performance is almost the same. 5.2.7. Before Functional Area at High Entry Volume Table 24 Mean Volume at HEV before FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 2142.4 53.5 13.8 2112.7 2172.0 1987.5 2207.6 2 15 2185.6 27.7 7.1 2170.3 2201.0 2143.4 2232.5 3 15 2192.7 22.0 5.7 2180.5 2204.9 2160.8 2235.1 4 15 2197.4 21.7 5.6 2185.4 2209.5 2159.7 2255.3 Total 60 2179.5 39.7 5.1 2169.3 2189.8 1987.5 2255.3 PAGE 86 68Table 25 ANOVA Results of Mean Volume at HEV before FA Sum of Squares df Mean Square F Sig. Between Groups 28694.7 3 9564.9 8.346 .000 Within Groups 64175.8 56 1146.0 Total 92870.5 59 Table 26 Tukey Results of Mean Volume at HEV before FA Sig. TO TT PO PT TO N/A .005 .001 .000 TT .005 N/A .940 .776 PO .001 .940 N/A .981 PT .000 .776 .981 N/A 2100 2120 2140 2160 2180 2200 2220 TOTTPOPT Ramp TypeVolume Figure 30 Mean Volume Comparisons at HEV before FA The simulation run results before functional area at scenario 3, the volume greater than the freeway capacity, are list at table 24, the ANOVA analysis are list at table 25. Since F test shows significant, Tukey analysis is necessary. Figure 30 is the illustration of mean volume comparison. It can be concluded that before functional area of an exit ramp at high entry volume, there were significant difference of traffic volume generated at threelane freeway for different exit types. Unlike the previous scenario1 and 2, which have more traffic volume at tapered onelane exit ramps, this scenario has more traffic volume at twolane exit and parallel type exit instead of tapered onelane exit ramp. It comes to one of conclusions; twolane exit and parallel type exit have higher discharging rate to compare with tapered one lane exit ramp, the difference is 2%, 2.3% and 2.6% respectively. When the entry traffic volume is PAGE 87 69 greater than the capacity, a part of vehicles will build up at the entry node, the higher the capacity of a given exit type, the less the build up at the entry node, the higher the traffic volume can go through a node pairs, in another word, a link. But the difference between twolane tapered exit ramps has insignificant di fference with parallel ty pe exit in terms of traffic discharging volume. 5.2.8. Within Functional Area at High Entry Volume The simulation run results within functional area at scenario 3, the volume greater than the freeway capacity, are list at table 27, the ANOVA analysis are list at table 28. Since F test shows significant, Tukey analysis is necessary. Table 27 Mean Discharging Volume at HEV within FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 2099.4 111.5 28.8 2037.6 2161.2 1911.9 2289.6 2 15 2110.7 43.6 11.3 2086.5 2134.9 2002.6 2154.4 3 15 2045.9 38.9 10.0 2024.4 2067.5 1993.7 2135.9 4 15 2032.2 29.1 7.5 2016.0 2048.3 1975.4 2086.3 Total 60 2072.1 71.5 9.2 2053.6 2090.5 1911.9 2289.6 Table 28 ANOVA Results of Mean Discharging Volume at HEV within FA Sum of Squares df Mean Square F Sig. Between Groups 67753.2 3 22584.4 5.406 .002 Within Groups 233944.3 56 4177.6 Total 301697.5 59 Table 29 Tukey Results of Mean Discharging Volume at HEV within FA Sig. TO TT PO PT TO N/A .963 .118 .030 TT .963 N/A .039 .008 PO .118 .039 N/A .937 PT .030 .008 .937 N/A PAGE 88 70 1980 2000 2020 2040 2060 2080 2100 2120 TOTTPOPT Ramp TypeVolume Figure 31 Mean Volume Comparisons at HEV within FA Figure 31 is the illustration of mean volume comparison. It can be concluded that before functional area of an exit ramp, when the entry volume of freeway is greater than the capacity, there were significant difference of traffic volume generated at threelane freeway for different exit types. The different exit ramp pairs are TOPT, TTPO, and TTPT, tapered twolane exit ramp has the highest main line volu me while the parallel twolane exit ramp has the lowest main line volume. In terms of exit type, PT has 2.5% less traffic than TT. Thats probably because that tapered type design gives the vehicles along the freeway a higher running speed, the discharging volume of tapered twolane is the highest. 5.2.9. After Functional Area at High Entry Volume Table 30 Mean Volume at HEV after FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 1774.3 250.1 64.6 1635.8 1912.8 1412.5 2111.3 2 15 1865.4 141.8 36.6 1786.8 1943.9 1665.9 2084.4 3 15 1845.1 42.0 10.8 1821.8 1868.4 1792.5 1928.8 4 15 1849.8 41.6 10.7 1826.8 1872.9 1775.7 1932.7 Total 60 1833.6 147.3 19.0 1795.6 1871.7 1412.5 2111.3 PAGE 89 71Table 31 ANOVA Results of Mean Volume at HEV after FA Sum of Squares df Mean Square F Sig. Between Groups 73810.4 3 24603.5 1.142 .340 Within Groups 1206226.1 56 21539.7 Total 1280036.6 59 The simulation run results after functional area at scenario 3, the volume greater than the freeway capacity, are list at table 29, the ANOVA analysis are list at table 30. Since F test shows insignificant, Tukey analysis is unnecessary. Figure 32 is the illustration of mean volume comparison. It can be concluded that after functional area of an exit ramp, when the entry volume of freeway is greater than capacity, there are no significant difference among these four types of exit ramp in terms of traffic discharging volume. 1720 1740 1760 1780 1800 1820 1840 1860 1880 TOTTPOPT Ramp TypeVolume Figure 32 Mean Volume Comparisons at HEV after FA 5.3. Summary This chapter researched the traffic discharging volume characteristics of four exit ramp types. The finding of this chapter can be summarized at table 32 and 33. Table 32 ANOVA Findings for Discharging Volume Before Functional Area Within Functional Area After Functional Area PAGE 90 72LEV N Y N MEV N Y N HEV Y Y N Table 33 Tukey Findings for Discharging Volume Before Functional Area Within Functional Area After Functional Area LEV N/A TOPT N/A MEV N/A TOPO, TOPT N/A HEV TOTT, TOPO, TOPT TOPT ,TTPO, TTPT N/A N/A: not applicable. It was found that within functional area of exit ramp, no matter how much is the entry volume, the discharging volume are statistically different among these four types of exit ramp. But one exit ramp pair seemed significant at all entry volumes: tapered onelane and parallel twolane exit ramp. Tapered onelane exit has more traffic volume than parallel exit type, no matter onelane or twolane. It reasonable because there is no auxiliary lane at tapered onelane exit while parallel exit type has one or two au xiliary lane, the main line bears less traffic volume as a consequence. Normally, the parallel type exit tamp bear less traffic volume, hence has lower traffic density and better LOS comparing with tapered type exit ramp, but for the parallel exit tamp, there are no significant difference between onelane or twolane exit ramp. In most cases, its the same for tapered onelane exit and twolane exit, except at high entry volume. Tapered twolane exit ramp has the highes t main line volume while the parallel twolane exit ramp has the lowest main line volume. Thats probably because that tapered type design gives the vehicles along the freeway a higher running speed, the discharging volume of tapered twolane is the highest. In terms of exit type, parallel type has 6.9% and 3.7% less traffic than tapered type when the exit ramp has one lane and two lanes respectively within functional area. PAGE 91 73 General, in terms of traffic discharging volume, the tapered twolane exit ramp has the best operational performance. It has the highest discharging rate compared with other three exit type. PAGE 92 74 Chapter 6 Traffic Speed Comparisons 6.1. Introduction The previous chapters research the traffic discharging volume characteristics of different exit types. This chapter analyzes the speed patterns at exit ramps based on the traffic data collected from the CORSIM simulation. The experiment design for speed analyses is the same as that in traffic volume analyses in pervious chapters. A total 7500 feet freeway was deployed to detect the speeds of vehicles passing them. It compares the traffic operational speed before, within and after the functional area of an exit ramp. The 7500 feet length freeway was divided into three parts for comparison, the first 2500 feet length was believed before the functional area of exit ramp, motorist were assumed to drive similar to a long freeway segment without the influence of onramp and exit ramp; the second 2500 feet length was believed within the functional area of exit ramp, actually, the start of auxiliary la ne occurs within this segment, the traffic turbulence is believed to happen mostly within this area, traffic speed is deemed at giant derivation; the third 2500 feet length was believed the exiting vehicle cleared from the freeway mainline the remaining vehicles will sp eed up to recover the lost time caused by queuing, avoiding and/or unnecessary lane changing. Different from the volume discharging at exit ramps, the definition of speed at work zones is the same as that in freeway. There is no controversial and different between speed at work zones and that on freeway. In classical traffic flow theories there were two methods to record traffic speed in macroscopic speed characteristics. One was timemean speed and the other was spacemean speed. PAGE 93 75 Macroscopic speed characteristics were those speed characteristics of vehicle groups passing a point or short segment during a specified period of time or traveling over longer sections of highway. Timemean speed and spacemean speed were two types of methods to describe the speed conditions. Timemean speed was the average or mean of individual speeds recorded for vehicles passing a particular point or short segment over a selected time period. The equation was as follows. ANOVA and Turkey test are used for the statistical comparisons. 6.2. Mean Speed Comparisons The designed three scenarios are corresponding to traffic volume less than capacity, close to capacity and greater than capacity respectively. All three scenarios are run 5 times for the four exit ramp types. 6.2.1. Before Functional Area at Low Entry Volume The simulation run results before functional area at scenario 1, the entry volume are lower than the capacity, are list at table 34, the ANOVA analysis are list at table 35. Since F test shows insignificant, Tukey analysis is unnecessary. Figure 33 is the illustration of mean speed comparison. It can be concluded that before functional area of exit ramp, when the entry volume of freeway is lower than the capacity, there were no significant difference of traffic speed generated at threelane freeway. This is the same thing as traffic discharging volume generated. Table 34 Mean Speed at LEV before FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 67.805 .55 .14 67.5 68.1 66.9 68.6 2 15 67.775 .53 .14 67.5 68.1 66.7 68.4 3 15 67.643 .56 .14 67.3 67.9 66.7 68.6 4 15 67.800 .65 .17 67.4 68.2 66.6 68.9 Total 60 67.8 .56 .073 67.6 67.9 66.6 68.9 PAGE 94 76Table 35 ANOVA Results of Mean Speed at LEV before FA Sum of Squares df Mean Square F Sig. Between Groups 0.2 3 .086 .261 .853 Within Groups 18.4 56 .329 Total 18.7 59 67.55 67.6 67.65 67.7 67.75 67.8 67.85 TOTTPOPT Ramp TypeSpeed Figure 33 Mean Speed Comparisons at LEV before FA 6.2.2. Within Functional Area at Low Entry Volume Table 36 Mean Speed within Functional Area at LEV within FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 66.611 .846 .22 66.1 67.1 65.4 68.0 2 15 66.702 .674 .17 66.3 67.1 65.6 67.8 3 15 66.735 .701 .18 66.3 67.1 65.8 68.1 4 15 66.851 .758 .20 66.4 67.3 65.6 67.9 Total 60 66.7 .734 .095 66.5 66.9 65.4 68.1 Table 37 ANOVA Results of Mean Speed at LEV within FA Sum of Squares df Mean Square F Sig. Between Groups .441 3 .147 .263 .852 Within Groups 31.317 56 .559 Total 31.758 59 PAGE 95 77 66.45 66.5 66.55 66.6 66.65 66.7 66.75 66.8 66.85 66.9 TOTTPOPT Ramp TypeSpeed Figure 34 Mean Speed Comparisons at LEV within FA The simulation run results within functional area at scenario 1, the entry volume are lower than the capacity, are list at table 36, the ANOVA analysis are list at table 37. Since F test shows insignificant, Tukey analysis is unnecessary. Figure 34 is the illustration of mean speed comparisons. It can be concluded that within functional area of exit ramp, when the entry volume of freeway is lower than the capacity, there were no significant difference of traffic speed generated at threelane freeway. This is the same thing as traffic volume generated. 6.2.3. After Functional Area at Low Entry Volume The simulation run results after functional area at scenario 1 are list at table 38, the ANOVA analysis are list at table 39. Since F test shows insignificant, Tukey analysis is unnecessary. Table 38 Mean Speed at LEV after FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 66.582 .547 .14 66.3 66.9 65.8 67.5 2 15 66.521 .466 .12 66.3 66.8 65.7 67.4 3 15 66.560 .635 .16 66.2 66.9 65.5 68.1 4 15 66.653 .672 .17 66.3 67.0 65.5 67.7 Total 60 66.579 .572 .074 66.4 66.7 65.5 68.1 PAGE 96 78Table 39 ANOVA Results of Mean Speed at LEV after FA Sum of Squares df Mean Square F Sig. Between Groups .139 3 .046 .135 .939 Within Groups 19.198 56 .343 Total 19.337 59 66.45 66.5 66.55 66.6 66.65 66.7 TOTTPOPT Ramp TypeSpeed Figure 35 Mean Speed Comparisons at LEV after FA Figure 35 is the illustration of mean speed comparisons. It can be concluded that after functional area of exit ramp, when the entry volume of freeway is lower than the capacity, there were no significant difference of traffic speed generated at threelane freeway. This is the same thing as traffic volume generated. To sum up, in terms of running speed, when the entry volume is lower than the capacity, there is no significant difference among these four types of exit ramp. 6.2.4. Before Functional Area at Medium Entry Volume Table 40 Mean Speed at MEV before FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 57.184 .246 .064 57.0 57.3 56.7 57.5 2 15 57.225 .318 .082 57.0 57.4 56.8 57.8 3 15 57.262 .276 .071 57.1 57.4 56.7 57.7 4 15 57.078 .239 .062 56.9 57.2 56.7 57.4 Total 60 57.187 .274 .035 57.1 57.2 56.7 57.8 PAGE 97 79Table 41 ANOVA Results of Mean Speed at MEV before FA Sum of Squares df Mean Square F Sig. Between Groups .284 3 .095 1.281 .290 Within Groups 4.143 56 .074 Total 4.428 59 56.95 57 57.05 57.1 57.15 57.2 57.25 57.3 TOTTPOPT Ramp TypeSpeed Figure 36 Mean Speed Comparisons at MEV before FA The simulation run result before functional area at scenario 2, the traffic entry volume close to the capacity, are list at table 40, the ANOVA analysis are list at table 41. Since F test shows insignificant, Tukey analysis is unnecessary. Figure 36 is the illustration of mean speed comparisons. It can be concluded that before functional area of exit ramp, when the entry volume of freeway is lower than the capacity, there were no significant difference of traffic speed generated at threelane freeway. This is the same thing as traffic volume generated. 6.2.5. Within Functional Area at Medium Entry Volume The simulation run results within functional area at scenario 2, the volume close to the freeway capacity, are list at table 42, the ANOVA analysis are list at table 43. Since F test shows significant, Tukey analysis is ne cessary. Table 44 is the Tukey test results. Figure 37 is the illustration of mean speed comparisons. It can be concluded that within functional area of exit ramp, when the entry volume is close to the capacity, there are significant difference between different exit ramps, the ramp type pair are TO and PT, PAGE 98 80 which is tapered onelane and parallel twolane exit type, parallel twolane exit has the faster main line speed than tapered onelane exit. But there is no significant difference between parallel onelane or twolane exit type. Table 42 Mean Speed at MEV within FA N Mean Std. Std. 95% Confidence Interval for Mean Minimum Maximum Deviation Error Lower Bound Upper Bound 1 15 55.359 1.365 .352 54.6 56.1 53.1 56.6 2 15 55.712 .838 .216 55.2 56.2 54.0 56.8 3 15 56.203 .541 .140 55.9 56.5 55.4 57.0 4 15 56.230 .457 .118 56.0 56.5 55.5 56.9 Total 60 55.876 .928 .120 55.6 56.1 53.1 57.0 Table 43 ANOVA Results of Mean Entry Volume at MEV within FA Sum of Squares df Mean Square F Sig. Between Groups 7.895 3 2.632 3.432 .023 Within Groups 42.940 56 .767 Total 50.835 59 Table 44 Tukey Results of Mean Speed at MEV within FA Sig. TO TT PO PT TO N/A .690 .051 .042 TT .690 N/A .423 .375 PO .051 .423 N/A 1.00 PT .042 .375 1.00 N/A 54.8 55 55.2 55.4 55.6 55.8 56 56.2 56.4 TOTTPOPT Ramp TypeSpeed Figure 37 Mean Speed Comparisons at MEV within FA PAGE 99 81 6.2.6. After Functional Area at Medium Entry Volume The simulation run results after functional area at scenario 2, the volume close to the freeway capacity, are list at table 45, the ANOVA analysis are list at table 46. Since F test shows insignificant, Tukey analysis is unnecessary. Figure 38 is the illustration of mean speed comparisons. It can be concluded that after functional area of exit ramp, when the entry volume is close to the capacity, there are no significant difference between different exit ramps. Table 45 Mean Speed at MEV after FA N Mean Std. Std. 95% Confidence Interval for Mean Minimum Maximum Deviation Error Lower Bound Upper Bound 1 15 56.277 .382 .099 56.1 56.5 55.5 57.0 2 15 56.097 .540 .139 55.8 56.4 55.3 56.9 3 15 56.209 .489 .126 55.9 56.5 55.1 57.0 4 15 56.236 .473 .122 56.0 56.5 55.5 57.3 Total 60 56.205 .467 .060 56.1 56.3 55.1 57.3 Table 46 ANOVA Results of Mean Speed at MEV after FA Sum of Squares df Mean Square F Sig. Between Groups .269 3 .090 .398 .755 Within Groups 12.607 56 .225 Total 12.876 59 56 56.05 56.1 56.15 56.2 56.25 56.3 TOTTPOPT Ramp TypeSpeed Figure 38 Mean Speed Comparisons at MEV after FA PAGE 100 82 To sum up, when the entry volume is close to the capacity of exit ramp, there are still has limited difference among difference exit ramps, except the pair of TOPT within the functional area, tape red onelane exit has the lowest running speed. 6.2.7. Before Functional Area at High Entry Volume The simulation run results before functional area at scenario 3, the volume greater than the freeway capacity, are list at table 16, the ANOVA analysis are list at table 17. Since F test shows significant, Tukey analysis is necessary. Table 47 Mean Speed at HEV before FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 35.257 4.755 1.227 32.6 37.9 25.7 43.9 2 15 46.449 5.908 1.525 43.2 49.7 37.9 52.0 3 15 51.871 .324 .084 51.7 52.0 51.3 52.5 4 15 51.819 .261 .067 51.7 52.0 51.4 52.3 Total 60 46.349 7.767 1.002 44.3 48.3 25.7 52.5 Table 48 ANOVA Results of Mean Speed at HEV before FA Sum of Squares df Mean Square F Sig. Between Groups 2751.982 3 917.327 63.603 .000 Within Groups 807.666 56 14.423 Total 3559.648 59 Table 49 Tukey Results of Mean Speed at HEV before FA Sig. TO TT PO PT TO N/A .000 .000 .000 TT .000 N/A .001 .002 PO .000 .001 N/A 1.000 PT .000 .002 1.000 N/A PAGE 101 83 0 10 20 30 40 50 60 TOTTPOPT Ramp TypeSpeed Figure 39 Mean Speed Comparisons at HEV before FA Figure 39 is the illustration of mean speed comparisons. It can be concluded that before functional area of exit ramp, when the entry volume is greater than the capacity, there are significant difference between different exit ramps. Except the parallel onelane exit and parallel twolane exit type, all othe r exit type pairs are statistically different. Tapered onelane exit has the lowest running speed, while the parallel exit types have the highest running speed. It can be concluded that parallel type exit ramp can retain higher entry speed (from 60mph to approximately 51 mph), the tapered exit ramp type are easily losing their original speed. But the differe nce between parallel onelane and parallel twolane are insignificant. In terms of exit type, para llel exit has 32% and 10% highe r speed than tapered exit at onelane and twolane exit respectively. The percentage is much higher than that of discharging volume. In terms of exit number, tapered twolane has 24.1% higher speed than tapered onelane. That is still much higher than the discharging volume. It can be concluded from the simulation data that speed are easier to be lost than the discharging volume. They are more sensitive to the entry volume. PAGE 102 84 6.2.8. Within Functional Area at High Entry Volume The simulation run results within functional area at scenario 3, the volume greater than the freeway capacity, are list at table 50, the ANOVA analysis are list at table51. Since F test shows significant, Tukey analysis is necessary. Table 50 Mean Speed at HEV within FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 29.184 4.931 1.273 26.4 31.9 21.9 36.3 2 15 39.778 5.172 1.335 36.9 42.6 29.0 48.0 3 15 49.708 .841 .217 49.2 50.2 47.8 50.9 4 15 49.822 .712 .1839 49.4 50.2 48.3 50.6 Total 60 42.123 9.277 1.197 39.7 44.5 21.9 50.9 Table 51 ANOVA Results of Mean Speed at HEV within FA Sum of Squares df Mean Square F Sig. Between Groups 4345.848 3 1448.616 110.841 .000 Within Groups 731.879 56 13.069 Total 5077.727 59 Table 52 Tukey Results of Mean Speed at HEV within FA Sig. TO TT PO PT TO N/A .000 .000 .000 TT .000 N/A .000 .000 PO .000 .000 N/A 1.000 PT .000 .000 1.000 N/A PAGE 103 85 0 10 20 30 40 50 60 TOTTPOPT Ramp TypeSpeed Figure 40 Mean Speed Comparisons at HEV within FA Figure 40 is the illustration of mean speed comparisons. It can be concluded that within functional area of exit ramp, when the entry volume is greater than the capacity, there are significant difference between different exit ramps. Except the parallel onelane exit and parallel twolane exit type, all othe r exit type pairs are statistically different. Tapered onelane exit has the lowest running speed, while the parallel exit types have the highest running speed. It can be concluded that parallel type exit ramp can retain higher entry speed (from 60mph to approximately 50 mph), the tapered exit ramp type are easily losing their original speed. Thats quite the same as before the functional area of exit ramp. But still, the difference between PO and PT are insignificant. In terms of exit type, para llel exit has 41.3% and 20.2% higher speed than tapered exit for onelane and twolane exit respectively. In terms of exit lane number, twolane has 26.6% higher speed than onelane for tapere d type. That is still more significant than the discharging volume. 6.2.9. After Functional Area at High Entry Volume The simulation run results after functional area at scenario 3, the volume greater than the freeway capacity, are list at table 53, the ANOVA analysis are list at table 54. Since F test shows significant, Tukey analysis is necessary. PAGE 104 86Table 53 Mean Speed at HEV after FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 15 48.856 .665 .172 48.5 49.2 47.6 50.0 2 15 48.856 .564 .146 48.5 49.2 47.8 49.5 3 15 50.567 .667 .172 50.2 50.9 49.5 52.0 4 15 50.653 .540 .139 50.4 50.9 49.3 51.4 Total 60 49.733 1.067 .138 49.4 50.0 47.6 52.0 Table 54 ANOVA Results of Mean Speed at HEV after FA Sum of Squares df Mean Square F Sig. Between Groups 46.198 3 15.399 41.129 .000 Within Groups 20.967 56 .374 Total 67.165 59 Table 55 Tukey Results of Mean Speed at HEV after FA Sig. TO TT PO PT TO N/A 1.000 .000 .000 TT 1.000 N/A .000 .000 PO .000 .000 N/A .980 PT .000 .000 .980 N/A 47.5 48 48.5 49 49.5 50 50.5 51 TOTTPOPT Ramp TypeSpeed Figure 41 Mean Speed Comparisons at HEV after FA Figure 41 is the illustration of mean speed comparisons. It can be concluded that after functional area of exit ramp, when the entry volume is greater than the capacity, there are significant difference between different exit ramps. The parallel exit types have PAGE 105 87 very obviously difference with tapered exit types, but the onelane exit and twolane exit has very limited difference. It is obvious that parallel exit type has faster running speed comparing with tapered exit type. In terms of exit type, parallel has 3.4% and 3.5% higher speed than tapered exit for onelane and twolane respective ly. Although it is still signif icant statistically, but the gap can be omitted comparing with what happened within the functional area. 6.3. Summary Traffic speed characteristics at different exit ramp are different according to the entry traffic volume, the ANOVA and Tukey findings can be tabled here. It was found that at high entry volume, no matter its before, within or after functional area of an exit ramp, there are significant difference between exit ramp pairs. Except the pair of POPT, all other pairs are statically different before and within functional area of exit ramp. After functional area, except the pairs of TOTT and POPT, all other pairs are different. Table 56 ANOVA Findings for Speed Before Functional Area Within Functional AreaAfter Functional Area LEV N N N MEV N Y N HEV Y Y Y Table 57 Tukey Findings for Speed Before Functional Area Within Functional AreaAfter Functional Area LEV N/A N/A N/A MEV N/A TOPO TOPT N/A HEV TOTT,TOPO,TOPT TTPO,TTPT TOTT,TOPO,TOPT TTPO,TTPT TOPO,TOPT TTPO,TTPT The running speed has 10% to 32% difference between the tabled pairs before the functional area; it also has 20.2% to 41.3% difference within the functional area. After functional area, the difference is reduced to 3.4% and 3.5% respectively. It seemed that speed is not easily to be preserved as traffic discharging volume. PAGE 106 88 To sum up, speeds generated are mostly alike at low or medium entry volumes, but at high volumes, parallel type exit ramp can have higher operational speed to compare with tapered type exit ramp. But the differenc e between parallel twola ne exit and parallel onelane exit is not significant. PAGE 107 89 Chapter 7 Lane Change Comparisons 7.1. Introduction The previous chapters research the traffic speed characteristics of different exit types. This chapter analyzes the lane change characteristics at exit ramps based on the traffic data collected from the CORSIM simulation. Conventional traffic flow theory dictates that flow on a freeway is usually constrained only by a small number of critic al locations or bottle necks. When active, these bottlenecks cause queues that can stretch for several miles and reduce flow on other parts of the network. Bottlenecks are often thought to arise over short distances and are usually modeled as if they occur at discrete points since the resulting queues are thought to be much longer then the bottleneck region.XIV Their book presents evidence that the delay causing phenomena may actually occur over extended distances. Some of which may occur downstream of the apparent bottleneck where drivers are accelerating away from the queue, while related phenomena are observed in the queue, over a mile upstrea m of the apparent bottleneck. It is shown that lane change maneuvers are responsible for some of the losses, reducing travel speed and consuming capacity when vehicles enter a given lane. These losses in one lane are not fully balanced by gains in other lanes. The lane change maneuver was not clearly researched at exit ramp area. The experiment design for lane change number analyses is the same as that in traffic volume and traffic speed analyses in pervious two chapters. A total 7500 feet freeway was deployed to detect the speeds of vehicles passing them. It compares the average lane change number before, within and after the functional area of an exit ramp. The 7500 feet length freeway was divided into three parts for PAGE 108 90 comparison, the first 2500 feet length was believed before the functional area of exit ramp, motorist were assumed to drive simi lar to a long freeway segment without the influence of onramp and exit ramp; the second 2500 feet length was believed within the functional area of exit ramp, actually, the start of auxiliary lane occurs within this segment, the traffic turbulence is believed to happen mostly within this area, traffic volume at different lane, traffic speed and total lane change maneuver is deemed at giant derivation ; the third 2500 feet length was believed the exiting vehicle cleared from the freeway mainline (although in some cases, th e exiting vehicles are forced to drive along the freeway mainline because the headway space at the auxiliary lane are too short to make a safe lane change, in another word, they missed their destination), the remaining vehicles will speed up to recover the lost time caused by queuing, avoiding and/or unnecessary lane changing. ANOVA and Turkey test are used for the statistical comparisons. 7.2. Total Lane Change Number Comparisons The designed three scenarios are corresponding to traffic volume less than capacity, close to capacity and greater than capacity respectively. All three scenarios are run 5 times for the four exit ramp types. 7.2.1. Before Functional Area at Low Entry Volume The simulation run results before functional area at scenario 1, the volume less than the freeway capacity, are list at table 58, the ANOVA analysis are list at table 59. Since F test shows insignificant, Tukey analysis is unnecessary. Table 58 Mean Lane Change Number at LEV before FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 5 210.0 24.6 11.0 179.5 240.5 187 240 2 5 203.2 23.4 10.4 174.2 232.2 176 234 3 5 217.6 21.5 9.6 190.9 244.3 196 251 4 5 210.8 10.9 4.9 197.3 224.3 201 227 Total 20 210.4 19.8 4.4 201.1 219.7 176 251 PAGE 109 91Table 59 ANOVA Results of Lane Change Number at LEV before FA Sum of Squares df Mean Square F Sig. Between Groups 1560.000 3 520.000 1.404 .251 Within Groups 20744.400 56 370.436 Total 22304.400 59 195 200 205 210 215 220 TOTTPOPT Ramp TypeLane Change Number Figure 42 Mean Lane Change Comparisons at LEV before FA Figure 42 is the illustration of mean lane change number comparisons. It can be concluded that before functional area of exit ramp, when the entry volume is less than the capacity, there are no significant difference between different exit ramps. This is quite the same thing as the traffic discharge volume and speed analysis. 7.2.2. Within Functional Area at Low Entry Volume The simulation run results within functional area are list at table 60, the ANOVA analysis are list at table 61. Since F test shows the total lane change number of these four types of exit ramp is significant, Tukey analysis is necessary. It can be concluded that within functional area of exit ramp, when the entry volume of freeway is lower than the capacity, there were significant difference of total lane change number generated at threelane freeway. It is different from the analysis of discharging volume and speed. That is not difficult to understand, within functional, the lane number for different exit types are different, especially the parallel twolane exit ramp, it has fivelane when close to the physical nose area (threelane main line and two PAGE 110 92 auxiliary lanes). In contrast, the tapered onela ne exit ramp has threelane all the way in the main line area. Within Functional Area at Low Entry Volume in terms of exit type, parallel type has 41.3% and 24% higher lane change number than tapered type for onelane exit and twolane exit respectively. In terms of exit number, twolane exit has 30.1% and 9.5% than onelane exit for tapered type and parall el type. It seemed that exit type has more impact on the lane change number than the exit lane number. Table 60 Mean Lane Change Number at LEV within FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 5 168.4 4.9 2.2 162.3 174.4 163 174 2 5 240.8 7.3 3.3 231.7 249.9 234 251 3 5 286.8 13.8 6.2 269.6 303.9 266 302 4 5 317.0 24.1 10.8 287.0 346.9 289 355 Total 20 253.2 59.0 13.2 225.6 280.8 163 355 Table 61 ANOVA Results of Lane Change Number at LEV within FA Sum of Squares df Mean Square F Sig. Between Groups 62720.950 3 20906.983 98.305 .000 Within Groups 3402.800 16 212.675 Total 66123.750 19 Table 62 Tukey Results of Lane Change Number at LEV within FA Sig. TO TT PO PT TO N/A .000 .000 .000 TT .000 N/A .001 .000 PO .000 .001 N/A .022 PT .000 .000 .022 N/A PAGE 111 93 0 50 100 150 200 250 300 350 TOTTPOPT Ramp TypeLane Change Number Figure 43 Mean Lane Change Comparisons at LEV within FA 7.2.3. After Functional Area at Low Entry Volume The simulation run results after functional area are list at table 63, the ANOVA analysis are list at table 64. Since F test shows the total lane change number of these four types of exit ramp is significant, Tukey analysis is necessary. Table 63 Mean Lane Change Number at LEV after FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 5 156.0 11.0 4.9 142.3 169.7 142 170 2 5 173.4 14.9 6.7 154.9 191.9 163 199 3 5 164.8 10.0 4.5 152.4 177.2 152 178 4 5 150.6 11.0 4.9 137.0 164.2 141 164 Total 20 161.2 14.1 3.1 154.6 167.8 141 199 Table 64 ANOVA Results of Lane Change Number at LEV after FA Sum of Squares df Mean Square F Sig. Between Groups 1506.000 3 502.000 3.555 .038 Within Groups 2259.200 16 141.200 Total 3765.200 19 Table 65 Tukey Results of Lane Change Number at LEV after FA Sig. TO TT PO PT TO N/A .136 .653 .888 TT .136 N/A .669 .036 PO .653 .669 N/A .271 PT .888 .036 .271 N/A PAGE 112 94 135 140 145 150 155 160 165 170 175 180 TOTTPOPT Ramp TypeLane Change Number Figure 44 Mean Lane Change Comparisons at LEV after FA Figure 44 is the illustration of mean lane change comparisons after functional area at low entry volume; it seemed that tapered twolane and parallel twolane exit ramp have the significant lane change number. The para llel twolane exit has th e least lane change number while the tapered twolane exit has the most lane change number. After functional at low entry volume, in te rms of exit type, parallel has 13.1% less lane change number than tapered exit at twolane. In terms of exit lane number, twolane have 10% more lane change number at tapered type, but it has 8.6% less lane change number at parallel type. To summary, at low entry volume, in terms of total lane change number, there are no significant difference among these four types of exit ramp, except after the functional area. The tapered twolane has the largest lane change number. 7.2.4. Before Functional Area at Medium Entry Volume The simulation run results before functional area at scenario 2 are list at table 66, the ANOVA analysis are list at table 67. Since F test shows the total lane change number of these four types of exit ramp is insignificant, Tukey analysis is unnecessary. Figure 45 is the illustration of mean lane change comparis ons before functional area at medium entry volume; it seemed although the parallel twolane exit ramp has the most lane change number before the functional area, its not st atistically different. Parallel twolane exit ramp has 8% higher lane change number than tapered twolane exit ramp. PAGE 113 95Table 66 Mean Lane Change Number at MEV before FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 5 142.40 6.189 2.768 134.72 150.08 134 150 2 5 140.60 10.015 4.479 128.16 153.04 128 153 3 5 143.80 15.353 6.866 124.74 162.86 125 162 4 5 152.80 13.330 5.962 136.25 169.35 140 175 Total 20 144.90 11.809 2.641 139.37 150.43 125 175 Table 67 ANOVA Results of Lane Change Number at MEV before FA Sum of Squares df Mean Square F Sig. Between Groups 441.800 3 147.267 1.067 .391 Within Groups 2208.000 16 138.000 Total 2649.800 19 130 135 140 145 150 155 TOTTPOPT Ramp TypeLane Change Number Figure 45 Mean Lane Change Comparisons at MEV before FA 7.2.5. Within Functional Area at Medium Entry Volume Table 68 Mean Lane Change Number at MEV within FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 5 410.4 23.2 10.4 381.6 439.2 373 430 2 5 497.6 30.4 13.6 459.9 535.3 445 523 3 5 560.6 28.4 12.7 525.3 595.9 536 607 4 5 654.4 36.6 16.4 609.0 699.8 615 703 Total 20 530.7 95.5 21.4 486.0 575.4 373 703 PAGE 114 96 Table 69 ANOVA Results of Lane Change Number at MEV within FA Sum of Squares df Mean Square F Sig. Between Groups 158816.950 3 52938.983 58.687 .000 Within Groups 14432.800 16 902.050 Total 173249.750 19 Table 70 Tukey Results of Lane Change Number at MEV within FA Sig. TO TT PO PT TO N/A .002 .000 .000 TT .002 N/A .020 .000 PO .000 .020 N/A .001 PT .000 .000 .001 N/A The simulation run results within functional area at scenario 2 are list at table 68, the ANOVA analysis are list at table 69. Since F test shows the total lane change number of these four types of exit ramp is significant, Tukey analysis is necessary. Within Functional Area at medium entry volu me, in terms of exit type, parallel type has 26.8% and 24% higher lane change number than tapered type for onelane exit and twolane exit respectively. In terms of exit number, twolane exit has 17.5% and 14.3% than onelane exit for tapered type and parall el type. It seemed that exit type has more impact on the lane change number than the exit lane number. 0 100 200 300 400 500 600 700 TOTTPOPT Ramp TypeLane Change Number Figure 46 Mean Lane Change Comparison at MEV within FA Figure 46 is the illustration of mean lane change comparisons within functional area at medium entry volume; it seemed that all these four types of exit ramp are statistically PAGE 115 97 different. The parallel twolane exit ramp has the most lane change number within the functional area; the tapered onelane exit type has the least lane change number. 7.2.6. After Functional Area at Medium Entry Volume Table 71 Mean Lane Change Number at MEV after FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 5 204.8 9.7 4.3 192.8 216.8 195 216 2 5 214.0 16.7 7.5 193.2 234.8 187 232 3 5 206.6 4.5 2.0 201.0 212.2 200 211 4 5 215.8 17.2 7.7 194.4 237.2 191 234 Total 20 210.3 13.0 2.9 204.2 216.4 187 234 Table 72 ANOVA Results of Mean Lane Change Number at MEV after FA Sum of Squares df Mean Square F Sig. Between Groups 439.400 3 146.467 .849 .487 Within Groups 2758.800 16 172.425 Total 3198.200 19 195 200 205 210 215 220 TOTTPOPT Ramp TypeLane Change Number Figure 47 Mean Lane Change Comparisons at MEV after FA The simulation run results after functional area at scenario 2 are list at table 71, the ANOVA analysis are listed at table 72. Since F test shows the total lane change number of these four types of exit ramp is insignificant, Tukey analysis is unnecessary. PAGE 116 98 Figure 47 is the illustration of mean lane change comparisons after functional area at medium entry volume; it seemed that all these four types of exit ramp are statistically insignificant. 7.2.7. Before Functional Area at High Entry Volume Table 73 Mean Lane Change Number at HEV before FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 5 211.8 53.5 23.9 145.4 278.2 168 292 2 5 178.8 50.2 22.4 116.4 241.1 128 248 3 5 142.0 10.6 4.8 128.8 155.2 128 153 4 5 144.4 8.8 3.9 133.5 155.3 135 156 Total 20 169.2 45.1 10.1 148.1 190.3 128 292 The simulation run results before functional area at scenario 3, the volume greater than the freeway capacity, are list at table 73, the ANOVA analysis are list at table 74. Since F test shows the total lane change nu mber of these four types of exit ramp is significant, Tukey analysis is necessary. The Tukey test results are listed at table 75. Table 74 ANOVA Results of Mean Lane Change Number at HEV before FA Sum of Squares df Mean Square F Sig. Between Groups 16308.950 3 5436.317 3.900 .029 Within Groups 22300.800 16 1393.800 Total 38609.750 19 Table 75 Tukey Results of Lane Change Number at HEV before FA Sig. TO TT PO PT TO N/A .519 .042 .051 TT .519 N/A .428 .485 PO .042 .428 N/A 1.000 PT .051 .485 1.000 N/A Figure 48 is the illustration of mean lane change comparisons before functional area at high entry volume; it seemed that only tapered onelane exit ramp has statistically significant difference with parallel onela ne exit ramp. Other ramp types have no significant difference. Unlike th e traditional concept, it is the tapered exit type, not the PAGE 117 99 parallel exit type has the most lane change number. It should not count too much since the deviation of TO be the biggest too. At high entry volume before the functional area, in terms of exit type, parallel has 33% and 19.2% less lane change number than tapered exit for onelane and twolane respectively. 0 50 100 150 200 250 TOTTPOPT Ramp TypeLane Change Number Figure 48 Mean Lane Change Comparisons at HEV before FA 7.2.8. Within Functional Area at High Entry Volume The simulation run results within functional area at scenario 3, the volume greater than the freeway capacity, are list at table 76, the ANOVA analysis are list at table 77. Since F test shows the total lane change nu mber of these four types of exit ramp is significant, Tukey analysis is necessary. Table 76 Mean Lane Change Number at HEV within FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 5 635.8 44.7 20.0 580.2 691.3 574 677 2 5 657.0 51.8 23.2 592.6 721.3 614 724 3 5 718.8 37.6 16.8 672.1 765.5 680 770 4 5 815.8 45.8 20.5 758.9 872.7 739 855 Total 20 706.8 82.9 18.5 668.0 745.6 574 855 PAGE 118 100Table 77 ANOVA Results of Lane Change Number at HEV within FA Sum of Squares df Mean Square F Sig. Between Groups 97730.150 3 32576.717 15.890 .000 Within Groups 32802.400 16 2050.150 Total 130532.550 19 Table 78 Tukey Results of Lane Change Number at HEV within FA Sig. TO TT PO PT TO N/A .879 .047 .000 TT .879 N/A .177 .000 PO .047 .177 N/A .018 PT .000 .000 .018 N/A Figure 49 is the illustration of mean lane change comparisons within functional area at high entry volume; it seemed that the follow ing exit ramp pairs are significant different: TOPO, TOPT, TTPT, and POPT. The parallel twolane exit type has the highest lane change number, while the tapered onelane exit type has the least lane change numbers. Within functional area at high entry volu me, in terms of exit type, parallel has 11.5% and 19.5% higher lane change number to compare with tapered type for onelane exit and twolane exit respectively. In terms of exit lane number, twolane has 11.9% more lane change maneuver than onelane exit at parallel type. 0 200 400 600 800 1000 TOTTPOPT Ramp TypeLane Change Number Figure 49 Lane Change Comparisons at HEV within FA PAGE 119 101 7.2.9. After Functional Area at High Entry Volume The simulation run results after functional area at scenario 3, the volume greater than the freeway capacity, are list at table 79, the ANOVA analysis are list at table 80. Since F test shows the total lane change nu mber of these four types of exit ramp is significant, Tukey analysis is necessary. Check table 81. Table 79 Mean Lane Change Number at HEV after FA 95% Confidence Interval for Mean Ramp Type N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 5 315.0 15.4 6.9 295.8 334.2 303 339 2 5 275.8 25.9 11.6 243.7 307.9 251 316 3 5 251.4 21.3 9.5 224.9 277.9 223 277 4 5 244.8 11.6 5.2 230.3 259.3 227 257 Total 20 271.7 33.3 7.4 256.1 287.4 223 339 Table 80 ANOVA Results of Mean Lane Change Number at HEV after FA Sum of Squares df Mean Square F Sig. Between Groups 15136.950 3 5045.650 13.467 .000 Within Groups 5994.800 16 374.675 Total 21131.750 19 Table 81 Tukey Results of Mean Lane Change Number at HEV after FA Sig. TO TT PO PT TO N/A .026 .000 .000 TT .026 N/A .231 .092 PO .000 .231 N/A .948 PT .000 .092 .948 N/A Figure 50 is the illustration of mean lane change comparisons after functional area at high entry volume; it seemed that the exit ramp pair: TOTT, TOPO, and TOPT are statistically significant. Tapered onelane exit has the most lane change number after functional area, while the parallel twolane exit ramp type has the least lane change number. It is not difficult to understand; tapered on elane exit ramp has less discharging rate than other exit ramps, especially the parallel exit ramp, when the traffic volume is PAGE 120 102 relatively low, most vehicles can take exit at the exit ramp area, after functional area, most vehicles still stay at the freeway main line will continue their destination, making the unnecessary lane change number less. Nevertheless, when the entry volume is much higher than the capacity, more amount of vehicles at tapered onelane exit ramp will not be discharged and forced to continue driving on the main line, making the lane change number more after the functional to compare with other types of exit ramp type. At high entry volume after functional area, in terms of exit type, parallel has less number of lane changes, the percentage is 25.3% and 12.7% for onelane and twolane exit respectively. In terms of exit lane number, twolane has 14.2 less number of lane change than onelane at tapered type. 0 50 100 150 200 250 300 350 TOTTPOPT Ramp TypeLane Change Number Figure 50 Mean Lane Change Comparisons at HEV after FA 7.3. Summary The findings from this chapter are summarized at table 82, table 83. It can be concluded that lane changing number is the most complicated factor, no matter at low entry volume, medium entry volume, or high entry volume, the exit ramp pairs are different except a few ramp pairs. Within functional area, parallel type exit ramp has more lane changing number; twolane exit ramp has more lane changing number. From the lane changing number of view, PAGE 121 103 tapered type exit is better than parallel ty pe exit; onelane exit ra mp is better than twolane exit ramp. Within Functional Area at low entry volume, in terms of exit type parallel type has 41.3% and 24% higher lane change number than tapered type for onelane exit and twolane exit respectively. In terms of exit number, twolane exit has 30.1% and 9.5% than onelane exit for tapered type and parallel type It seemed that exit type has more impact on the lane change number than the exit lane number. Before functional area at medium entry volum e, parallel twolane exit ramp has 8% higher lane change number than tapered twolane exit ramp. Within Functional Area at medium entry volu me, in terms of exit type, parallel type has 26.8% and 24% higher lane change number than tapered type for onelane exit and twolane exit respectively. In terms of exit number, twolane exit has 17.5% and 14.3% than onelane exit for tapered type and parall el type. It seemed that exit type has more impact on the lane change number than the exit lane number. At high entry volume before the functional area, in terms of exit type, parallel has 33% and 19.2% less lane change number than tapered exit for onelane and twolane respectively. Within functional area at high entry volu me, in terms of exit type, parallel has 11.5% and 19.5% higher lane change number to compare with tapered type for onelane exit and twolane exit respectively. In terms of exit lane number, twolane has 11.9% more lane change maneuver than onelane exit at parallel type. At high entry volume after functional area, in terms of exit type, parallel has less number of lane changes, the percentage is 25.3% and 12.7% for onelane and twolane exit respectively. In terms of exit lane number, twolane has 14.2% less number of lane change than onelane at tapered type. PAGE 122 104Table 82 ANOVA Findings for Lane Change Number Before Functional Area Within Functional Area After Functional Area LEV N Y Y MEV Y Y Y HEV Y Y Y Table 83 Tukey Findings for Lane Change Number Before Functional Area Within Functional Area After Functional Area LEV N/A All TOTT, TTPT, POPT MEV TTPT All TOPT HEV TOPO, TOPT TTPO, TTPT TOPO, TOPT, TTPO TTPT, POPT TOTT, TOPO, TOPT TTPO, TTPT PAGE 123 105 Chapter 8 Sensitivity Analysis Sensitivity analysis is used to determine ho w sensitive a model is to changes in the value of the parameters of the model and to changes in the structure of the model. Parameter sensitivity is usually performed as a series of tests in which the modeler sets different parameter values to see how a change in the parameter causes a change in the dynamic behavior of the stocks. By showing how the model behavior responds to changes in parameter va lues, sensitivity analysis is a useful tool in model building as well as in model evaluation. .Sensitivity analysis helps to build confidence in the model by studying the uncertainties that are often associated with parameters in models. In this chapter, the parameter sensitivity was executed for entry volume, free flow speed, grade, truck percentage, restrictions to truck and the location of exit sign. All these factors are the external factors and were not researched well in the past studies. The purpose of sensitivity research at this chapte r is trying to compare the impact of these external factors on the design of exit ramp, in another word, for instance, is truck restricted to the right two most lane has more impact on a certain exit type than other types? ANOVA and Tukey methodology were applied for comparisons. Linear regression model were developed also for the change of one variable and all available variables as well. It was found that most these input parameters are sensitive to the traffic discharging volume, operational speed and total lane changing number. PAGE 124 106 8.1. Entry Volume To compare the effects of different entry volume on different freeway exit ramps, in terms of traffic volume, operational speed and total lane change number, an analysis of ANOVA and Tukey was conducted on the simulation data. It is common sense that entry volume has a significant impact on the link traffic volume, running speed and total lane change number generated, but the correlation factor within and the functional area may not necessary be the same for these four types of exit ramp, according to the research results of previous chapter, we focus on the traffic features within the functional area, what happened before and after functional area is not necessary the research interest again.. 8.1.1. Entry Volume Sensitivity before Functional Area Table 84 and figure 51 shows that the impact of entry volume on running speed is significant. With the increase of entry volume, running speed decreases. But after 1800pcphpl (entry volume at more than 5400vph), the impact is insignificant according to Tukey analysis. The R2 is 0.981; it indicates a strong relation between entry volume and running speed. Table 84 Entry Volume Sensitivity on Running Speed before FA Sum of Squares df Mean Square F Sig. Between Groups 142.959 6 23.827 289.346 .000 Within Groups 16.716 203 .082 Total 159.676 209 Table 85 Entry Volume Sensitivity on Total Lane Change Number before FA Sum of Squares df Mean Square F Sig. Between Groups 11008.029 6 1834.671 13.294 .000 Within Groups 28015.800 203 138.009 Total 39023.829 209 PAGE 125 107 y = 0.395x + 59.191 R2 = 0.981 56 56.5 57 57.5 58 58.5 59 3600420048005400600066007200 Entry VolumeSpeed Figure 51 Entry Volume Sensitivity on Running Speed before FA Table 85 and figure 52 shows that the en try volume has significant impact on total lane change number, the lane change number reaches the highest point at the 1800pcphpl, that means as the increase of entry volume, the lane change number increase until it meet the capacity, 1800pcphpl. After that, although there are more vehicles need make a lane change to exit, the space between vehicles are not sufficient to let exiting vehicles make a lane change. The R2 is 0.0095, it indicated than lane change has very limited relation with entry volume before functional area. High volume do not necessary mean large number of lane change, lane change is restricted by the capacity of the given freeway. y = 0.3571x + 128.29 R2 = 0.0095 0 20 40 60 80 100 120 140 160 3600420048005400600066007200 Entry VolumeLane Change Number Figure 52 Entry Volume Sensitivity on Total Lane Change Number before FA PAGE 126 108 8.1.2. Entry Volume Sensitivity within Functional Area Table 86, 87 and Figure 53, 54 shows the entry volume has significant impact on running speed and total lane change number wi thin functional area, its almost the same as before functional area in terms of running speed. Although the speed at entry volume 2400pcphl, it is insignificant. But the characteristics of lane change number are different; it seemed that most lane change number will happen at functional area with the increase of entry volume. The R2 is 0.9678 and 0.9509 for speed and lane change number respectively, that means within functional area, the linear regr ession model fit the speed and lane change number quiet well. Table 86 Entry Volume Sensitivity on Running Speed within FA Sum of Squares df Mean Square F Sig. Between Groups 380.616 6 63.436 30.019 .000 Within Groups 428.980 203 2.113 Total 809.596 209 Table 87 Entry Volume Sensitivity on Total Lane Change Number within FA Sum of Squares df Mean Square F Sig. Between Groups 767248.629 6 127874.771 148.393 .000 Within Groups 174930.900 203 861.729 Total 942179.529 209 y = 0.6571x + 53.9 R2 = 0.9678 47 48 49 50 51 52 53 54 3600420048005400600066007200 Entry VolumeSpeed Figure 53 Entry Volume Sensitivity on Running Speed within FA PAGE 127 109 y = 28.929x + 261.43 R2 = 0.9509 0 100 200 300 400 500 3600420048005400600066007200 Entry VolumeLane Change Number Figure 54 Entry Volume Sensitivity on Total Lane Change Number within FA 8.1.3. Entry Volume Sensitivity after Functional Area Table 88, 89 and Figure 55, 56 shows the impact on running speed and total lane change number still significant after functional area. The R2 is 0.9547 and 0.7457 for speed and total lane change respectively. Again, speed is directly controlled by entry volume while the function of lane change are more complicated. Table 88 Entry Volume Sensitivity on Running Speed after FA Sum of Squares df Mean Square F Sig. Between Groups 105.904 6 17.651 86.056 .000 Within Groups 41.637 203 .205 Total 147.541 209 Table 89 Entry Volume Sensitivity on Total Lane Change Number after FA Sum of Squares df Mean Square F Sig. Between Groups 85343.314 6 14223.886 37.574 .000 Within Groups 76848.000 203 378.562 Total 162191.314 209 PAGE 128 110 y = 0.3486x + 53.313 R2 = 0.9547 49.5 50 50.5 51 51.5 52 52.5 53 53.5 3600420048005400600066007200 Entry VolumeSpeed Figure 55 Entry Volume Sensitivity on Running Speed after FA y = 8.5714x + 162.57 R2 = 0.7457 0 50 100 150 200 250 3600420048005400600066007200 Entry VolumeLane Change Number Figure 56 Entry Volume Sensitivity on Total Lane Change Number after FA 8.1.4. Entry Volume Sensitivity Sum up To sum up, the operational speed and total lane change number are sensitive to the entry volume, no matter for what parts of the functional area. When the entry volume reaches certain point, say, 1800pcphpl, basically the capacity of freeway, the running speed before functional are almost the same due to the discharging limit of exit ramp. It seemed lane change number goes with the increase of entry volume while the running speed decrease with the increase of entry volume. The lane change number meets a threshold when the entry volume is 1800pcphpl. PAGE 129 111 8.2. Free Flow Speed The free flow speed may impact the link traffic volume, operational speed and lane change number; the analysis results are list below at table 90, 91and 92 for the free flow speed on link traffic volume and total la ne change number, before functional area. In order to eliminate the impact of entr y volume, the entry volume was focused on 2000pcphpl. 8.2.1. Free Flow Speed Sensitivity before Functional Area Table 90, 91 and 92 are the free flow speed sensitivity analysis on freeway exit ramp before functional area. It was found that before functional area, the discharging volume is not sensitive to running speed, but sensitiv e to the total lane change number. The R2 is 0.1761 and 0.998 for discharging volume and lane change respectively. With the increase of free flow speed, the lane change number decrease significantly. Table 90 Free Flow Speed Sensitivity on Link Volume before FA Sum of Squares df Mean Square F Sig. Between Groups 77.173 3 25.724 .041 .989 Within Groups 35015.001 56 625.268 Total 35092.174 59 Table 91 Free Flow Speed Sensitivity on Total Lane Change Number before FA Sum of Squares df Mean Square F Sig. Between Groups 33082.050 3 11027.350 55.766 .000 Within Groups 11073.600 56 197.743 Total 44155.650 59 Table 92 Tukey Results of Free Flow Speed on Total Lane Change Number before FA Sig. 55mph 60mph 65mph 70mph 55mph N/A .001 .000 .000 60mph .001 N/A .002 .000 65mph .000 .002 N/A .000 70mph .000 .000 .000 N/A PAGE 130 112 y = 0.29x + 2013.8 R2 = 0.1761 2012 2012.5 2013 2013.5 2014 2014.5 2015 2015.5 2016 55606570 Free Flow SpeedDischarging Volume Figure 57 Free Flow Speed Sensitivity on Link Volume before FA y = 20.6x + 189.5 R2 = 0.998 0 50 100 150 200 55606570 Free Flow SpeedLane Change Number Figure 58 Free Flow Speed Sensitivity on Total Lane Change Number before FA 8.2.2. Free Flow Speed Sensitivity within Functional Area The free flow speed sensitivity analysis within functional area is summarized at table 93, 94 and 95. Figure 59, 60 are the illustrations. The R2 is 0.3984 and 0.4393 for discharging volume and lane change maneuver respectively. It indicates that the traffic flow is more complicated within functio nal area than before functional area. Table 93 Free Flow Speed Sensitivity on Link Volume within FA Sum of Squares df Mean Square F Sig. Between Groups 53.898 3 17.966 .001 1.000 Within Groups 1589537.645 56 28384.601 Total 1589591.542 59 PAGE 131 113Table 94 Free Flow Speed Sensitivity on Lane Change Number within FA Sum of Squares df Mean Square F Sig. Between Groups 18669.000 3 6223.000 11.542 .000 Within Groups 30192.000 56 539.143 Total 48861.000 59 Table 95 Free Flow Speed Sensitivity Tukey Analysis Sig. 55mph 60mph 65mph 70mph 55mph N/A .987 .755 .000 60mph .987 N/A .911 .000 65mph .755 .911 N/A .000 70mph .000 .000 .000 N/A y = 0.54x + 1998.2 R2 = 0.3984 1994 1995 1996 1997 1998 1999 55606570 Free Flow SpeedDischarging Volume Figure 59 Free Flow Speed Sensitivity on Link Volume within FA y = 10.5x + 429.5 R2 = 0.4393 350 360 370 380 390 400 410 420 430 55606570 Free Flow SpeedLane Change Number Figure 60 Free Flow Speed Sensitivity on Lane Change Number within FA PAGE 132 114 It was found that within functional area of exit ramps, the free flow speed was not sensitive to link volume but sensitive to total lane change number. The total lane change number increase with the increase of free flow speed, but decrease after 60mph. 8.2.3. Free Flow Speed Sensitivity after Functional Area The free flow speed sensitivity analysis afte r functional area is listed below table 96 and table 97, 98. Figure 61 and 62 are the illustrations of the analysis results. The R2 is 0.4701 and 0.4709. that means after functional area, the relational between free flow speed and discharging volume and lane change are not easily be explained by a simple linear model. Table 96 Free Flow Speed Sensitivity on Link Volume after FA Sum of Squares df Mean Square F Sig. Between Groups 3632.041 3 1210.680 .064 .979 Within Groups 1057962.122 56 18892.181 Total 1061594.163 59 Table 97 Free Flow Speed Sensitivity on Lane Change Number after FA Sum of Squares df Mean Square F Sig. Between Groups 10475.250 3 3491.750 15.519 .000 Within Groups 12600.000 56 225.000 Total 23075.250 59 Table 98 Tukey Results of Free Flow Speed on Lane Change Number after FA Sig. 55mph 60mph 65mph 70mph 55mph N/A .003 .956 .000 60mph .003 N/A .013 .128 65mph .956 .013 N/A .000 70mph .000 .128 .000 N/A PAGE 133 115 y = 4.85x + 1764 R2 = 0.4701 1730 1735 1740 1745 1750 1755 1760 1765 55606570 Free Flow SpeedDischarging Volume Figure 61 Free Flow Speed Sensitivity on Link Volume after FA y = 8.2x + 228.5 R2 = 0.4709 170 180 190 200 210 220 230 55606570 Free Flow SpeedLane Change Number Figure 62 Free Flow Speed Sensitivity on Lane Change Number after FA 8.2.4. Free Flow Speed Sensitivity Sum up The free flow speed sensitivity analysis summarized here, it seemed that free flow speed has limited impact on the link volume, but has significant impact on the total lane change number, within the increase of free flow speed, the lane change number decrease greatly. Thats because in CORSIM simulation, vehicles are forced to change lanes when the headway space is less than 2 seconds, th e higher free flow speed will maintain a longer headway space, hence need less lane change number. PAGE 134 116 8.3. Freeway Grade Freeway grade has significant impact on traffic operational speed, according to some previous research. Heavy vehicles, especially the trucks, were observed more speed reduction at upgrade. 8.3.1. Freeway Grade Sensitiv ity before Func tional Area Table 99, 100, 101 and 102 are the ANOVA and Tukey results for the freeway grade impact on speed and total lane change number. The R2 is 0.5095 and 0.0043 for speed and lane change number respectively, It can be concluded that before functional area of an exit ramp, the up grade has significant imp act on the speed, but the impact on the total lane change number are not as significant as that of speed. Table 99 Freeway Grade Sensitivity on Running Speed before FA Sum of Squares df Mean Square F Sig. Between Groups 18044.568 4 4511.142 5294.784 .000 Within Groups 59.640 70 .852 Total 18104.208 74 Table 100 Tukey Results on Grade Sensitivity on Running Speed before FA Sig. 6 3 0 3 6 6 N/A 1.000 .996 .000 .000 3 1.000 N/A .992 .000 .000 0 .996 .992 N/A .000 .000 3 .000 .000 .000 N/A .000 6 .000 .000 .000 .000 N/A Table 101 Freeway Grade Sensitivity on Lane Change Number before FA Sum of Squares df Mean Square F Sig. Between Groups 30015.600 4 7503.900 19.936 .000 Within Groups 26348.400 70 376.406 Total 56364.000 74 Table 102 Tukey Results of Grade on Lane Change Number before FA Sig. 6 3 0 3 6 6 N/A .980 .604 .000 .106 3 .980 N/A .905 .000 .317 0 .604 .905 N/A .000 .834 3 .000 .000 .000 N/A .000 6 .106 .317 .834 .000 N/A PAGE 135 117 y = 7.95x + 73.35 R2 = 0.5095 0 10 20 30 40 50 60 70 63036 GradeSpeed Figure 63 Freeway Grade Sensitivity on Running Speed before FA y = 0.9x + 142.3 R2 = 0.0043 0 50 100 150 200 63036 GradeLane Change Number Figure 64 Freeway Grade Sensitivity on Lane Change Number before FA 8.3.2. Freeway Grade Sensitivity within Functional Area Table 103, 104, 105 and 106 are the ANOVA and Tukey results of freeway grade sensitive analysis on running speed and total lane change number. The R2 is 0.6835 and 0.8108 for speed and total lane change number respectively. That means grade has significant impact on running speed and total lane change number within functional area. It seemed that negative has limited impact on the running speed, but positive grade has significant impact on the running speed. PAGE 136 118Table 103 Freeway Grade Sensitivity on Running Speed within FA Sum of Squares df Mean Square F Sig. Between Groups 12632.373 4 3158.093 770.628 .000 Within Groups 286.866 70 4.098 Total 12919.239 74 Table 104 Tukey Results of Grade Sensitivity on Running Speed within FA Sig. 6 3 0 3 6 6 N/A 1.000 .814 .000 .000 3 1.000 N/A .784 .000 .000 0 .814 .784 N/A .000 .000 3 .000 .000 .000 N/A .000 6 .000 .000 .000 .000 N/A Table 105 Freeway Grade Sensitivity on Lane Change Number within FA Sum of Squares df Mean Square F Sig. Between Groups 626452.080 4 156613.020 156.606 .000 Within Groups 70003.200 70 1000.046 Total 696455.280 74 Table 106 Tukey Results of Grade on Lane Change Number within FA Sig. 6 3 0 3 6 6 N/A 1.000 .693 .000 .000 3 1.000 N/A .734 .000 .000 0 .693 .734 N/A .000 .000 3 .000 .000 .000 N/A 1.000 6 .000 .000 .000 1.000 N/A y = 7.4x + 68.8 R2 = 0.6835 0 10 20 30 40 50 60 70 63036 GradeSpeed Figure 65 Freeway Grade Sensitivity on Running Speed within FA PAGE 137 119 y = 43.4x + 341.8 R2 = 0.8108 0 100 200 300 400 500 600 63036 GradeLane Change Number Figure 66 Freeway Grade Sensitivity on Lane Change Number within FA 8.3.3. Freeway Grade Sensitivity after Functional Area The ANOVA and Tukey results of sensitivity analysis of freeway grade after freeway functional area are listed at table 107,108, 109 and 110. The R2 is 0.766 and 0.8064 for running speed and total lane change number respectively; the linear model fits it pretty well, that means not like before functional area, the speed and lane change number can be explained by freeway grade if other variables are not considered. It is observed that positive grade has significant impact on the running speed, vehicles experience large speed deductio n at upgrade hill, but the negative slope has limit impact one the running speed. The total lane change number increased significantly while the grade increases. In another word, there are more lane changes at uphill. Table 107 Freeway Grade Sensitivity on Running Speed after FA Sum of Squares df Mean Square F Sig. Between Groups 8891.772 4 2222.943 1649.270 .000 Within Groups 94.348 70 1.348 Total 8986.121 74 Table 108 Tukey Results of Grade Sensitivity on Running Speed after FA Sig. 6 3 0 3 6 6 N/A 1.000 .457 .000 .000 3 1.000 N/A .411 .000 .000 0 .457 .411 N/A .000 .000 3 .000 .000 .000 N/A .000 6 .000 .000 .000 .000 N/A PAGE 138 120Table 109 Freeway Grade Sensitivity on Lane Change Number after FA Sum of Squares df Mean Square F Sig. Between Groups 2734584.000 4 683646.000 718.935 .000 Within Groups 66564.000 70 950.914 Total 2801148.000 74 Table 110 Tukey Results of Grade Sensitivity on Lane Change Number after FA Sig. 6 3 0 3 6 6 N/A .999 .841 .000 .000 3 .999 N/A .705 .000 .000 0 .841 .705 N/A .000 .000 3 .000 .000 .000 N/A .000 6 .000 .000 .000 .000 N/A y = 6.7x + 68.1 R2 = 0.766 0 10 20 30 40 50 60 70 63036 GradeSpeed Figure 67 Freeway Grade Sensitivity on Speed after FA y = 123x 14 R2 = 0.8064 0 100 200 300 400 500 600 700 63036 GradeLane Change Number Figure 68 Freeway Grade Sensitivity on Lane Change Number after FA PAGE 139 121 8.3.4. Freeway Grade Sensitivity Sum up Vehicles experience significant speed redu ction at uphill freeway, no matter before, within or after functional area of freeway exit ramp. Normally, the up grade will impact the heavy truck more because of their weight and the ability of climbing, when the traffic volume is high, heavy truck will block the headway space, leaves less chance for passenger cars to make a lane change, hence the passenger cars suffer speed reduction too. 8.4. Truck Percentage The sensitivity analysis for truck percentage is listed here. It is natural that more truck makes the fleet less flexibly and r uns slower, especially at mountainous area. 8.4.1. Freeway Truck Percentage Sensitivity before Functional Area The ANOVA and Tukey results for truck percentage sensitive analysis are listed here. The R2 is 0.7964 and 0.5873 for speed and lane change respectively. It can be concluded that the truck percentage has no impact on the running speed at flat freeway, but more truck percentage means less lane change number before functional area, the results is statistically significant. Table 111 Truck Percentage Sensitivity on Running Speed before FA Sum of Squares df Mean Square F Sig. Between Groups .224 4 .056 .459 .766 Within Groups 8.531 70 .122 Total 8.755 74 Table 112 Truck Percentage Sensitivity on Lane Change Number before FA Sum of Squares df Mean Square F Sig. Between Groups 1822.800 4 455.700 7.341 .000 Within Groups 4345.200 70 62.074 Total 6168.000 74 PAGE 140 122Table 113 Tukey Results of Truck Percentage on Lane Change Number before FA Sig. .04 .08 .12 .16 .20 .04 N/A 1.000 1.000 .988 .000 .08 1.000 N/A 1.000 .988 .000 .12 1.000 1.000 N/A .988 .000 .16 .988 .988 .988 N/A .002 .20 .000 .000 .000 .002 N/A y = 0.0324x + 57.06 R2 = 0.7964 57 57.05 57.1 57.15 57.2 57.25 0.040.080.120.160.2 Truck PercentageSpeed Figure 69 Truck Percentage Sensitivity on Running Speed before FA y = 2.69x + 140.73 R2 = 0.5873 115 120 125 130 135 140 0.040.080.120.160.2 Truck PercentageLane Change Number Figure 70 Truck Percentage Sensitivity on Lane Change Number before FA 8.4.2. Freeway Truck Percentage Sensitivity within Functional Area The ANOVA and Tukey analysis for freewa y truck percentage sensitivity within functional area are summarized here. The R2 is 0.7579 and 0.5973 for speed and lane change respectively. It seemed that truck perc entage has limited impact on running speed, but it does impact the total lane change number. More truck along a freeway segment makes less available headway gap, causing bigger speed deviation, when vehicles close PAGE 141 123 to exit ramp functional ar ea, the exiting vehicles will make more unnecessary lane changes. Table 114 Truck Percentage Sensitivity on Running Speed within FA Sum of Squares df Mean Square F Sig. Between Groups 15.282 4 3.820 1.613 .181 Within Groups 165.774 70 2.368 Total 181.056 74 Table 115 Truck Percentage Sensitivity on Lane Change Number within FA Sum of Squares df Mean Square F Sig. Between Groups 38777.520 4 9694.380 10.784 .000 Within Groups 62924.400 70 898.920 Total 101701.920 74 Table 116 Tukey Results of Truck Percentage on Lane Change Number within FA Sig. .04 .08 .12 .16 .20 .04 N/A 1.000 1.000 .000 .016 .08 1.000 N/A 1.000 .000 .016 .12 1.000 1.000 N/A .000 .016 .16 .000 .000 .000 N/A .430 .20 .016 .016 .016 .430 N/A y = 0.276x + 51.262 R2 = 0.7579 49 49.5 50 50.5 51 51.5 0.040.080.120.160.2 Truck PercentageSpeed Figure 71 Truck Percentage Sensitivity on Running Speed within FA PAGE 142 124 y = 12.1x + 385.1 R2 = 0.5973 360 380 400 420 440 460 480 0.040.080.120.160.2 Truck PercentageLane Change Number Figure 72 Truck Percentage Sensitivity on Lane Change Number within FA 8.4.3. Freeway Truck Percentage Sensitivity after Functional Area The ANOVA and Tukey analysis for truck perc entage sensitivity are list in this subchapter. The R2 is 0.5448 and 0.6465 for speed and lane change number respectively. The truck percentage has limited impact on running speed, but still gave significant impact on the total lane change number. More truck means more lane change, especially unnecessary lane change when the passenger cars are blocked by truck. Table 117 Truck Percentage Sensitivity on Running Speed after FA Sum of Squares df Mean Square F Sig. Between Groups .256 4 .064 .278 .892 Within Groups 16.113 70 .230 Total 16.368 74 Table 118 Truck Percentage on Lane Change Number after FA Sum of Squares df Mean Square F Sig. Between Groups 3659.520 4 914.880 11.517 .000 Within Groups 5560.800 70 79.440 Total 9220.320 74 Table 119 Tukey Results of Truck Percentage on Lane Change Number after FA Sig. .04 .08 .12 .16 .20 .04 N/A 1.000 1.000 .834 .000 .08 1.000 N/A 1.000 .834 .000 .12 1.000 1.000 N/A .834 .000 .16 .834 .834 .834 N/A .000 .20 .000 .000 .000 .000 N/A PAGE 143 125 y = 0.0309x + 51.295 R2 = 0.5448 51.2 51.25 51.3 51.35 51.4 51.45 51.5 51.55 0.040.080.120.160.2 Truck PercentageSpeed Figure 73 Truck Percentage Sensitivity on Speed after FA y = 4.023x + 203.58 R2 = 0.6465 195 200 205 210 215 220 225 230 235 0.040.080.120.160.2 Truck PercentageLane Change Number Figure 74 Truck Percentage Sensitivity on Lane Change Number after FA 8.4.4. Freeway Truck Percentage Sensitivity Sum up It is observed from the simulation data that truck percentage has significant impact on the total lane change number, no matter be fore, within or after functional area of an exit ramp; more truck percentage means more unnecessary lane change. Not like the freeway grade, the truck percentage has limited impact on the running speed. 8.5. Restrictions to Truck The heavy trucks are restricted to a certain lane or lanes may impact the traffic operational characteristics on freeway exit ramp, few researches have focused on this PAGE 144 126 field. Thanks to the traffic simulation soft, it is easy to compare the difference of restrictions to truck by changing a parameter. 8.5.1. Restrictions to Truck sensitivity before Functional area Table 120 and 121 summarize the ANOVA results of restrictions to truck sensitivity before exit ramp functional area, because the independent variable has only two values, 0 or 1, the linear model is unnecessary here. Restrictions to truck to a certain lane or lanes seemed has limited impact on the running speed, but will decrease the total lane change number before functional area. it must be noted here that since the variable restrictions to truck has only values: 1 for restricted to right two most lanes and 0 for no restrictions for truck, the Tukey can not be performed. Table 120 Restrictions to Truck Sensitivity on Running Speed before FA Sum of Squares df Mean Square F Sig. Between Groups .052 1 .052 .068 .795 Within Groups 159.624 208 .767 Total 159.676 209 Figure 75 Restrictions to Truck Sensitivity on Running Speed PAGE 145 127Table 121 Restrictions to Truck Sensitivity on Lane Change Number before FA Sum of Squares df Mean Square F Sig. Between Groups 4667.143 1 4667.143 28.256 .000 Within Groups 34356.686 208 165.176 Total 39023.829 209 Figure 76 Restrictions to Truck Sensitivity on Lane Change Number before FA 8.5.2. Restrictions to Truck Sensitivity within Functional Area Table 122 Restrictions to Truck Sensitivity on Running Speed within FA Sum of Squares df Mean Square F Sig. Between Groups 1.417 1 1.417 .365 .547 Within Groups 808.179 208 3.885 Total 809.596 209 Table 123 Restrictions to Truck Sensitivity on Lane Change Number within FA Sum of Squares df Mean Square F Sig. Between Groups 35568.043 1 35568.043 8.160 .005 Within Groups 906611.486 208 4358.709 Total 942179.529 209 PAGE 146 128 Figure 77 Restrictions to Truck Sensitivity on Running Speed within FA Figure 78 Restrictions to Truck Sensitivity on Lane Change Number within FA The ANOVA results for restrictions to truc k sensitivity within functional area are listed at table 122 and 123. Whether trucks are restricted to a certain lane (lanes) or not have limited impact on the running speed, but have significant impact on the total lane change number. Restricted to the right two most lanes will have less lane change number. 8.5.3. Restrictions to Truck Sensitivity after Functional Area The ANOVA results for restrictions to truck sensitivity after functional area are listed at table 124 and 125. PAGE 147 129Table 124 Restrictions to Truck Sensitivity on Running Speed after FA Sum of Squares df Mean Square F Sig. Between Groups 1.823 1 1.823 2.602 .108 Within Groups 145.718 208 .701 Total 147.541 209 Table 125 Restrictions to Truck Sensitivity on Lane Change Number after FA Sum of Squares df Mean Square F Sig. Between Groups 27703.543 1 27703.543 42.847 .000 Within Groups 134487.771 208 646.576 Total 162191.314 209 Figure 79 Restrictions to Truck Sensitivity on Running Speed after FA Figure 80 Restrictions to Truck Sensitivity on Lane Change Number after FA PAGE 148 130 8.5.4. Restrictions to Truck Sensitivity Sum up The results of restrictions to truck usage of a certain lane or lanes are summarized here, it was found that when trucks are restricted to the right two most lane, there will be less lane change number comparing with trucks are not restricted. But the restrictions seemed has limited impact on the operational speed of automobiles running on the freeway. It is recommended that when design the exit ramp, trucks should be restricted to the right two most lane, it significant decrease the total lane change number while has slight impact on the vehicles operational speed. 8.6. Location of Exit Sign Locations of exit sign is important in the design of exit ramp, a too short distance of exit sign from the place it poled to the physical nose of exit ramp may not give the motorists enough reaction time to take the exiting maneuver while motorists experience a too long distance may forget to take a leave when approaching the exit ramp. The default value in CORSIM is 2500 ft, in this study; it is set from 1500 ft to 5000 ft with 500 ft increment. 8.6.1. Location of Exit Sign Sensitivity before Functional Area The ANOVA results of location of exit sign sensitivity before functional area are listed at table 126 and 127 for running speed and total lane change number. The Tukey results are too large to be shown in one page. It shows that from 1500 ft to 2500 ft, the total lane change number is not significant, but after 2500 ft of exit sign, with the increase of the distance, the lane change number increase significant. The R2 is 0.4245 and 0.9405 for speed and lane change number. The lane change number can be explained pretty well by the location of the exit sign. Before functional area, the location of exit sign has limited impact on the operational speed at freeway segment. PAGE 149 131Table 126 Location of Exit Sign Sensitivity on Running Speed before FA Sum of Squares df Mean Square F Sig. Between Groups 2.011 7 .287 1.143 .341 Within Groups 28.142 112 .251 Total 30.153 119 Table 127 Location of Exit Sign Sensitivity on Lane Change Number before FA Sum of Squares df Mean Square F Sig. Between Groups 493464.000 7 70494.857 528.051 .000 Within Groups 14952.000 112 133.500 Total 508416.000 119 y = 0.0373x + 57.241 R2 = 0.4245 56.6 56.7 56.8 56.9 57 57.1 57.2 57.3 57.4 15002000250030003500400045005000 Sign LocationSpeed Figure 81 Location of Exit Sign Sensitivity on Running Speed before FA y = 26.702x + 94.214 R2 = 0.9405 0 50 100 150 200 250 300 350 15002000250030003500400045005000 Sign LocationLane Change Number Figure 82 Location of Exit Sign Sensitivity on Lane Change Number before FA PAGE 150 132 8.6.2. Location of Exit Sign Sensitivity within Functional Area The ANOVA analysis results of location of exit sign sensitivity within functional area are summarized here. Tukey analysis for the impact on the lane change number was performed; the R2 is 0.6546 and 0.9222 for speed and lane change maneuver respectively. It seemed that the relationship between location of exit sign and the lane change number are very apparent. The ANOVA tells than from 1500 ft to 2000 ft, 2500 ft, the difference is insignificant, the difference of 4500 ft and 5000 ft are not significant too. Table 128 Location of Exit Sign Sensitivity on Running Speed within FA Sum of Squares df Mean Square F Sig. Between Groups 16.595 7 2.371 1.355 .231 Within Groups 195.918 112 1.749 Total 212.513 119 Table 129 Location of Exit Sign Sensitivity on Lane Change Number within FA Sum of Squares df Mean Square F Sig. Between Groups 739892.400 7 105698.914 346.611 .000 Within Groups 34154.400 112 304.950 Total 774046.800 119 y = 0.132x + 54.665 R2 = 0.6546 53.5 54 54.5 55 55.5 56 15002000250030003500400045005000 Sign LocationSpeed Figure 83 Location of Exit Sign Sensitivity on Running Speed within FA PAGE 151 133 y = 32.131x + 476.21 R2 = 0.9222 0 100 200 300 400 500 15002000250030003500400045005000 Sign LocationLane Change Number Figure 84 Location of Exit Sign Sensitivity on Lane Change Number within FA It seemed that within functional area of an exit ramp, the location of exit sign has limited impact on the running speed, but does impact on the total lane change number. The longer the location sign, the less the total lane change number, at 4500 ft, it meet a certain threshold, and the total lane change number are not reduced greatly. 8.6.3. Location of Exit Sign Se nsitivity after Functional Area The ANOVA analysis for the location of exit sign sensitivity after functional area is list here, from table 130 to table 131. Figure 85 and figure 86. Table 130 Location of Exit Sign Sensitivity on Running Speed after FA Sum of Squares df Mean Square F Sig. Between Groups 4.360 7 .623 2.533 .019 Within Groups 27.535 112 .246 Total 31.895 119 PAGE 152 134 y = 0.0464x + 55.949 R2 = 0.3076 55.2 55.4 55.6 55.8 56 56.2 56.4 56.6 15002000250030003500400045005000 Sign LocationSpeed Figure 85 Location of Exit Sign Sensitivity on Running Speed after FA Table 131 Location of Exit Sign Sensitivity on Lane Change Number after FA Sum of Squares df Mean Square F Sig. Between Groups 3719.325 7 531.332 1.804 .093 Within Groups 32982.000 112 294.482 Total 36701.325 119 y = 1.7512x + 219.27 R2 = 0.5251 190 195 200 205 210 215 220 15002000250030003500400045005000 Sign LocationLane Change Number Figure 86 Location of Exit Sign Sensitivity on Lane Change Number after FA The Tukey test for running speed after functional area shows that at 4000 ft exit sign distance, vehicles have the highest running speed, after that distance, say, the distance is longer than 4000 ft, the difference between running speed are not significant. PAGE 153 135 After functional area, the R2 is 0.3076 and 0.5251 for speed and lane change number respectively. Its probably because when the exit sign location is round or above 4000 ft, vehicles has less lane change number within functional area, more vehicles successfully exit from the exit ramp; making the remaining vehicles runs more smooth after functional area, but when the sign location is less than 4000 ft, there are more unprepared motorists that trying to make an exit, some of them may take a jump lane change successfully, some may not, remaining on the freeway segment, making the operational speed after functional area slower. 8.6.4. Location of Exit Sign Sensitivity Sum up Location of exit sign does have a significant impact on the operational speed and total lane change number before, within or after functional area of an exit. Before functional area, difference sign distance has limited impact on running speed, but longer sign distance means big lane change number; within the functional area, impact on the running speed is still insignifi cant but longer sign dist ance means less lane change number; after functional area, the im pact on the total lane change number is limited while sign distance has significant impact on the running speed. It can be concluded that from 4000 ft to 5000 ft sign distance is desirable in the design of exit ramp. 8.7 Linear Regression Model for Exit Ramp Four exit ramp types have different traffic operational characteristics, it might be necessary to build four different linear regres sion models corresponds four different exit ramps. Some finished researches also support that there are no one linear regression model suit for four types of exit ramp. At this research, the linear regression model is built for tapered onelane exit only; one reason is the regression model is for illu stration purpose only, because the model only involve a few variables, a few variables are not enough to explicate the complication of real world traffic flow. PAGE 154 136 Because the traffic operation features was studied before, within and after the functional area of an exit ra mp, the linear regression model should reflect the different also. There are two dependent variables in our re gression model, one is the running speed and the other is the total lane change number running speed has dire ct relation with the LOS while the total lane ch ange number has direct relation with safety issues. The linear regression model (LRM) for tapered onelane exit of running speed is summarized at table 132,133 and 134. Its before the functional area. Table 132 LRM for Speed of Tapered OneLane Exit before FA Model R R Square Adjusted R Square Std. Error of the Estimate 1 .985 .971 .970 .370406 Table 133 ANOVA of Speed Modeling of Tapered OneLane Exit before FA Model Sum of Squares df Mean Square F Sig. Regression 2094.600 5 418.920 3053.348 .000 Residual 62.975 459 .137 Total 2157.575 464 Table 134 Coefficients of Speed Modeling of Tapered OneLane Exit before FA Unstandardized Coefficients Standardized Coefficients 95% Confidence Interval for B Collinearity Statistics Model B Std. Error Beta t Sig. Lower Bound Upper Bound ToleranceVIF Constant 4.592 .506 9.083.0003.5985.585 Volume .000 .000 .276 33.778.000.001 .001 .949 1.053 Speed .948 .008 .957 119.213.000.932 .963 .986 1.014 Truck % .697 .645 .009 1.082.280.570 1.964 .969 1.032 Sign Location 8.1E005 .000 .025 3.078.002.000 .000 .959 1.042 Lane Restriction .032 .043 .006 .745 .456.052 .116 .916 1.092 From the table results, we can concluded that the model of running speed fit the linear pretty well with R2 0.971. Entry volume, initial speed and sign location are significant factors in the linear regression model. The truck percentage and restricted to a certain lane or lanes are not significant factors in the model. PAGE 155 137 The linear regression model for tapered one lane exit of total lane change is summarized at table 135,136 and 137. Its before the functional area. Table 135 LRM for Lane Change Number before FA Model R R Square Adjusted R Square Std. Error of the Estimate 1 .925 .855 .854 19.442 Table 136 ANOVA of Lane Change Number Modeling Number before FA Model Sum of Squares df Mean Square F Sig. Regression 1026940 5 205388.095 543.354 .000 Residual 173502.2 459 378.000 Total 1200443 464 Table 137 Coefficients of Lane Change Number Modeling before FA Unstandardized Coefficients Standardized Coefficients 95% Confidence Interval for B Collinearity Statistics Model B Std. Error Beta t Sig. Lower Bound Upper Bound Tolerance VIF Constant 240.871 26.535 9.078.000188.726293.015 Volume .003 .001 .051 2.802.005.001 .005 .949 1.053 Speed 4.255 .417 .182 10.199.0005.0753.435 .986 1.014 Truck % 181.206 33.833 .097 5.356.000247.693114.720 .969 1.032 Sign Location .064 .001 .841 46.413.000.061 .067 .959 1.042 Lane Restriction 21.901 2.253 .180 9.720.00026.32917.473 .916 1.092 This model fits the lane change number pretty well too, all independent variables are significant. The linear regression model for tapered onelane exit of running speed is summarized at table 138,139 and 140. Its within the functional area. Table 138 LRM for Speed within FA Model R R Square Adjusted R Square Std. Error of the Estimate 1 .776 .602 .597 2.232376 Table 139 ANOVA of Running Speed Modeling within FA Model Sum of Squares df Mean Square F Sig. Regression 3455.533 5 691.107 138.679 .000 Residual 2287.428 459 4.984 Total 5742.961 464 PAGE 156 138Table 140 Coefficients of Speed Modeling within FA Unstandardized Coefficients Standardized Coefficients 95% Confidence Interval for B Collinearity Statistics Model B Std. Error Beta t Sig. Lower Bound Upper Bound Tolerance VIF Constant 7.144 3.047 2.345.019 13.1321.157 Volume .001 .000 .175 5.785.000 .001 .000 .949 1.053 Speed 1.054 .048 .653 22.009.000 .960 1.148 .986 1.014 Truck % 24.330 3.885 .187 6.263.000 31.96416.696 .969 1.032 Sign Location .001 .000 .222 7.381.000 .001 .001 .959 1.042 Lane Restriction 2.034 .259 .242 7.861.000 2.5421.525 .916 1.092 It can be concluded that the model fits th e linear less well than before the functional area. The traffic features are more complicated within functional area than before functional area. Speed is difficult to estimate. Table 141 LRM for Lane Change Number within FA Model R R Square Adjusted R Square Std. Error of the Estimate 1 .897 .804 .802 31.485 Table 142 ANOVA of Lane Change Number Modeling within FA Model Sum of Squares df Mean Square F Sig. Regression 1864809 5 372961.777 376.230 .000 Residual 455012.7 459 991.313 Total 2319822 464 Table 143 Coefficients of Lane Change Number Modeling within FA Unstandardized Coefficients Standardized Coefficients 95% Confidence Interval for B Collinearity Statistics Model B Std. Error Beta t Sig. Lower Bound Upper Bound Tolerance VIF Constant 389.820 42.971 9.072.000 305.376474.264 Volume .046 .002 .563 26.546.000 .043 .050 .949 1.053 Speed 1.722 .676 .053 2.548.011 3.049.394 .986 1.014 Truck % 355.790 54.789 .136 6.494.000 248.121463.459 .969 1.032 Sign Location .076 .002 .716 33.904.000 .080 .071 .959 1.042 Lane Restriction 11.813 3.649 .070 3.237.001 18.9834.462 .916 1.092 PAGE 157 139 The linear regression model for tapered onelan e exit of total lane change number is summarized at table 141,142 and 143. Its within the functional area. It can be concluded that the model fits th e linear less well than before the functional area. The traffic features are more complicated within functional area than before functional area. Total la ne change number is difficult to estimate. The initial speed is not a significant factor in the modeling of total lane change number. The linear regression model for tapered onelane exit of running speed is summarized at table 144,145 and 146. Its after the functional area. Table 144 LRM for Speed after FA Model R R Square Adjusted R Square Std. Error of the Estimate 1 .826 .682 .678 1.821448 Table 145 ANOVA of Speed Modeling after FA Model Sum of Squares df Mean Square F Sig. Regression 3258.483 5 651.697 196.432 .000 Residual 1522.812 459 3.318 Total 4781.295 464 Table 146 Coefficients of Speed Modeling after FA Unstandardized Coefficients Standardized Coefficients 95% Confidence Interval for B Collinearity Statistics Model B Std. Error Beta t Sig. Lower Bound Upper Bound Tolerance VIF Constant 9.281 2.486 3.733.000 14.1664.396 Volume .000 .000 .052 1.931.054 .000 .000 .949 1.053 Speed 1.052 .039 .714 26.918.000 .975 1.129 .986 1.014 Truck % 19.019 3.17 .161 6.000.000 25.24812.791 .969 1.032 Sign Location .001 .000 .215 7.998.000 .001 .001 .959 1.042 Lane Restriction 2.032 .211 .265 9.626.000 2.4471.617 .916 1.092 After functional area, the traffic features are not as smooth as before the functional area, some vehicles was forced stay in the freeway mainline make the speed distribution lager and less predicable. PAGE 158 140Table 147 LRM for Lane Change Number after FA Model R R Square Adjusted R Square Std. Error of the Estimate 1 .701 .491 .486 16.892 Table 148 ANOVA of Lane Change Number Modeling after FA Model Sum of Squares df Mean Square F Sig. Regression 126452.3 5 25290.451 88.630 .000 Residual 130975.0 459 285.348 Total 257427.2 464 Table 149 Coefficients of Lane Change Number Modeling after FA Unstandardized Coefficients Standardized Coefficients 95% Confidence Interval for B Collinearity Statistics Model B Std. Error Beta t Sig. Lower Bound Upper Bound Tolerance VIF Constant 239.647 23.054 10.395.000 194.341284.952 Volume .014 .001 .515 15.061.000 .012 .016 .949 1.053 Speed 1.776 .362 .164 4.899.000 2.4881.063 .986 1.014 Truck % 76.03729.395 .087 2.587.010 18.271133.803 .969 1.032 Sign Location .004 .001 .105 3.086.002 .006 .001 .959 1.042 Lane Restriction 20.130 1.958 .358 10.283.000 23.97716.283 .916 1.092 The linear regression model for tapered onelane exit of lane change number is summarized at table 147,148 and 149. Its after the functional area. After functional area, the traffic features are not as smooth as before the functional area, some vehicles was forced stay in the freeway mainline make the lane change number distribution lager and less predicable. PAGE 159 141 Chapter 9 Summary, Conclusions and Recommendations The summary, conclusions and recommendations of simulation study on freeway exit ramp are wrapped up in this chapter. 9.1. Summary This paper researched traffic flow characteristics of different exit ramps by the method of traffic simulation software. The four different exit ramps are tapered onelane, tapered twolane, parallel onelane and parallel twolane. The traffic simulation software applied in this paper is TSISCORSIM 6.0 and HCS. The internal parameters of CORSIM, such as the headway distribution, the lane distribution, the carfollowing sensitivity, etc, were validated by HCS for the purpose of creditability and accuracy. A 7500 feet freeway segment was built for the purpose of analysis and comparisons, in order to focus on the traffic flow characteristics of exit ramp itself, the traffic flow impact from upstream/downstream onramp/of framp and arterial road access point were eliminated by assuming that there is no closely spaced upstream or downstream onramp/offramp or other traffic interfere facil ity. And the capacity of exit ramp terminal with the access point of arterial road is not a concern. That means the length of exit ramp is long enough, no vehicles will backup to the freeway. Although the keystone is the traffic flow characteristics within functional area of an exit ramp, which is 2500 feet from the exit gore point to freeway upstream, the research scope was extended upstream 2500 feet from the functional area and downstream 2500 feet from the functional area for the purpose of comparisons. PAGE 160 142 Three MOEs generated directly by CORSIM output file were used as the main parameters to describe the traffic flow characteristics and for the purpose of comparisons for the four types of exit ramp. The three MOEs are volume discharging rate, operational speed and total lane change number. Volume discharging rate and operational speed are used to describe the traffic oper ation while lane change number Because CORSIM is a stochastic simulation model, in order to eliminate the random error, sufficient runs must be met to get the reliable resu lts. ANOVA and Tukey analysis were used for statistical purpose. ANOVA was used to test if the difference between exit ramp pairs is statistically significant or just from random errors of each runs. Tukey was used to tell which exit ramp pair or pairs were different from other exit ramp pairs. Four VBA programs were developed to generate the different combinations of geometry variables, traffic flow factors as well as traffic control factors. Because almost all scenarios are incorporated into the combination, no calibration effect is necessary to revive the real situation. Three typical scenarios were selected from the CORSIM simulation files. The three scenarios are corresponding to low traffic volume, medium traffic volume and high traffic volume, more specifically, its the v/c ratio <0.8, close to 1.0 but <1.2 and greater than 1.4. However, no exact v/c ratio is availa ble in this paper due to the magnificent data process and analysis. The simulation results support the point of view that microscopic flow theories are befitted well for study of exit ramp areas. CORSIM is good traffic simulation software and has a high accuracy and accountability in simulation the real case traffic. The researcher found that four typical types of exit ramp do have different traffic performance, no matter at low v/c ratio, medium v/c ratio or high v/c ratio. The factors that affect the performance of each exit ramp are entry volume, free flow speed, truck percentage, grade of freeway, restrictions to truck usage of a special lane/lanes and the location of exit sign. PAGE 161 143 The functional area has the most complicated traffic flow characteristics comparing with upstream of functional area and downstream of functional area. The capacity of an exit ramp is assumed to be the maximum average flow discharging rate, the operational speed of an exit ramp is controlled by free flow speed at uncongested conditions while the operational speed are more controlled by other factors, such as lane change maneuver, truck percentage and location of exit sign, etc. General linear models for different factors are set for illustrating the internal relationship of operational speed and related va riables. The general linear models for lane change maneuver are set up as well. 9.2. Conclusions The research results for the traffic flow characteristics of each exit ramp are listed below. The comparisons of volume discharging rate, operational speed and total lane change number for these four exit ramps are summarized also. Sensitivity analysis results of selected factors are concluded as well. 9.2.1. Volume Discharge Rate At uncongested conditions, the volume discharg e rate is statistically the same for all types of exit ramp, but at congested conditio ns, a ramp with higher capacity has higher volume discharging rate. Although from the ma croscope point of view, the parallel type and the tapered type have the same capacity if the exit lane number is the same, the parallel types have higher capacity while tapered types have lower capacity based on microscope simulations. Normally, the parallel type bear less traffic volume at freeway mainline, hence it has better LOS comparing with tapered type exit ramp, but there are no significant difference between parallel onelane and parallel twolane exit ramp. In terms of exit type, parallel type has 6.9% and 3.7% less traffic than tapered type when the exit ramp has onelane and twolane respectively within functional area. PAGE 162 144 General, in terms of traffic discharging volume, the tapered twolane exit ramp has the best operational performance. It has the highest discharging rate compared with other three exit type. 9.2.2. Operational Speed For the research of speed, it was found that the speed are controlled by free flow speed at uncongested conditions, the free flow speed equals to the operational speed statistically, at congested conditions, operational speed are hard to predicate because many other factors impact the running speed and lane change maneuver. The speed deduction rate is more significant than volume discharge rate. The operational speed at parallel types of exit ramp is more easily to be preserved than tapered type exit ramp. The operational speed has 10% to 32% difference between the exit pairs before the functional area; it also has 20.2% to 41.3% difference within the functional area. After functional area, the difference is reduced to 3.4% and 3.5% respectively. Still, tapered twolane exit ramp has the best performance in terms of operational speed in most cases. 9.2.3. Total Lane Change Number Lane change maneuver was found to be the most complicated MOE of exit ramp. No matter for uncongested conditions or congested conditions, the exit ramp pairs are different in most cases. Normally, tapered type has less lane change number while parallel type has significant lane change number. The parallel twolane has the most number of lane change maneuver. Within Functional Area at low entry volume, parallel type has 41.3% and 24% higher lane change number than tapered type for onelane exit and twolane exit respectively. Twolane exit has 30.1% and 9.5% than onelane exit for tapered type and parallel type. It seemed that exit type has more impact on the lane change number than the exit lane number. PAGE 163 145 Within functional area at medium entry volume, parallel type has 26.8% and 24% higher lane change number than tapered type for onelane exit and twolane exit respectively. Twolane exit has 17.5% and 14.3% than onelane exit for tapered type and parallel type. Within functional area at high entry volume, parallel has 11.5% and 19.5% higher lane change number to compare with tapered type for onelane exit and twolane exit respectively. Twolane has 11.9% more lane change maneuver than onelane exit at parallel type. It can be concluded that the tapered twolane exit ramp has the best performance in terms of lane change maneuver. 9.2.4. Sensitivity Analysis Almost all of the levels in the selected fa ctors are statistically significant as for the operational speed and lane change maneuver, as well as for the volume discharge rate. It seemed that free flow speed has limited impact on the link volume, but has significant impact on the total lane change number, with the increase of free flow speed, the lane change number decrease greatly. Freeway grade makes vehicles experience significant speed reduction at uphill freeway, no matter before, within or after functional area of freeway exit ramp, especially for heavy vehicles. It is observed from the simulation data that truck percentage has significant impact on the total lane change number, no matter before, within or after functional area of an exit ramp; more truck percentage me ans more unnecessary lane change. Not like the freeway grade, the truck perc entage has limited impact on the running speed. But it causes exceedingly total lane change number, causing safety concerns. It is suggested that a special traffic sign of devices be posted ahead of exit ramp, reminding motorists of the present of large potation of truck. PAGE 164 146 It was found that when trucks are restricted to the right two most lane, there will be less lane change number comparing with trucks are not restricted. But the restrictions seemed has limited impact on the operational speed of automobiles running on the freeway. Location of exit sign does have a significant impact on the operational speed and total lane change number before, within or after functional area of an exit, based on the data analysis of simulation suns. It can be concluded that from 4000 ft to 5000 ft sign distance is desirable in the design of exit ramp. The linear regression model within the functi onal area fits the data less well than before the functional area in terms of traffic speed and total lane change number. The traffic features are more complicated within functional area than before functional area. Speed and lane change number is difficult to estimate. The R2 is .602 and .804 respectively. 9.3. Recommendations Based on the research results and conclusions, it is recommended to design tapered twolane exit ramp at all desirable locations. It is practical to design tapered onelane exit at the first beginning of project and reserve the right of way for future tapered twolane exit. Parallel types are only recommended for the limited right of way between the arterial road and the freeway. In another word, parallel type are only good if the designer has to move the ramp structure from adjacent to arterial right of way to freeway right of way due to the geometry restriction. It is recommended not to build an exit ramp at uphill area, when ramp close to the uphill area, the capacity would be deducted to o much making the exit ramp a button neck area. PAGE 165 147 It is recommended that when design the exit ramp, trucks should be restricted to the right two most lane, it significant decrease the total lane change number while has slight impact on the vehicles operational speed. It is recommended that the desirable location of exit sign is from 4000 ft to 5000 ft. The findings and results are based on the traffic simulations and some assumptions, the further researches and improvements are needed in the following two fields, one is about the simulation software, another is about the exit ramp researches. 9.3.1. Simulation Software The research of volume discharging rate, operational speed and lane change maneuver are based one CORSIM simulation, though CORSIM is very reliable to reproduce the real world situation, there are still certain gap between simulation and field data, calibration and/or validation effect are still necessary to make better results; Although the user can adjust the distance of exit sign location in CORSIM, only one exit sign is allowed at CORSIM. At real situation, more than one exit sign may exist. CORSIM should design more than one exit sign to reproduce the real situation. CORSIM has a parameter called driver fami liarity, which is used to set up the distribution of driver familiarity with paths. But this parameter can only be applied to NETSIM, which is arterial road; CORSIM may assign this parameter to freeway also. Another parameter in CORSIM is called headway distribution; it can set up the headway distribution, such as normal distribution, erlang distribution for the whole roadway network. But CORSIM can not set different headway distribution for freeway and for arterial road separately. The CORS IM developer need consider this, because normally freeway and arterial road have different headway distribution characteristics. 9.3.2. Exit Ramp The traffic flow characteristics may different for twolane main and threelane mainline, this study only investigates the tr affic flow characteristics and compares the traffic flow difference of different exit ramp at threelane mainline, more researches is PAGE 166 148 necessary to investigate the traffic flow characteristics of twolane mainline and more than threelane mainline; This dissertation focus on the exit ramp traffi c flow characteristics itself, the impact from upstream and downstream weaving is ignored. If there are closely spaced upstream onramp or/and downstream onramp/offramps, the compli cated weaving maneuver will influence the traffic operation of the target o fframp, which should be very well studied at future research; This study assume that the capacity of exit terminal with the arterial road is not a concern, at some real case, when the exiting volume is too high to be discharged effectively at the arterial terminal; or the ramp effective length is not long enough, the backed up volume may influence the traffic performance of exit ramp, in this case, the traffic flow characteristics of each ramp type may different from this research, further studies is needed to address this concern; The traffic operational characterizes of other exit ramp type, such as design an acceleration lane after exit ramp physical area, this kind of design gives the vehicles which accidentally at the exit lane an backup chance to merge into the mainline again. The traffic merging and diverging maneuver happened at that segment may impact the traffic flow within the functional area and after functional area. The traffic flow characteristic should be researched as well. PAGE 167 149 References I USDOT, FHWA. Statistical Models of Accidents on Interchange Ramps and Speed Change Lanes. K.M. Bauer and D.W. Harwood II Kristine Williams, Huaguo Zhou, Larry Hagen and Waddah, Farah. Center for Urban Transportation Research, Florida Department of Transportation. Benefit and cost analysis of strategic Acquisition of Limited Access RightofWay near Interchanges III ITE Journal, May 1999, p 5054. Safety of Evaluation of Acceleration and Deceleration Lane Lengths. Joe Bared, Greg L. Giering and Davey L. Warren IV Journal of Transportation Research Board, No.1908, Transportation Research Board of the National Academies, Washington, D.C., 2005, p 8895. Calibration of Predictive Models for Estimating Safety of Ramp Design Configurations. Dominique Load and James A. Bonneson V Dallas Area Rapid Transit (DART). Operational Analysis of Terminating Freeway Auxiliary Lanes with OneLane Exit and TwoLane Exit RampsCase Study. Ralph A.Batenhorst, Jeff G.Gerken VI Virginia Polytechnic Institute and State University. Analysis of Freeway Weaving Areas Using Corridor Simulator and Highway Capacity Manual. Suresh Ramachandran VII Texas Transportation Institute Managed Lane Ramp and Roadway Design Issues. Kay Fitzpatrick, Marcus A. Brewer, and Steven Venglar. VIII Texas Transportation Institute/TTI Communications. The Texas A&M University System. Simulation Model Performance Evaluation for Congested Freeway Operations Mark D. Middleton, P.E., and Scott A. Cooner PAGE 168 150 IX University of Hawaii at Manoa. Department of Civil and Environmental Engineering. Data Gathering for Freeway Simulation Us ing Unintrusive Sensors and Satellite Telemetry Panos D. Prevedouros, Ph.D. X FHWA Office of Operations Research and Development. Identifying and Accessing Key WeatherRelated Parameters and Their Impacts on Traffic Operations Using Simulation XI Transportation Research Record 1705 Paper No. 003272 Influence of Experimental Pavement Markings on Urban Freeway ExitRamp Traffic Speeds. Richard A. Retting, Hugh W. McGee, and Charles M. Farmer XII Bijan Behzadi, FDOT D7 Session 57. Guide Signing for Multilane Freeway Exits with an Optional Lane. XIII Kangyuan Zhu, the Florida State University, College of engineering, Traffic capacity and speed analysis of freeway work zones based on computer simulation. XIV Serge P. Hoogendoorn, Stefan Luding, Piet H. L. Bovy, Michael Schreckenberg and Dietrich E. Wolf. LaneChange Maneuvers Consuming Freeway Capacity PAGE 169 151 Bibliography Highway Capacity Manual. Transportation Rese arch Board. National Research Council Washington, D.C.2000. A Policy on Geometric Design of Highways and Streets. American Association of State Highway and Transportation Officials. 2004 Edition. Advanced CORSIM Training Manual. Minnesota Department of Transportation. Microsoft Office Excel 2003 Programming In side out. Wayne S. Freeze, Felicia Buckingham. Microsoft Press (03/01/2004). Statistics for Research third edition chapter 10 Techniques for OneWay Analysis of Variance. Wiley Interscience Shirley Dowdy and Stanley Weardon. MIT System Dynamics in Education Project by Lucia Breiervoa & Mark ChoudhariAn Introduction to Sensitivity Analysis Traffic Flow Fundamentals. Adolf D. May. Publisher: Prentice Hall. TRAFED Users Guide. ITT Industries, In c., Systems Division. FHWA Office of Operations Research, Development and Technolopy. Types and characteristics of ramprelated motor vehicle crashes on urban interstate roadways in Northern Virginia Anne T. McCartt, Veronika Shabanova Northrup and Richard A. Retting. PAGE 170 About the Author Xu Wang received a Bachelors Degree in Traffic Engineering from Wuhan Urban Construction Institute in 1991 and a Masters Degree from Southeast University in 2004. He has ten years of roadway construction, s ite supervision and in tersection geometric design from 1991 to 2001 in Zhenjiang New Area. In the second half of 2004, he worked at China Academy of Urban Planning and Design as a traffic planning engineer until he entered the Ph.D. program at the University of South Florida in 2005. While in the Ph.D. program at the Univers ity of South Florida, he finished a few FDOT and STC project in traffi c planning and traffic safety. He also worked for the civil department as a T.A. He made several oral presentations at regu lar seminar meetings of civil department of University of South Florida. xml version 1.0 encoding UTF8 standalone no record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd leader nam Ka controlfield tag 001 002007392 003 fts 005 20090619093026.0 006 med 007 cr mnuuuuuu 008 090619s2008 flu s 000 0 eng d datafield ind1 8 ind2 024 subfield code a E14SFE0002332 035 (OCoLC)403799851 040 FHM c FHM 049 FHMM 090 TA145 (Online) 1 100 Wang, Xu. 0 245 Freeway exit ramp traffic flow research based on computer simulation h [electronic resource] / by Xu Wang. 260 [Tampa, Fla] : b University of South Florida, 2008. 500 Title from PDF of title page. Document formatted into pages; contains 151 pages. Includes vita. 502 Dissertation (Ph.D.)University of South Florida, 2008. 504 Includes bibliographical references. 516 Text (Electronic dissertation) in PDF format. 3 520 ABSTRACT: Interstate highways are one of the most important components of the transportation infrastructure in America. Freeway ramps play an important role in the whole interstate transportation system. This paper researches the traffic flow characteristics of four typical exit ramps in USA, which are tapered onelane exit, tapered twolane exit, parallel onelane exit and parallel twolane exit. Computer simulation software, such as CORSIM and HCS are applied as the main tools in this research. ANOVA and Tukey are used for statistical purpose. It compares the maximum capacity, average running speed and the total lane change number of those four exit ramps. It is found that no matter in terms of traffic discharging rate or total lane charging number; the tapered twolane exit has the best operational performance. Tapered onelane exit ramp has the least capacity. Parallel onelane exit and parallel twolane exit have very limited traffic operational difference in terms of capacity and running speed. It is recommended that parallel twolane exit ramp should not be designed along the freeway if the right of way along arterial road is enough. It is observed from the simulation data that the grade of freeway, truck percentage, restricted to the truck use of certain lane(s) and the location of exit sign have significant impact on the running speed and total lane change number. An uphill can decrease the running speed dramatically while more truck brings more lane change, causing safety concerns. It is found that when trucks are restricted to the right two most lane, there will be less lane change number comparing with trucks are not restricted. Location of exit sign operates well at the distance between 4000 ft to 5000 ft. does have a significant impact on the operational speed and total lane change number before, within or after functional area of an exit, based on the data analysis of simulation runs. 538 Mode of access: World Wide Web. System requirements: World Wide Web browser and PDF reader. 590 Advisor: Jian John Lu, Ph.D. 653 Speed Lane change Corsim ANOVA Tukey 690 Dissertations, Academic z USF x Civil & Environmental Engineering Doctoral. 773 t USF Electronic Theses and Dissertations. 4 856 u http://digital.lib.usf.edu/?e14.2332 