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Revenue management techniques applied to the parking industry

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Title:
Revenue management techniques applied to the parking industry
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Rojas, Daniel
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University of South Florida
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Subjects / Keywords:
Parking modeling
Logistic regression
Yield management
Pricing
Neural network
Prediction
Dissertations, Academic -- Industrial Engineering -- Masters -- USF   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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Abstract:
ABSTRACT: The time spent searching for a parking space increases air pollution, driver frustration, and safety problems impacting among other issues, traffic congestion and as consequence the environment. In the United States, parking represents a $20 billion industry (National Parking Association, 2005), and research shows that a car is parked on average 90 percent of the time. To alleviate this problem, more parking facilities should be built or intelligent models to better utilize current facilities should be explored. In this thesis, a general methodology is proposed to provide solutions to the parking problem. First, stated preference data is used to study drivers' choice/behavior. Parking choices are modeled as functions of arrival time, parking price, age, income and gender. The estimated values show that choice is relatively inelastic with respect to distance and more elastic with respect to price.^ The data is used to estimate the price elasticity that induces drivers to change their behavior. Second, neural networks are used to predict space availability using data provided by a parking facility. The model is compared with traditional forecasting models used in revenue management. Results show that neural networks are an effective tool to predict parking demand and perform better than traditional forecasting models. Third, the price elasticity that induces drivers to change their choice or behavior is determined. Finally, taking as an input the forecasting results obtained from the neural network and the price elasticity, parking spaces are optimally allocated at different price levels to optimize facility utilization and increase revenue. This research considers a parking facility network consisting of multiple parking lots with two, three and four fare classes and utilizes revenue management techniques as a mean to maximize revenue and to stimulate and diversify demand.^ ^The output indicates the number of parking spaces that should be made available for early booking to ensure full utilization of the parking lot, while at the same time attempting to secure as many full price parking spaces to ensure maximization of revenue.
Thesis:
Thesis (M.S.I.E.)--University of South Florida, 2006.
Bibliography:
Includes bibliographical references.
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Statement of Responsibility:
by Daniel Rojas.
General Note:
Title from PDF of title page.
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Document formatted into pages; contains 118 pages.

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oclc - 187301881
usfldc doi - E14-SFE0001835
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ABSTRACT: The time spent searching for a parking space increases air pollution, driver frustration, and safety problems impacting among other issues, traffic congestion and as consequence the environment. In the United States, parking represents a $20 billion industry (National Parking Association, 2005), and research shows that a car is parked on average 90 percent of the time. To alleviate this problem, more parking facilities should be built or intelligent models to better utilize current facilities should be explored. In this thesis, a general methodology is proposed to provide solutions to the parking problem. First, stated preference data is used to study drivers' choice/behavior. Parking choices are modeled as functions of arrival time, parking price, age, income and gender. The estimated values show that choice is relatively inelastic with respect to distance and more elastic with respect to price.^ The data is used to estimate the price elasticity that induces drivers to change their behavior. Second, neural networks are used to predict space availability using data provided by a parking facility. The model is compared with traditional forecasting models used in revenue management. Results show that neural networks are an effective tool to predict parking demand and perform better than traditional forecasting models. Third, the price elasticity that induces drivers to change their choice or behavior is determined. Finally, taking as an input the forecasting results obtained from the neural network and the price elasticity, parking spaces are optimally allocated at different price levels to optimize facility utilization and increase revenue. This research considers a parking facility network consisting of multiple parking lots with two, three and four fare classes and utilizes revenue management techniques as a mean to maximize revenue and to stimulate and diversify demand.^ ^The output indicates the number of parking spaces that should be made available for early booking to ensure full utilization of the parking lot, while at the same time attempting to secure as many full price parking spaces to ensure maximization of revenue.
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Revenue Management Techniques A pplied to the Parking Industry by Daniel Rojas A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Industrial Engineering Department of Industrial and Ma nagement Systems Engineering College of Engineering University of South Florida Major Professor: Gr isselle Centeno, Ph.D. Edward Mierzejewski, Ph.D. Kingsley Reeves, Ph.D. Date of Approval: November 2, 2006 Keywords: parking modeling, logistic regr ession, yield management, pricing, neural network, prediction Copyright 2006, Daniel Rojas

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DEDICATION To my Mom, Dad, Mauricio, Juan Alberto, Andres, Fernando, Christine and Valeria

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ACKNOWLEDGEMENTS I would like to thank Dr. Grisselle Cent eno for her incredible support and help throughout these years. Her encouragemen t and motivation was essential to the completion of this work. Also, I would like to thank my thesis committee Doctors Kingsley Reeves and Edward Mierzejewski whose guidance was extremely important during this journey. Also, I want to thank Aldo Fabregas for his support throughout all these years. I also want to recognize my family for their support through al l these years. Mom you are my hero and you will always be. Finally, heartfelt thanks go to the two people that have changed my life for the best: Christine (my wife) and Valeria (my beautiful daughter).

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i TABLE OF CONTENTS LIST OF TABLES.............................................................................................................iv LIST OF FIGURES............................................................................................................v ABSTRACT.....................................................................................................................viii CHAPTER 1 INTRODUCTION........................................................................................1 1.1 The Parking Industry.................................................................................................3 1.2 Parking Problem Overview.......................................................................................4 1.3 General Problem Description and Approach............................................................7 1.4 Thesis Organization..................................................................................................8 CHAPTER 2 LITERATURE REVIEW.............................................................................9 2.1 Parking Policy...........................................................................................................9 2.1.1 Parking Pricing.................................................................................................12 2.1.2 Parking Choice/Behavior.................................................................................14 2.1.3 Parking Design and Technology......................................................................17 2.2 Summary.................................................................................................................20 CHAPTER 3 PROBLEM STATEMENT.........................................................................22 3.1 Introduction and Motivation...................................................................................22 3.2 Research Objectives................................................................................................23 3.3 Research Methodology...........................................................................................24 CHAPTER 4 REVENUE MANAGEMENT APPLIED TO PARKING.........................26 4.1 Introduction.............................................................................................................26 4.2 Parking Revenue Management Process..................................................................29 4.3 Revenue Management Literature............................................................................32 4.3.1 Seat Inventory Control.....................................................................................32 4.3.2 Demand Forecasting........................................................................................34 4.3.3 Overbooking....................................................................................................35 4.3.4 Pricing..............................................................................................................36 CHAPTER 5 MARKET SEGMENTATION...................................................................37 5.1 Introduction.............................................................................................................37 5.2 Stated Preference versus Revealed Preference Survey...........................................39 5.3 Stated Preference Parking Survey...........................................................................41 5.3.1 Stimulus Material.............................................................................................42

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ii 5.3.2 Survey Design..................................................................................................42 5.3.3 Survey Procedure.............................................................................................45 5.3.4 Results..............................................................................................................46 5.4 Logit Model............................................................................................................50 5.4.1 Logit Model Results.........................................................................................52 CHAPTER 6 PARKING DEMAND FORECASTING MODELS..................................54 6.1 Introduction.............................................................................................................54 6.2 Time Series Forecasting Methods...........................................................................57 6.2.1 Moving Average..............................................................................................57 6.2.2 Simple Exponential Smoothing.......................................................................58 6.2.3 Holts Model....................................................................................................59 6.2.4 Winters Model................................................................................................60 6.3 Causal Models.........................................................................................................61 6.3.1 Introduction to Neural Networks.....................................................................61 6.3.1.1 Training.....................................................................................................63 6.3.1.2 Overfitting and Generalization.................................................................64 6.4 Parking Demand Predictor Model..........................................................................66 6.5 Performance Measures............................................................................................68 6.5.1 Mean Absolute Percentage Error (MAPE)......................................................68 6.5.2 Mean Absolute Deviation (MAD)...................................................................68 6.5.3 Mean Square Error (MSE)...............................................................................69 6.5.4 Root Mean Square Error (RMSE)....................................................................69 6.5.5 Tracking Signal (TS)........................................................................................70 6.5.6 Mean Error.......................................................................................................70 6.6 Comparison of Forecasting Techniques..................................................................70 6.7 Discussion...............................................................................................................75 CHAPTER 7 CAPACITY CONTROL MODEL.............................................................77 7.1 Introduction.............................................................................................................77 7.2 Capacity Control Model..........................................................................................79 7.2.1 Expected Marginal Revenue Model.................................................................81 7.2.1.1 Littlewoods Two Class Model.................................................................82 7.2.1.2 Expected Marginal Seat Revenue-version a (EMSR-a)............................85 7.2.1.3 Expected Marginal Seat Revenue-version b (EMSR-b)...........................86 7.3 Application to the Parking Industry........................................................................87 7.4 Summary.................................................................................................................91 CHAPTER 8 CONCLUSIONS AND FUTURE RESEARCH........................................93 REFERENCES.................................................................................................................96 APPENDICES................................................................................................................101 Appendix A: Stated Preference Survey......................................................................102 Appendix B: Stated Preference Survey Raw Data......................................................107

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iii Appendix C: Scenario Results....................................................................................109 Appendix D: Forecasting Models Results..................................................................111 Appendix E: Neural Network Code in MatLab..........................................................113 Appendix F: Statistical Test of MSE..........................................................................115 Appendix G: Capacity Control Models......................................................................117

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iv LIST OF TABLES Table 1: Parking Literature Overview..............................................................................10 Table 2: Revenue Management Characteristics and Examples........................................27 Table 3: Stated Preference Survey Demographics............................................................41 Table 4: Parking Survey Scenarios...................................................................................44 Table 5: Logit Model Results...........................................................................................53 Table 6: Performance Comparison for the Various Forecasting Models.........................72 Table 7: Protection Levels for Two Classes.....................................................................88 Table 8: Protection Levels for Three Fare Classes...........................................................88 Table 9: Protection Levels for Four Fare Classes.............................................................89 Table 10: Simulation of Revenue Performance................................................................90 Table 11: RM Capacity Control Example........................................................................91 Table 12: Survey Raw Data Results...............................................................................107 Table 13: Littlewood's Two Class Model Results..........................................................117 Table 14: Three Classes Data.........................................................................................117 Table 15: Four Classes Data...........................................................................................117 Table 16: EMSR-a for Three Classes.............................................................................117 Table 17: EMSR-b for Three Classes.............................................................................117 Table 18: EMSR-a for Four Classes...............................................................................117 Table 19: EMSR-b for Four Classes...............................................................................118

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v LIST OF FIGURES Figure 1: Parking Problem Broader Context......................................................................5 Figure 2: General Problem Description and Approach.......................................................8 Figure 3: Parking Revenue Management Process............................................................30 Figure 4: Parking Market Segments.................................................................................38 Figure 5: Stated Preference versus Revealed Preference Survey.....................................40 Figure 6: Parking Survey Example...................................................................................45 Figure 7: Stated Preference Survey Results......................................................................47 Figure 8: Stated Preference Survey ResultsOn Time.....................................................48 Figure 9: Stated Preference Survey Results-Late.............................................................49 Figure 10: Demand Curve for Cl osest Parking Lot-Early................................................49 Figure 11: Demand Curve for Closest Parking Lot-Late..................................................50 Figure 12: Neural Network Model....................................................................................62 Figure 13: Neural Netw ork Parking Model......................................................................66 Figure 14: Neural Network Architecture..........................................................................67 Figure 15: Raw Data for Parking Occupancy...................................................................71 Figure 16: Graphical Representations for Different Forecasting Methods.......................71 Figure 17: Relationships among Performance Measures..................................................73 Figure 18: Mean Error......................................................................................................74 Figure 19: Tracking Signal...............................................................................................75

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vi Figure 20: Revenue Generated for One Segment.............................................................77 Figure 21: Revenue Generated for Two Segments...........................................................78 Figure 22: Example of Nested Booking Limits................................................................80 Figure 23: Decision Tree..................................................................................................83 Figure 24: Number of Fare Classes vs. Total Revenue....................................................89 Figure 25: Survey Case Scenario Sample.......................................................................103 Figure 26: Case Scenario # 1..........................................................................................104 Figure 27: Case Scenario # 2..........................................................................................104 Figure 28: Case Scenario # 3..........................................................................................104 Figure 29: Case Scenario # 4..........................................................................................104 Figure 30: Case Scenario # 5..........................................................................................104 Figure 31: Case Scenario # 6..........................................................................................104 Figure 32: Case Scenario # 7..........................................................................................105 Figure 33: Case Scenario # 8..........................................................................................105 Figure 34: Case Scenario # 9..........................................................................................105 Figure 35: Case Scenario # 10........................................................................................105 Figure 36: Case Scenario # 11........................................................................................105 Figure 37: Case Scenario # 12........................................................................................105 Figure 38: Case Scenario 1 Results................................................................................109 Figure 39: Case Scenario 2 Results................................................................................109 Figure 40: Case Scenario 3 Results................................................................................109 Figure 41: Case Scenario 4 Results................................................................................109 Figure 42: Case Scenario 5 Results................................................................................109

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vii Figure 43: Case Scenario 6 Results................................................................................109 Figure 44: Case Scenario 7 Results................................................................................109 Figure 45: Case Scenario 8 Results................................................................................109 Figure 46: Case Scenario 9 Results................................................................................109 Figure 47: Case Scenario 10 Results..............................................................................109 Figure 48: Case Scenario 11 Results..............................................................................109 Figure 49: Case Scenario 12 Results..............................................................................109 Figure 50: Moving Averag e Forecasting Results...........................................................110 Figure 51: Exponential Smoothing Forecasting Results.................................................110 Figure 52: Holt's Model Forecasting Results..................................................................111 Figure 53: Winter's Mode l Forecasting Results..............................................................111 Figure 54: Neural Network Forecasting Results.............................................................112

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viii REVENUE MANAGEMENT TECHNIQUE S APPLIED TO THE PARKING INDUSTRY Daniel Rojas ABSTRACT The time spent searching for a parki ng space increases air pollution, driver frustration, and safety problems impacting am ong other issues, tra ffic congestion and as consequence the environment. In the Unite d States, parking repr esents a $20 billion industry (National Parking Asso ciation, 2005), and research show s that a car is parked on average 90 percent of the time. To alleviate this problem, more parking facilities should be built or intelligent models to better utilize current facilities should be explore d. In this thesis, a general methodology is proposed to provide solutions to the parking problem. First, stated preference data is used to study drivers choi ce/behavior. Parking choices are modeled as functions of arrival time, parking price, age, income and gender. The estimated values show that choice is relatively inelastic with respect to distance a nd more elastic with respect to price. The data is used to estimat e the price elasticity that induces drivers to change their behavior. Second, neural networ ks are used to predict space availability using data provided by a park ing facility. The model is compared with traditional forecasting models used in revenue management.

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ix Results show that neural networks are an effective tool to predict parking demand and perform better than traditional forecasti ng models. Third, the pr ice elasticity that induces drivers to change thei r choice or behavior is determ ined. Finally, taking as an input the forecasting results obtained from th e neural network and the price elasticity, parking spaces are optimally allocated at different price levels to optimize facility utilization and increase revenue. This research considers a parking facility network consisting of multiple parking lots with two, three and four fare classes an d utilizes revenue mana gement techniques as a mean to maximize revenue and to stimulat e and diversify demand. The output indicates the number of parking spaces that should be made available for early booking to ensure full utilization of the parking lot, while at th e same time attempting to secure as many full price parking spaces to ensure maximization of revenue.

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1 CHAPTER 1 INTRODUCTION More than 41,000 Americans die as a result of 6 million traffic accidents on the nation roadways system each year. This is the equivalent of 115 people each day, or one every 13 minutes. Traffic accidents injure d 3.2 million Americans in 2000. Most crash survivor remains with multiple injuries w ho account for $150 billion a year on Nations Health care costs (Intelligent Vehicle Initia tive, 2000). Congested roadways which slow transit vehicles are also anot her reason why the statistics shown above are so high. The United States Federal Highway Administration forecasts that the severity of traffic congestion will continue to increase at signif icant rates in all U.S. urban areas, unless specific actions are taken. Demand for highway travel by Ameri cans continues to grow as population increases, particularly in metropolitan ar eas. Between 1980 and 1999, route miles of highways increased 1.5 percent wh ile vehicle miles of travel increased 76 percent. The Texas Transportation Institute showed that in 2000, the 75 largest metropolitan areas experienced 3.6 billion vehiclehours of delay, resulting in 2 1.6 billion liters (5.7 billion gallons) in wasted fuel and $67.5 billion in lost productivity. Traffic volumes also are projected to continue to incr ease. The volume of freight m ovement alone is forecast to nearly double by 2020 (United States Depart ment of Transportation, 2003). Without intervention, we can only expect these costs to increase as more and more drivers occupy our roads.

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2 The traditional approach to relieve congestion was to invest on the expansion of highway capacity. However, highway capacity has not kept pace with the growth in vehicles miles traveled. As a result congestion has grown st eadily worse. Also, highway expansion results in considerab le disruptions on traffic. Furthermore, large highway construction projects are expensive, and they do not offer long term solutions. Construction of a large highway may be e nough to alleviate congestion for a couple of years; however, after certain periods of time the highway w ould need another expansion to keep up with the traffic demand. The highway system would reach a point where expansion of new roads and highways would not be possible due to space and cost limitations. Currently, the United States transpor tation agencies are changing from the traditional expansion strategy. Agencies ar e focusing on the optimization of existing infrastructures. The U.S. Department of Transportation (DOT) is one of the leading institutions on the research of new optimi zation technologies th at would reduce the number of traffic accidents in the United Stat es each year. This agency is studying the development and applications of In telligent Transportation Systems. Intelligent Transportation Systems (ITS) is one of the leading technologies in the reduction of traffic congestion. Intelligent tr ansportation encompasses the full scope of information technologies used in transportation, including control, computation and communication, as well as the algorithms, databases and human interfaces within intelligent transportatio n systems (ITS Journal, 2002). Joining these technologies to the transportation system is expected to reduce th e number of traffic accidents, deaths, time, and money. The future of ITS is very promising, and already many states around the

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3 United States are implementing this tec hnology to their highway systems. The innovative prepaid toll program and the 511 real-time traffic information are clear examples of the application of ITS. 1.1 The Parking Industry Parking plays an important role in the tr affic system since all vehicles require a storage location when they are not being used to transport pa ssengers. Most major cities continually struggle with parking limitations violations and cost Its availability influences where people travel and how they commute, impacting am ong other issues, air pollution, driver frustration, traffic safety, a nd especially congestio n which continues to be one of the most critical problems faced by urban America (Axhausen and Polak, 1991) and (Innovative Mobility, 2002). For over a decade, European cities have been investigating intelligent parking mechanisms and are finding substantial benefits. In addition, several German cities that have in telligent parking, such as dynamic parking signs that direct drivers to the nearest vacan t parking structure, have reported 15 percent less traffic in their downtowns when compared to cities that do not used advance technology for parking routing (Axhausen and Polak, 1991). The US infrastructure needs to be fortified by advancing knowledge on park ing modeling and integr ating advances in technology to better plan for capacity needs (Centeno and Rojas, 2006). In parking terms, capacity planning can be defined as the "science" of predicting the quantity and specific attributes of parki ng facilities and spaces needed to satisfy the forecasted demand. Currently, capacity planning methods do not provide efficient results because most of the time the huge amount of dynamic input data is ignored and not many

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4 demand scenarios are considered even though a high uncertainty in th e forecasts typically exists. 1.2 Parking Problem Overview It is extremely important to define a parking architecture that would combine different technologies to solve the parki ng problem. The parking problem can be described from two perspectives: drivers poin t of view and parking management point of view. The objective for drivers is to find the closest parking space to their destination at the lowest possible cost and as fast as po ssible. The objective for managers is to maximize their revenues. An ideal parking ar chitecture must consider these perspectives to find alternative solutions to the parking problem. Figure 1 presents a genera l overview of the parking problem and a proposed approach to provide drivers with reliable info rmation on the parking lot state. A parking management system will inform drivers with alternatives on where and when to park. During the last years, parking reservations systems are becoming mo re popular especially in large metropolitan areas such as San Francisco, Chicago, Los Angeles, and Philadelphia. Parking reservation systems pr ovides drivers with real -time information on the availability of parking spaces for facilities that provide the service. The basic idea of this type of system is that drivers would reserve a parking space in advance through the internet or cell-phone. Other companies that provide traffic information for navigation systems such as XM Satellite Radio Holdi ngs Inc have introduced parking reservation systems as part of their services. Driver s can search for available parking spaces by looking at the navigation system that pr ovides real-time information of parking occupancy.

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5 The question might be why companies are allocating so many resources to develop this type of systems. The answer could be that parking is actually a huge business. In the United States, parking represents a $20 bil lion industry (National Parking Association, 2005). This among all the previous statistics presented before make the parking problem very attr active for research purposes. The response of the public for this type of reservat ion systems is very positive as re vealed by a female user from San Francisco to the Wall Street Journal on Marc h 2006 during an interview. She uses the system to reserve parking spaces in the trai n station that she tran sfers to commute to work. Without this option, she would have opted to drive her car to work, a nondesirable alternative since public tr ansportation alleviates congestion. Figure 1: Parking Problem Broader Context Unfortunately, the problem with reservat ion systems currently in the market is that they have increased the cost of parking since drivers have to pay a higher fare when they reserve a space in advance. This has prov ided critics of such systems with facts to diminish the use of them. However, parking reservation systems can be extremely useful if they are used to control parking demand. For example, managers/planners can c ontrol the demand of drivers on certain facilities with high utilizati on by diverting drivers to fac ilities with low utilization. Drivers that reserve a parking space in adva nce would be rewarde d with lower fares since they have provided parking manager/planne rs with information in advance. On the

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6 other hand, drivers who do not reserve a space and just show up on the parking facility would be charged a higher fare. This c ould be achieved through the introduction of pricing strategies. However, to determine op timal pricing strategies, it is necessary to first study the state of the system and to predic t future states of park ing facilities. For a reservation system to work efficiently, pa rking managers/planner s need a prediction model to determine the number of parking spac es available. After the various states of the system are well known, the next step is to efficiently allocate the parking spaces to demand. These ideas are the basis for revenue management. Revenue management also known as yield management has ma inly been used in the airline and hote l industries. The principle of revenue management is to sell the right product to the right customer at the right time and for the right price. In the park ing problem this can be translated to selling the right parking space to the ri ght driver at the right time a nd for the right price. The previous statements assume that the same pr oduct could be sold at different prices and that there are several types of customers for th e same product. For example, in the airline industry there are business trav elers and leisure travelers. The later being a customer segment that would prefer to pay less for their seats by sacrificing changes in their schedules. Business travelers, on the other ha nd, would pay higher rates for the same seat because they do not have much flexibility on their schedules. These characteristics are also present in the parking problem setting si nce a parking space can be sold at different price to different customer segments demons trating that revenue management techniques are relevant for the parking problem solution.

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7 1.3 General Problem Description and Approach Figure 2 presents the general problem description and overview to provide solutions to the parking problem. At the top level of the methodology is the parking reservation system. This type of system, as previously described, is already in place in various cities around the US. Th e main ingredient to have a reservation system in place is a well designed information system that a llows parkers to reserve a parking space in advance. In this thesis, revenue manageme nt techniques are proposed as an input to parking reservation systems. However, in formation systems are out of scope. The revenue management process would be applied to the parking proble m. First, market segmentation would be studied through a parking behavior/c hoice survey. The objective of market segmentation is to determine if drivers are willing to pay higher fares under certain factors such as arrival time, time to destination, and price. After drivers have been segmented, the next step is to predic t parking space availability. This thesis proposes a neural network model as an altern ative to other traditional forecasting models such as moving average, exponential smoothi ng, Holts model, and Winters model to predict parking space availability. The results of the prediction model are extremely useful since they would be used as an input later to optimally allocate available parking spaces. Revenue management theory states that a parking space could be sold at different fare rates. The goal is to determine what is the price difference that would influence drivers to change their parking choice. This will be studied through parking behavior/choice models. Finally, these resu lts and the ones obtained from the prediction model will be used to determine how many parking spaces should be reserved for each drivers segment.

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8 Figure 2: General Problem Description and Approach 1.4 Thesis Organization This thesis is organized as follows: Chap ter 2 identifies the most important studies related to parking studies. Chapter 3 describes the problem statement and the motivation for this research. Chapter 4 introduces revenue management and how it can be adapted to suit the parking problem. Chapter 5 presen ts market or drivers segmentation and presents drivers characteristics regarding th eir willingness to pay higher fares for the same parking space under certain factors such as arrival time, time to destination, and price. Chapter 6 presents a comparison of di fferent forecasting models to predict parking demand with a proposed neural network model. Chapter 7 presents the capacity control model where parking spaces are optimally allocated to different pricing strategies to maximize revenue. Finally, Chapter 8 presents the conclusions and future research of this study, as well as future research opportunities.

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9 CHAPTER 2 LITERATURE REVIEW The research methods used for mode ling parking systems have varied in complexity, ranging from simple empirical st udies and heuristics to advanced techniques for mapping complex parking non-linearity. In the following subsections, a brief summary of the main parking components addr essed in the literatu re, and the models developed are presented. The reviewed articles have been classi fied according to the parking factor under study, that is, policy, prici ng, choice/behavior, technology and parking design. Table 1 presents an overview of how the parking l iterature has been organized and the most significant articles review ed under each category. 2.1 Parking Policy Parking policy has been studied to provi de tools for effec tive policy decisions such as changes in the number of parking spaces, number of park ing facilities or new traffic enforcement. Feeney (1989) presents a review of quantitativ e results relating to the impact of parking policy on the parking and travel demand. Disaggregated modal choice models; disaggregate parking location m odels and site-specific studies of parking behavior were examined.

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10 Table 1: Parking Literature Overview Title Year Policy Choice Pricing Design Technology A Review of the Impact of Parking Policy Measures on Travel Demand 1989 A Parking Model Hierarchy 1991 Study of Parking and Traffic Demand: A Traffic Restraint Analysis Model (TRAM) 1997 The Effects of Parking Measures on Traffic Congestion 1986 A Stochastic User Equilibrium Assignment M odel for the Evaluation of Parking Policies 1993 A nested logit model of parking location choice 1993 Mixed Logit Estimation of Parking Type Choice 2004 Development of parking choice models for special event 2003 Modeling time. Dependent travel choice problems in road networks with multiple user classes 2006 Modeling Parking 1999 A Probabilistic Approach to Evaluate St rategies for Selecting a Parking Space 1998 The Impact of the Parking Situation in Shopping Centers on Store Choice Behavior 1998 Raising Commuter Parking Prices-An Empirical Study 1982 Parking Subsidies and Travel Choices: Assessing the Evidence 1990 An Opportunity to Reduce Minimum Parking Requirements 1995 Parking Policies and Road Pricing 2000 The Economics of Regulatory Parking Polici es: The (im)possibilities of Parking Policies 1995 PARKSIM/1: A Network Model for Parking Facility Design 1986 Modeling Shopping Centre Traffic Movement (1): Model Validation 1998 Evaluating ITS Management Strategies: A Systems Approach 2000 The Research on the Key Technologies for Improving Efficiency of Parking Guidance System 2003 Parking Guidance and Information Sy stems : Performance and Capability 1990 Understanding the Demand for Access Information 1998 Behavioral Impact of A Broadcast Parking Information Service in Nottingham 1991 Revenue Management Techniques A pplied to the Parking Industry 2006 10

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11 It was found that disaggregated models of parking location choice we re highly correlated with parking prices a nd supply restrictions. Young and Taylor (1991) developed a hi erarchy of microcomputer models and information systems that can investigate pa rking policy and study the level of service provided by parking systems. It outlines six parking models that can be used to address parking issues from an urban to a parking lo t level. The most important feature of this hierarchy is that it allows data to be passed from one level to anothe r, enabling a realistic representation of the total parking system. Scholefield Bradley, and Skinner (1997) developed a computer simulation model TRAM fo r testing policies to control parking, as well as other types of traffic restraint. The po lices of interest in this study were: pricing and capacity reductions. The objective of this study was to determine the extent to which parking controls can be useful in reducing traffic congestion. Parking policy has a significant impact on urban management. Several authors including Visser and Van der Mede (1986) ha ve concluded that parking policy has an influence on the parking, the transportation, and the socio-economic systems. Despite the significance of parking policy, only a small number of models related to evaluation of parking policy have been built. Bifulco (1993) develops an interacti on model of supply and demand to evaluate various parking policies. The model is applied at Avellino, a small town in southern Italy. A generalized random utility choice model is used to represent such demand. Additionally, a supply model is created in four zones considering parking types such as free on street parking, metered on street parking, on street parking with limited duration, on street metered and limited parking, off st reet parking, and illeg al parking. Model

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12 capabilities and characteristics are compared to other model types including Eldin and CLAMP. Unlike other models, this model can be dynamic and multimodal while allowing multiple users and considering feedbacks on path, mode, destination, timing, and the demand/supply interaction. The mode l designed proves that, through the parking supply of neighboring zones, a high parking demand in a specific zone is satisfied. 2.1.1 Parking Pricing Pricing has been proposed as an effec tive policy option to minimize the parking problem. Miller and Everett (1982) presented an empirical study to determine the impact of parking price increase on commuting beha vior at a sample of 15 worksites in metropolitan Washington, DC. The study rev ealed that removing free parking and raising parking rates influen ced significant shifts to highe r-occupancy modes, but that the shifts were not uniform in direction or ma gnitude across the sites. Furthermore, the authors provide a discussion of policy imp lications derived from the study such as: Parking pricing strategies can be eff ective in reducing the number of work commute automobile The effectiveness of new parking rate s depends on many factors (external and site specific) Under certain parking supply conditions, parking pricing strategies can have adverse impacts, such as increasing the use of single-occupant autos Some carpoolers may shift to tran sit as parking rates increase Unlike most other transportation syst em management strategies, imposing parking prices can result in significant revenues

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13 Willson and Shoup (1990) reviewed severa l empirical studies of how employerpaid parking affects employees travel choice. It was concluded th at parking subsidies increase solo driving. It was also found that when parking subsides were removed, a significant amount of solo drivers shift to carpools and/or transit. The case studies reviewed reveal that ending employer-paid parking reduces the number of solo drivers by between 19 and 81 percent, and reduces the nu mber of autos driven to work by between 15 and 38 percent. Shoup (1995) studied the effects legisl ation passed in California with the objective of reducing traffic congestion and air pollution. The legislation required employers who subsidize employee parking to offer employees the option to take the cash value of parking subsidy, in lieu of the parking itself. The legislation also required cities to reduce the parking requirements fo r developments that implement a parking cash-out program. The hypothesis is that by sh ifting subsides from parking to people will encourage drivers to carpool, ride mass transit, bicycle, or walk to work. A study of how the option to cash out employer-paid park ing will reduce parking demand and recommends a reduction in minimum pa rking requirements was presented. Several economists have advocated that drivers are not paying the true cost for commuting and most drivers park for free. The studies presented above revealed that removing free parking is an efficient tool to influence parking demand and reduce levels of congestion and air pollution. Calthrop, Proost and Dender (2000) used a numerical simulation model to study the e fficiency gains from differen t parking policies with and without a simple cordon system. The authors show that it is nece ssary to simultaneously determine the pricing of parking and road use. This study consider s an analysis of the

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14 welfare gains by combining both parking and road pricing simultaneously. The model shows that increasing parking prices produces higher welfare gains than the use of a single-ring cordon scheme. Howeve r, this result is lower th an a combination of a cordon charge with pricing parking spots. It has been shown in the literature quantitative and qualitative the many advantages of pricing strate gies when parking supply is limited. Researchers have studied the impact of pricing on the wor kplace and how employ ees react to these changes. The expectation is that employees will react to these changes by opting for different transportation modes. Also, it has been shown that pricing strategies can be made for each parking spot or a combinati on with road use. Vehoef, Nijkamp, and Rietveld (1994) present an economic analys is of regulatory parking policies as a substitute to road pricing. Three reasons of why parking f ees are superior to physical restrictions in parking space supply are di scussed. The disadvantages of regulatory parking policies in comparison to a system of road pricing are also stated: regulatory parking policies will always remain a secondbest option by nature, the risk for spillover (drivers who park in adjacent areas), enforcement of the po licy may by more expensive in the long run. 2.1.2 Parking Choice/Behavior Over the years several models have been developed to investigate drivers choice when deciding upon a parking lo cation or a parking space. The literature on parking choice assist parking policy makers to better understand the behavior of drivers at the time of choosing a parking space. Hunt a nd Teply (1993) provided a nested logit model of parking location choice using revealed preference data. The model was evaluated

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15 using data for a central business district ( CBD). The authors conclude that parking location choice is influenced by factors othe r than money cost and proximity to final destination. Other factors that influence pa rking location choice are: position relative to the trip being made, nature of the parking surface, and time for searching a parking space. Hess and Polak (2004) presented the result s of a study of parking choice behavior, based on stated preference data, collected in va rious city centre locations in the UK. The authors presented a mixed multinomial logit ( MMNL) model. The model is capable of including the random variation in preferences within groups of drivers that has been previously ignored in the literature. Through the inclusion of this factor other relevant factors such as access, search a nd egress time were identified. Sattayhatewa and Smith (2002) present a study on how drivers choose a parking lot during a special event. The authors pres ent a lot choice model (using logit function) and the joint parking lot destination choice and assignment model (using user equilibrium traffic assignment and entr opy maximization). Results re veal that walking time and driving cost are very im portant for drivers. Other important factors th at affect parking choice ar e presented in Lam et al. (2005). The authors found that parking behavi or is influenced by travel demand, walking distance, parking capacity, and parking price. Various parking choice models have been built to analyze and understand the decision process that drivers experience on a da ily basis when selecting a parking space. For example, Arnott and Rowse (1999) develo ped four models of parking including a structural model, an extended model incor porating several realistic complications, a general equilibrium model used for welfare analysis, and a model to study stochastic

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16 characteristics of parking. For simplicity, a city lying on the circumference of a circle is used to explore parking on a spatially symmetr ic area and disregarding flow congestion. In addition, Cassady and Kobza (2000) study the drivers parking decision process in a stochastic envir onment. By representing the results of stated preference surveys through network models, parking demand is analyzed. Parking strategies that drivers use are analyzed: 1) pick a row, clos est space and 2) cycling. In the first strategy, the driver chooses a row and the closest avai lable space from that row. In the second strategy, the driver chooses a row and, only if any of the closest 20 spaces are available, the closest space is selected. If not, the driver continues to the next row. If any of the closest 40 spaces is available, the closest sp ace is selected. Othe rwise, the customer comes back to the other row and chooses the closest available space. Performance measures studied include tota l walking distance, search time, and the sum of these two values. Conclusions rega rding the most accurate strategy to predict performance measures are made. Indeed, the first strategy yields more accurate results for search time as well as the combination of search time and walking time. In contrast, the second strategy provides more accurate results for walking time. Van der Waerden, Borgers, and Timme rmans (1998) designed and validated a hierarchical logit model of parking lot and store choice behavior to analyze how parking policy affects drivers behavior. Data is collected at City-Centre Veldhoven, a shopping center in the Eindhoven Me tropolitan area at the Netherla nds. Conclusions made after the study include: 1) walking distance has an im pact on drivers choice, 2) the drivers choice process could be accurately represente d by a sequential decision making process,

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17 and 3) the probability of selecting a parking space decreases as the size of the parking lot increases indicating that drivers tend to avoid long walking distances. 2.1.3 Parking Design and Technology Parking Design models are extremely impor tant for transportation planners since they can assist to determine the location of parking facilities and to evaluate design alternatives of parking faci lities. The interaction among th e parking facilities component and traffic systems was presented in Young (1986) through a simulation model (PARKSIM/1). Planners can use this model to determine the efficiency of a particular parking lot layout. Another discrete simu lation model was presented by Le and Young (1997). This model allows planners to understand the interaction among location of shops and the design of parking and traffic systems. Technology is playing an important role in the new design of parking and traffic systems. New developments of parking tec hnology have opened the door for researchers and planners to study and understand the effect of these technologies into the parking system. Maccubin and Hoel (2000) develope d a methodology to evaluate the different alternatives in technology for improving park ing management at change-mode facilities. The authors tested the methodology develope d using a computer simulation model to identify the benefits of different intelligent transportation systems solutions. Parking Guidance Information Systems is one of the technology alternatives used around the world to alleviate congestions. Yang, Liu and Wang (2003) presented a study on the key technologies needed for a successful implementa tion of a Parking Guidance and Information System in the city of Beijing, China. They also presented some of the problem that raised during the installation a nd running phase such as: (1) parking fees are

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18 not the same throughout the network; therefore, drivers do not move to parking lots as directed by the system; (2) users have difficulty understanding the meaning of the messages on the boards; (3) a survey was dist ributed an 20 percent of the respondents were aware of the system, but had not used it. After a PGI system is implemented, statis tical analysis of the effects of the PGI system on drivers behavior are developed from surveys. Elements studied in such surveys include level of awareness, understa nding, usage of PGI sy stems, and stated preference of information displayed. In a number of papers, surv eys are designed to differentiate results according to physical, trip purpose, and service time characteristics. Additionally, to identify the most crucial info rmation to be displaye d for a wide range of real time information such as park location, availability, waiting times, and prices are being studied. Conclusions regarding possi ble improvements to PGI systems are made based on the results of the su rvey. Suggestions to improve the implementation of PGI systems include increasing awareness a nd displaying new messages with traffic information appealing to drivers. To st udy the PGI system, tools used include data collection strategies (locati on, survey technique, survey method, sample size, etc.), statistical inference, and logit models of parking choice. A simplified system architecture of a PG I system is provided by Polak, et al. (1990) to individuals who are not familiar w ith the operations of PGI systems. Other topics discussed include benefits, component s, data collection, data transmission, and data processing of PGI systems. In additi on, the alternatives available for displaying information such as techniques, locations, a nd the information on the signs are studied. Approaches to the design and control of PGI systems are described as well. Results of

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19 different case scenarios from previous imp act and behavioral studies to analyze and evaluate PGI systems are briefly reviewed. Finally, some implications of current developments for future PGI systems are discussed. A more detailed study of the impact of PGI systems which evaluates the effects and driver reactions of PGI systems in seve ral cities in Japan is presented by Thompson and Takada (1995). The drivers cognitive information transmission process consisting of awareness, observation, understanding, belief and usage of PGI systems is used to understand the most critical nature of drivers reactions. A questionnaire survey was distributed, a nd a statistical analysis to measure the impact of PGI signs wa s provided based on the survey re sults. The information requested in the survey was based on revealed preference data. In addition, dr ivers were asked to provide information such as purpose of the trip trip origin, trip frequency, trip duration, vehicle type, gender, and age. The results of the survey suggest th at different types of drivers want different types of information to be displayed. The most requested parking information type by drivers is availability of car parks (61.1%), followed by waiting time at car parks (34.3%), location of car parks (29.4%), and how to find available car parks (22.0%). The study also shows which types of drivers are most likely to use PGI signs and that there is still a lack of believe in PGI systems. An alternative to PGI systems is revi ewed and evaluated by Polak, Vythoulkas, and Chatfield. This paper determines the ca uses of parking congest ion and explains the arguments of why a broadcast parking information was implemented in Nottingham. Furthermore, this article analyses the effect s of the broadcast park ing system on drivers behavior through survey. Thus, regular users of the system according to attributes such

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20 as gender, frequency of parking and search behavior are identified. The analysis developed is used mainly to monitor th e progress after the implementation of the broadcast parking system. Conclusions rega rding possible improvements to the system including increasing awareness and displaying new messages with traffic information are suggested. 2.2 Summary In this chapter, the parking literature has been reviewed fo r the parking factors considered. This thesis touc hes upon two of these: parki ng choice/behavior and parking pricing. As previously described, parking c hoice/behavior modeling approaches consider how drivers would react to change s in the availability or locati on of the parking facilities. Impact would be reflected on the day/time of the trip by changing destination or discarding the trip due to park ing concerns. These models are typically formulated as mode choice. Traditional mode choice models study how drivers respond to changes in the supply and operation of parking facilities. These responses are ty pically studied using logit models (logit models study how driv ers made choices among a finite set of alternatives) based on stated (hypothetical scenarios) an d revealed preference (actual data) data. Researchers have concluded that several factors such as parking price, walking distance, driving distance, parking surface, parking locati on, etc. influence parking choice/behavior. However, to our know ledge there is no evidence that the arrival time factor have been previously studied. Arrival time represents how much time in advance a driver ha s arrived to his/her destination. For example, a driver may arrive 5 or 15 minutes early to a meeting, class, or flight. Taking into account the time that it would take hi m/her to find a parking space

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21 and walk to the final destination, the driver has to make the decision between parking close to the final destination (typically higher fares) or further away (lower fare). Therefore, in this thesis the arrival time fact or is studied to determine the impact of time arrival on drivers parking choice behavior. The other parking factor that studied in this research is parking pricing, which has received attention from transportation res earchers and economists. Many models have been developed to analyze how increasing park ing price affects spac e utilization, transit service, work trips and single-occupancy ve hicle (SOV). The hypothe sis is that arrival time and willingness to pay are highly correlated In other words, drivers are willing to pay higher fares when they have an urgency to reach their destinati on. This research will explore this hypothesis a nd will attempt to repres ent price elasticity.

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22 CHAPTER 3 PROBLEM STATEMENT 3.1 Introduction and Motivation The problem considered in this research is revenue management in a parking facility network consisting of multiple parking lots with different number of fare classes. The objective is to maximize revenue and to stimulate and di versify demand. The manager in a parking facility should deci de how many parking spaces to reserve for customers or organizations willing to pay highe r fares for spaces located closer to their destination. A parking reservation system will identify customers who book in advanced or individual early bookings who will receive a discounted fare for their early or extended booking. Therefore, the decision is to dete rmine how many parking spaces should be made available for early booking to ensure full u tilization of the parki ng lot, while at the same time attempting to secure as many full price parking spaces to ensure maximization of revenue. This is a complex problem because in most instances demand cannot be determined with certainty. Also, some cu stomers who book in advanced may not show up, and the duration of stay fo r those who arrive as planne d will vary; that is, some drivers will stay longer than others. The parking problem is one of matching a probabilistic and sometimes unknown demand to a set of finite resources in a manner which will optimize profits or utilization of parking facilities. Parking facilities e xperience peak and low demand periods. The main problem is that during peak periods it is impossible to find an available parking

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23 space which results in drivers entering the pa rking lot to search a space that is not available. Therefore, parking managers need tools to advice drivers that there are not available parking spaces. There are two ways to approach this problem. One is to present drivers with current information of the state of the parking fa cilities, which can be accomplished with the introduction of Parking Guidance Information Systems (PGI) that show drivers where they can or cannot find a parking space. This is an alternative currently in place; however, th ere are some problems with PG I signs because drivers tend to not follow the information pr ovided due to a lack of believe on the acc uracy of it. The other alternative is to stimula te and diversify the demand with the introduction of pricing strategies. Usually, parking facilities form a netw ork of resources with the objective of providing storage space for a final destination. For exam ple, a university parking network is formed with a large number of park ing lots and garages. Each parking lot has the objective of providing storage for cars for a specific building (final destination). The problem with this network is that certain park ing facilities are utilized more than others. According to the previous de finition of revenue management, this tool would allow managers to shift some of th e high demand for certain park ing facilities to other lower demand facilities. This can be done by setting different pri ce schemes. It would allow managers to control and shift the demand and it also provides a source of revenue. 3.2 Research Objectives The objectives of this research are as follows: To develop a general methodology wh ich extends revenue management techniques to the parking problem

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24 To study and model parking choice/behavio r in terms of parking prices, time to destination (walking time + driving tim e) and arrival time using stated preference data To explore and compare neural networks as an alternative to traditional forecasting models to predict parking demand To compare different revenue management models to optimally allocate parking spaces Specifically, the following questions will be answered in this thesis: Can revenue management techniques be applied to the parking problem? Can neural network be used to predict parking availability? Does neural network perform better than other traditional forecasting models? What factors affect drivers behavior? Is it arrival time, price, and/or time to destination (walking ti me + driving time) Will drivers pay higher rates when they ar e under a time constraint? That is, will drivers pay a higher fare for parking closer to their final destination because they might be late to their m eeting, class, flight, etc.? What is the price difference that would induce drivers to change their parking behavior? How many spaces should be made available initially at various price levels (or, alternatively, for a given allocation scheme what are the optimal pricing levels)? 3.3 Research Methodology As shown in Chapter 1, (Figure 2 Le vel 2), a general methodology is proposed to provide solutions to the parking problem. The revenue management process will be

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25 applied to the parking problem First, stated preference data will be used to study drivers choice/behavior. The data collected will be analy zed through logistic regression. Second, neural networks will be used to pred ict space availability us ing data provided by a major parking facility. The model will be co mpared with traditional forecasting models used in revenue management. Third, the pric e elasticity that induces drivers to change their choice or behavior will be determined. Finally, taking as an input the forecasting results obtained from the neural network and the price elasticity, parking spaces will be optimally allocated at different price levels to optimize facility utilization and increase revenue.

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26 CHAPTER 4 REVENUE MANAGEMENT APPLIED TO PARKING 4.1 Introduction Revenue Management originated with th e deregulation of the US airline industry in the late 1970s. The entrance of new air lines offering extremely low fares created a complex challenge for major airlines. Revenue Management was introduced as a competitive tool to respond to the new challenges. It allowed airlines to compete on all levels of the market without compromising or decreasing revenue s. In addition, it enabled companies to better match the su pply and demand by introducing pricing strategies. Today, revenue management has in creased in popularity and is used not only in the airline industry bu t in firms with constrained capac ity such as hotels, cruise lines, car rentals, railways, and hospitals. The application of a revenue manageme nt system is not appropriate for all industries. Businesses that have successf ully embraced revenue management have many or all of the following characteristics: Limited capacity or resources only a fixed amount of products/resources is available, and additional inventory cannot be added without a signi ficant capital investment. Variable Demand low demand and high demand times can be identified. Perishable Product/Service at certain point in tim e the product or service will become worthless and it can no longer be sold.

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27 Market segmentation some customers are willing to pay different prices for the same product or service. Advanced sales through reservation systems co mbined with other technologies, selling products or services in advance. The parking industry has some similarities with the airline and hotel industry where revenue management is mostly used. Table 2, compares each characteristic previously described in the co ntext of the airline, hotel, rental car, and the parking industry. Table 2: Revenue Management Characteristics and Examples Airline Hotels Car Rental Parking Limited Capacity Only a limited number of seats can be sold on each trip. There is a maximum number of rooms that could be rented per day. There is a maximum number of cars available at each location. A limited number of spaces can be utilized. Variable Demand: High season is from April to September and December to February. High demand (in Florida) is during the summer months and at the end of the year Demand for cars is variable over time. Typically an increase demand is observed over long weekends and holidays. Business areas have higher demands during week days. Commercial areas over the weekends. Perishable product Service After departure, empty seats can not be sold Hotel rooms have a daily opportunity to be sold After business hours, no more cars could be rented Spaces have daily opportunities to the used. Market Segmentation: Passengers with emergencies are willing to pay more for the same seat. Late night arrivals are willing to pay a higher price for a room. Emergency situations can force people to rent a car at any price A person who is late for a flight departure is willing to pay a higher fee to park closer to the gate. Advance sales Seats can be reserved at least one year in advance Most hotels allow rooms to be reserved one year in advance Cars could be reserved two months in advance With the right system, parking spaces could be reserved in advance for different periods

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28 Parking garages have a fixe d number of parking spaces to sell (limited capacity). Also, some cars may stay longer in a park ing space than others (variable demand). Spaces have daily opportunities to be sold (per ishable product). When traveling by air, a customer who is late for a flight may be will ing to pay more for a cl oser parking space or any available space easy to find (market se gmentation). Parking Reservation Systems are being implemented in the United States. This type of systems allows drivers to reserve a parking space in advance (advance sales). In 1998, the revenue management problem was identified by Chatwin (1998) as the ho ttest area of new research in traffic management. Evidently, the parking industry represents a potential area to apply revenue management techniques for improvement. Parking plays an important role in the tr affic system since all vehicles require a storage location when they are not being used to transport pa ssengers. Most major cities continually struggle with parking limitations, violations and cost. Parking facilities experience peak and low demand periods. Th e problem increases during peak periods when it becomes challenging to find an ava ilable parking on a particular parking lot location. One alternativ e to this problem is to stimul ate and diversify the demand with the introduction of pricing strategies. Pricing is an importa nt element that can be used to increase profits by better matching supply and demand. The use of pricing strategies to increase the profit of a limited supply of assets is a common practice of Revenue Management. The manager in a parking facility can use several revenue management concepts to stimulate and diversify the parking demand. For example:

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29 The parking manager can charge a lower pr ice for drivers willing to reserve their space far in advance and a higher price fo r drivers looking for a space at the last minute. The parking manager can also charge a lower price for drivers with long-term contracts and a higher price for customers looking for a space at the last minute. The parking manager can charge a highe r price during periods of high demand and lower prices during periods of low demand. All of these are strategies that can be used to stimulate and diversify the parking demand. However, before they are applie d, a sounded procedure must be developed. The following section presents a specific methodology designed to implement revenue management techniques into the parking problem. 4.2 Parking Revenue Management Process A necessary characteristic to implemen t revenue management is a reservation system. Following examples from the air line, restaurants and car rentals, more companies and cities are offering reservation systems that allow people to reserve parking spaces online or by cell phone. Some cities that are offering this service include Baltimore, Chicago, New York, Philadelphi a, Boston and San Francisco. Parking reservation systems are seen as a competitive tool for parking companies who want to provide a better service to their customers. However, there are two major problems with the system. First, the reservation system show s drivers the availability of parking spaces through sensors embedded in the parking faciliti es. The problem is that this information only shows the availability at a point in tim e; therefore, drivers can reserve a space only for that period of time. In other words, drivers are not able to reserve a parking

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30 space two or three days in advance because the information is unavailable. The second problem is that customers usually have to pa y more for the parking space if they reserve it in advance. Through revenue management these problems are addressed, and solutions to enhance parking reservation systems are developed. Figure 3 shows the parking revenue manage ment process that should be followed at the time of incorporating revenue manageme nt into parking reservation systems. Figure 3: Parking Revenue Management Process First, parking managers mu st identify market segments for the same parking spaces. In the case of parking, market segmentation can be described as follows. There are drivers who have an emergency to arrive at a final destination; therefore, they are willing to pay a higher cost for a space closer to their destination. On the other hand, some customers may not be concerned with clos eness to their final destination; they are in this case more concerned with the cost of parking. These driver s are willing to walk a longer distance for a lower parking price. To accomplish this, we developed a stated preference parking survey which is di scussed in detail in Chapter 5. After the market has been segmented, th e next step is to predict customers demand (for every market segment) and space availability. In th e case of the airline industry, airlines need to forecast only the de mand of customer for different price fares. Since the capacity of an airplane varies from full and empty after a trip, airlines do not need to forecast the seat availability. On the other hand, hotels need not only to

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31 forecast demand for different customer segmen ts, but also room availability. It is necessary to forecast room availability because one customer may stay in a room for one day or for three, four, five days. This is very similar in the case of parking where some spaces may be occupied for minutes while othe rs may be occupied for hours. Therefore, for parking systems it is necessary to forecast customers demand and space availability. Traditionally, companies that have impl emented revenue management use several forecasting models to predict customer dema nd. These companies usually do not share their forecasting models for obvious reasons. However, it is known that the most popular models used in practice are linear regr ession, moving average, and exponential smoothing. All these models can be used to predict drivers demand and space availability. In this thesis we explored these models and several others and test which one is better and if any outperforms the othe rs for the parking scenario. Moreover, we explored neural network as a tool to predict drivers demand and space availability. In Chapter 6, we discussed neural network and compared it with other traditional forecasting model. The forecasting model is the base of a successful revenue management model because this information will be latter used by managers/planners to implement an adequate pricing strategy. This is the th ird step of the parking revenue management process. Parking managers/planners must decide how many spaces to reserve for full paying customers, and how many spaces to reserve at a discount. This can be seen as an inventory control problem. In Chapter 7, we present a model that addresses the space inventory problem.

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32 The last step in the implementation of the revenue management systems is to dynamically recalibrate the models. This m eans to monitor and control performance and update market response. It is necessary to constantly collect market data to update and recalibrate the forecasting and pricing models. 4.3 Revenue Management Literature Research on revenue management st arted in 1960s with the problem of overbooking. After airlines adopted the policy that a customer can cancel a ticket at any time without penalty, airlines were faced with the problem of overbooking and bumping. Researchers have studied the revenue ma nagement problem using a variety of approaches. The important elements of the revenue management problem that have been investigated are: seat inventory contro l, demand forecasting, overbooking and pricing. 4.3.1 Seat Inventory Control The objective of seat inventory control models is to optimally allocate seat inventory to passenger demand before the flig ht departs. The objective is to find the optimal number of seats that should be sold to each passenger segment. This will create a booking control policy that determines if a passenger request should be accepted or rejected at different periods of time before the flight departs. This problem has been studied as a singl e leg seat inventory control problem and as a network seat inventory control problem. In the single leg s eat inventory control problem every flight is optim ized separately. The booking policy for each flight is determined and optimized indepe ndently of all other flights. There are two categories of single leg solution methods: stat ic and dynamic solution methods.

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33 Static solution optimizes the seat inve ntory taking into acc ount static data. Littlewood (1972) introduced th e idea of marginal revenue. The objective is to equate the marginal revenue in each of the two fare classes. The idea is to not accept a low fare request when the expected revenue of selling th e same seat at the higher fare is high. This is model is known as Littlewoods ru le. In 1987, Belobaba extended Littlewoods rule to multiple nested fare classes and introduces the term expected marginal seat revenue (EMSR). The main disadvantage of th is method is that it do es not yield optimal booking limits when more than two fare cla sses are considered. To overcome this difficulties, Curry (1990), Brumelle and McGill (1993) and Wollmer (1992) introduced optimal policies for more than two classes. Dynamic solution methods for the seat inventory control problem monitor the state of the booking process over time and deci de to accept or reject a request based on the state of the system at that point in time. Some of the methods used to solve this problem include: discrete-time dynamic pr ogramming model -where demand for each fare class is modeled by a no homogeneous Po isson process, and dynamic and stochastic knapsack problem. In network seat inventory c ontrol, the complete networ k of flights offered by the airline is optimized simultaneou sly. One way to do this is to distribute the revenue of an origin-destination itinerary control to the individual legs. Williamson (1992) investigates different prorating strategies, such as prorating based on mil eage and on the ratio of the local fare levels.

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34 4.3.2 Demand Forecasting Demand forecasting is of critical impor tance in revenue management because booking control policies make use of demand fo recasts to determine the optimal booking control strategy which performs badly. Beckmann and Bobkowski (1958) compare diffe rent distributions to fit passenger arrival data (demand distribu tions). The authors compar e Poisson, Negative Binomial, and Gamma distributions. Results show th at the Gamma distribution is a good fit for passenger arrival data. Lyle (1970) models passenger demand distributions as composed of a Gamma systematic component with Poi sson random errors which leads to a negative binomial distribution. Other studies such as Shlifer and Vardi (1975) and Belobaba (1987) reveal that the normal distributi on is a good approximation for passenger demand distributions. The arrival process of individual booking re quest has been studied as a Poisson process. However, demand has also been st udied using historical data. Taneja (1978) described the use of traditional regression t echniques for aggregate airline forecasting. Furthermore, Sa (1987) used regression techniques and concl uded that regression techniques outperform traditional time series models or historical averages. McGill (1995) developed a multivariate multiple regres sion to test the correlation in multiple booking classes. Several researchers have al so used simple smoothing techniques as a forecasting tool. Other researchers such as Ben-Akiva ( 1987) have opted for forecasting demand using discrete choice behavior models wh ich are typically model through logistic regression.

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35 4.3.3 Overbooking Airlines have to deal with no-shows, cancellati ons, and denied boarding. Therefore, in order to prevent a flight from taking off with vacant seats, airlines tend to overbook a flight. The objective is to find the optimal level of seats that should be sold over the capacity of th e flight. Therefore, overbooking a flight reduces the probability that a seat will depart empty; however, it cr eates a risk of having more passengers than available seats. Overbooking is the olde st and most successful of the revenue management techniques. It has been estimated that in the airline industry 50 percent of reservations result in can cellations and no-shows and 15 percent of all seats will go unsold without some form of overbooking (Talluri and Van Ryzin, 2004 pp. 130). The overbooking problem has been studied from two approaches: sta tic overbooking models and dynamic overbooking models. Static over booking models do not take into account the dynamics of customer reservation and ca ncellation requests ov er time. The model find the optimal number of seats to overbook taken as an input the estimates from the current time until the day of departure. These optimization models were studied by Beckman (1958), Thompson (1961), and Tayl or (1962). These models find the maximum number of seats to overbook for one fare class. Shlifer and Vardi (1975) extended the models to allow two fa re classes and a two-leg flight. The dynamic overbooking models take in to account the dynami cs of customer reservations and can cellations over time. Rothst ein (1968) presented a dynamic programming model for the overbooking prob lem. Alstrup et al. (1986) showed a dynamic programming model for two fare classes.

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36 4.3.4 Pricing Pricing strategies are used in revenue management as a mechanism to respond to market demand. The objective of pricing mode ls is to find the optimal combination of price adjustments to maximize revenue. Econo mists have long advocated that pricing is an effective strategy for stra tegic and marketing decisions. Dana (1996) concluded that firms who offer products at di fferent prices and control th e capacity for the low prices, are in a unique competitive equilibrium. Gallego (1996) proposed a deterministic model to study pricing and market segmentation. The model is able to capture demand dispersion and demand recapture. Watherford (1994) presented a model that assumes normally distributed demands. The mean de mand is modeled as a linear function of price.

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37 CHAPTER 5 MARKET SEGMENTATION 5.1 Introduction The goals of market segmentation are to understand how customers are buying, what they value, and how much are they wi lling to pay (Talluri and Van Ryzin, 2004). To differentiate between the various segmen ts, the firm must define a set of product attributes or customer characteristics for a given segment. For ex ample, in the airline industry businesses travelers are willing to pay higher rates for a seat than leisure travelers. Businesses travelers would pay high er fares for a flight that matches his/her schedule. On the other hand, leisure travelers would vary their schedule for a lower fare. Some examples of market segments in the airline industry include business, leisure, students, children, youth, seniors, and military. Market segmentation can also be applied to the parking industry. The question is if there are different customer segments in parking, and if true, how to differentiate among them. To answer these questions, we would use an explicit screening mechanism based on observable characteristics. In othe r words, we would study drivers behavior and then we will classify them according to the observed type. Figure 4 shows some common segments bases for the parking industry.

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38 Demographics Time of Purchase Length of Stay Time of the Day Day of the Week Parking Space Figure 4: Parking Market Segments A brief explanation of each one of these segments follows. Demographics(age-based, gender-based, etc). For example, younger people may have less income; therefore, they are willing to pay less Time of purchasedrivers who reserve or buy a space in advance want to pay less. On the other hand, drivers who do not rese rve in advance and just show up into the parking lot are willing to pay higher fare. Day of the weekparking lots have peak demand during certain days of the week. For example, a parking lot at the airport would have peak on Mondays and lower demand on Saturday, Time of the dayparking lots also have peak de mand during certain hours of the day. For example, in a university parki ng lot demand would be low during early morning hours (5am-7am); however, de mand would be at a peak during the middle of the morning (10am-1pm). Then, demand would decrease in the afternoon hours.

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39 Length of staysome drivers may use a parking space for a few minutes while others may use the parking space for hours. Each one of these segments represents an opportunity for manager/planners to apply different pricing strategies for each segment. We conducted a stated preference surv ey to study drivers behavior. The objective of the survey is to identify different segments in the parking industry. Latter, we would apply different pric ing strategies that would al low us to maximize parking revenue and control parking demand. The next section describes in detail the survey and its results. 5.2 Stated Preference versus Revealed Preference Survey Previous parking demand modeling appr oaches have considered how parking demand (drivers) would react to changes in the availability or location of the parking facilities. Impact would be reflected on the day/time to do the trip or even changing destination or discarding the trip due to pa rking concerns. These models are typically formulated as mode choice. Traditional mode choice models study how drivers respond to changes in the supply and operation of parkin g facilities. These re sponses are typically studied using logit models. Logit models study how drivers made choices among a finite set of alternatives based on stated (hypothe tical scenarios) and revealed preference (actual data) data. Figure 5 is an illustration that compares a stated preference survey versus a revealed preference survey.

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40 HOME FACTORY CAR Price: $5 Time: 15 min BUS Price: $1 Time: 30 minREVEALED PREFERENCE SURVEY STATED PREFERENCE SURVEY HOME CAR Price: $5 Time: 15 min BUS Price: $1 Time: 30 min FACTORYRAPID TRAIN Price: $8 Time: 10 min Figure 5: Stated Preference versus Revealed Preference Survey In the revealed preference survey, the pa rticipant would have to choose (or reveal) the option that he/she currently uses to comm ute to work. In the stated preference, the participant would have to choos e among three alternatives (the rapid train is not currently working). The objective of this survey is to study the impact of the introduction of a rapid train into the current transportation network and to forecast its utilization. Stated preference surveys are used to de velop choice models and to estimate the impact of each factor (i.e. car-bus-rapid trai n, price, and time). The advantage of stated preference surveys over revealed preference is that they are extremely useful to study the impact of new options into the actual market The other advantage of stated preference surveys is that the research ers can control the factors under study. Th e disadvantage of

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41 stated preference surveys is that responde nts can answer one way under a hypothetical situation and respond another way under the real situation. It is necessary to take this into account at the time of producing conclusi ons that may overestimate the response of individuals. 5.3 Stated Preference Parking Survey A stated preference survey was conducted in this thesis to identify how drivers will react to changes on prices and which park ing facility would be selected for various set of scenarios and circumstances. The results will help us to differentiate among different segments in the pa rking industry. The data co llected from the survey is analyzed through logistic regression. Fifty one subjects were surv eyed in a pencil-and paper survey. Table 3 shows the demographics from the subjects interviewed. Table 3: Stated Preference Survey Demographics Demographics Subjects Percentage Male 33 65% Gender Female 18 35% Less than 20 0 0% 20-29 48 94% 30-39 1 2% 40-49 1 2% 50-59 1 2% Age 60 or older 0 0% Full-time 39 76% Employed Part-time 12 24% $15,000 49 96% $20,000 0 0% $30,000 1 2% $40,000 0 0% $50,000 0 0% $60,000 0 0% Income $70,000 1 2% Pay more for YES 40 78% reserved space NO 11 22% Reserve space YES 35 69% in advance NO 16 31%

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42 5.3.1 Stimulus Material Subjects were presented with twelve pa rking scenarios that were arranged in random order (Appendix A). Each of the pa rking scenarios consists of two parking facilities labeled Lot A and Lot B, and a final destination. Below each parking lot, the time that will take to reach the destination fr om the parking lot selected and the price for the parking lot were presented. Furthermore, a sign indicated how early subjects are from a meeting/class or activity. Drivers would choose either Lot A or Lot B taking into account all the factors presented (arrival time, price, and time to destination). The arrival time and price were the only factors that ch anged among scenarios. Subjects were also asked a set of questions that would help us to identify each subject according to age, gender, and income. 5.3.2 Survey Design Of the twelve parking scen arios, six present drivers the constraint that if they choose Lot B they may be late to their meeti ng/class or activity. The objective is to study if drivers are willing to pay more under this time constraint. The other six parking scenarios present drivers the opt ion of choosing Lot A or B without a time constraint. If they choose either Lot A or B, they would be on time to th eir meeting/class/activity. The objective in these scenarios is to measure if drivers are more concerned about time to destination or cost. Also, we would like to measure what is the price difference that induces drivers to change their parking be havior. For example, a subject who is presented the option of choosing Lot A ($10) versus Lot B ($5) (or 100% increase in price) may choose Lot B (the lower fare). Ho wever, as the price difference decreases Lot

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43 A ($6) versus Lot B ($5) (or 20% increase in price) the subject may be willing to choose Lot A ($6) because the price difference is not that high. Subjects were asked to choose a parking lot where they will park by considering the time to destination, price a nd arrival time. The time to destination indicates the time that will take the subject to reach the final destination from the parking lot selected. The time to destination is the walking time (from th e parking lot to the destination) plus the driving time (from the start sign to the parki ng lot). Traditionally, these factors, walking time and driving time, are st udied separately. Origina lly, the survey was designed considering these factors separa tely; however, when we presented the survey to subject, it was noted that drivers would add the time of each factor and combine them into a single time. This tendency occurred because the first factor that drivers ta ke into account is the arrival time. Their next decision would be ba sed on this factor. In other words, subjects choose the parking lot of their preference based on the possibili ty of being late and based on the price. Therefore, the walking time and driving time were combined into a single factor (Time to Destination). This makes it eas ier for subject to fill the survey since they do not have to make the calculations to de termine if they would be late to their meeting/class or activity. Price refers to the cost that drivers will have to pay if they choose either parking lot. Arrival time indicates how ea rly drivers are from their meeting/class or activity. Table 4 shows the twelve scenarios presented to the subjects.

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44 Table 4: Parking Survey Scenarios SCENARIO FACTORS LOT A LOT B 1 Time to Destination 10 min 5 min Cost $5 $10 Arrival Time 15 min early 15 min early 2 Time to Destination 10 min 5 min Cost $5 $9 Arrival Time 15 min early 15 min early 3 Time to Destination 10 min 5 min Cost $5 $8 Arrival Time 15 min early 15 min early 4 Time to Destination 10 min 5 min Cost $5 $7 Arrival Time 15 min early 15 min early 5 Time to Destination 10 min 5 min Cost $5 $6 Arrival Time 15 min early 15 min early 6 Time to Destination 10 min 5 min Cost $5 $5 Arrival Time 15 min early 15 min early 7 Time to Destination 10 min 5 min Cost $5 $10 Arrival Time 5 min early 5 min early 8 Time to Destination 10 min 5 min Cost $5 $9 Arrival Time 5 min early 5 min early 9 Time to Destination 10 min 5 min Cost $5 $8 Arrival Time 5 min early 5 min early 10 Time to Destination 10 min 5 min Cost $5 $7 Arrival Time 5 min early 5 min early 11 Time to Destination 10 min 5 min Cost $5 $6 Arrival Time 5 min early 5 min early 12 Time to Destination 10 min 5 min Cost $5 $5 Arrival Time 5 min early 5 min early It is important to note that this is no t a full experimental design. The reason is that a full experimental design will include a total of 36 scenarios. Twenty four of the possible combinations were discarded because they did not contribute with new data.

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45 They were basically a repetition of the 12 scen arios considered. Furthermore, thirty six scenarios may fatigue subject; therefore, this may induce to unrealistic answers. 5.3.3 Survey Procedure Subjects were asked to choose which parkin g lot they would pr efer by taking into account all the factors presente d (arrival time, time to destination, and price). A brief summary of the scope of the project and the instructions were given to the subjects (Appendix A). The instructi ons provided the subjects w ith enough information to calculate if they would be early or late to their meeting/class/activity when they choose either Lot A or B. For example in Figure 6, the sign shows that the subject has arrived 15 minutes early. Then, the subject would compare parking Lot A versus Lot B in terms of price and time to destination. In this example, if the subject parks in Lot A, he/she would arrive 5 minutes early to his/her destination. The cost of this selection is $5. DESTINATION START ARRIVED 15 minutes EARLY TIME TO DESTINATION = 10 min PRICE = $ 5 LOT A LOT B TIME TO DESTINATION = 5 min PRICE = $ 10 Figure 6: Parking Survey Example

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46 If the subject chooses parking lot B, he/she would 10 minutes early to his/her destination but the parking co st would be $10. Some subject s may be concerned with the price factor while other may be concerned with the time that they would spend walking. 5.3.4 Results The raw data collected on each subject for each scenario in the survey is attached as a table in Appendix B. In the table, the leftmost column contains the scenario numbers. Each of the other columns contains the letters of the lots chosen by one subject for each of the scenarios. The results for each scenario are summarized in Appendix C, which indicates the number of subjects who choose between minimum time to destination or Lot B (MTTD) or minimum cost or Lot A (MC). The survey was analyzed in the following manner. For the first six scenario s (subject will always be early to their destination), the number of times a subject c hoose either lot A or lot B were counted. If a driver chooses lot A, this indi cates that the driver is choos ing to minimize cost. On the other hand, a driver who chooses lot B indicate s that he/she is choosing to minimize the time to destination. Therefore, the rightmost column in Appendix B indicates the number of times a driver chooses either to mini mize time to destination (MTTD) or minimum cost (MC). For the other six scenarios (subject might be late to their destination if they choose lot A) the same procedure was followe d. The difference is that those subjects who choose lot A will be late to their destinatio n; therefore, they prefer to minimize cost even jeopardizing timeliness. Figure 7 shows the results of the survey.

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47 MTTD MC On Time Late 0% 20% 40% 60% 80% 100%Stated Preference Survey Results On Time Late Figure 7: Stated Preference Survey Results On the first six scenarios (on-time) 29% choose to minimize their time to destination (Lot B) and 71% of the subjects choose the parking lot with the minimum cost (Lot A). On the other six scenarios (l ate) 84% of the subjects choose the parking lot that will minimize their time to destination; th erefore, arrive to th eir meeting, class, etc on time and 16% would rather pay less. Figure 8 shows the responses of subjects when time was not a constraint. Scenario 1, 2, and 3 repres ent a 100%, 80%, and 60% pri ce difference. For these percentages most drivers choose the parking facility with the minimum cost (MC). However, scenario 4, which represents a 40 percent difference in price between the two facilities, shows a more balanced response from the subjects. That is, 55% of the subjects select the facility with the minimum cost while 45% the facility closest to the destination (higher cost). The same results can be seen on scenario 5 which represents a 20% price difference. Drivers are willing to pay for th e closest parking facility and as a result a higher cost. For this scenari o, 31% choose the facility with the minimum cost while 70% selected the facility closest to th e destination (highest cost).

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48 On Time0 10 20 30 40 50 60 # MTTD#MC Decision Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 $10 $9 $8 $7 $6 $5 $5 $5 $5 $5Subjects Figure 8: Stated Preference Survey ResultsOn Time These results are helpful for strategic purposes. For example, a parking manager has two parking facilities; one of the facili ties has 100% utilizati on while the other has only 50% utilization. Currently, both parking lo ts charge the same fare. However, the parking manager can implement a 40% difference in prices to balanc e the utilization for both facilities. This will not only increa se revenue but it will improve customer satisfaction and retention. On the other hand, if the objective is to divert drivers from one facility to another, a 100% or 80% differe nce in prices could accomplish this. Figure 9 shows the results from the survey when time was a constraint. The results indicate that drivers are willing to pay higher fares when they are under a time constraint since in all scen arios they choose the minimum time to destination (MTTD) while only a few choose the facility with the minimum cost (MC).

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49 Late0 10 20 30 40 50 60 # MTTD#MC Decision Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 $10 $9 $8 $7 $6 $5Subjects Figure 9: Stated Preference Survey Results-Late The results of the survey help to determine the parking demand. Figure 10 shows the parking demand for the closest parking lot to the destination when time is not a constraint. It is easy to se e how demand decreases as price increases. This means that drivers are willing to park further away to th e destination when they will not be late. Demand Curve for Closest Parking Lot-Early0 10 20 30 40 50 60 5678910 Price Demand Figure 10: Demand Curve for Closest Parking Lot-Early On the other hand, Figure 11 shows the parking demand for the closest parking lot to the destination when time is a constraint. The results show that drivers are willing to pay higher fares when they are under a time c onstraint. The demand curve appears to be more constant, and it does not decrease dramatically.

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50 Demand Curve for Closest Parking Lot-Late0 10 20 30 40 50 60 5678910 PriceDeman d Demand Figure 11: Demand Curve for Closest Parking Lot-Late The results of the survey will be analy zed in more detail in the next section through a logit model. 5.4 Logit Model In this thesis, the data collected on th e stated preference survey is used to construct a parking lot choice model. Th e model hypothesizes that parking choices depend upon arrival time, parking price, age, gender, and income. The sample data consists of choices from 51 subjects who co ntributed 612 data points or choices (51 subjects times 12 parking scenarios). The park ing literature states that factors such as walking distance, driving distance, parking type and parking pric e influence parking choice. However, to our knowledge the arriva l time factor has not been studied in the literature. This study allows us to prove that drivers are willing to pay higher fares when they are under a time constraint. The traditional methodology used by resear chers to study parking choice has been through logistic regression or l ogit models. This type of m odel is appropriate when the responses take on only two possible values repr esenting success and failure (binary data). In other words, logistic regression estimates the probability of a certain event occurring or, in our case, the probability that a driver s chooses between a two parking alternatives

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51 depending on different factors. Generally, the dependant va riable can take on only two responses such as presence/absence or succe ss/failure. The logistic regression does not make any assumption about the distribution of the independent variables. However, it assumes a binomial distribution for the errors. The logistic regression can be seen as a liner regres sion model such as ip i k k ix x, 1 1... where pi is the probability of event i to success or fail, xi is the independent variable for event i, and is a vector of regression coefficients. The problem with this model is that the probability pi can take only take values between zero and one, but the linear term k i kx can take any real value; therefore, there is not guarantee that the predicted values will be in the correct range. To avoid this problem a simple transformation on the probability to remove the range restrictions is performe d, and model the transformation as a linear function of the covariates. This transformation is a ccomplished by moving from the probability pi to the odds where i i ip p odds 1 It is important to note that there is no diff erence between working in probabilities or odds since they are both equivalent. However, the main advantage is that odds can take on any positive value; therefore, they have not ceiling restrictions. The next step is to eliminate the floor re strictions by calculating the logit or logodds logit ( pi) = i ip p 1 log

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52 Suppose that the logit of the probability pi is a linear function of the predictors logit ( pi) = i k k ix x, 1 1... where xi is a vector of covariates and is a vector of regression coefficients. The model is a generalized linear model with binomial response a nd link logit. By exponentiating the model logit ( pi) = i k k ix x, 1 1... it takes the form i k k i i k k ix x x x ie e p, 1 1 , 1 1... ...1 where pi is the probability of choosing parking lot i. The parameters k ,..., ,1are estimated by maximizing the log-likelihood function log L ( ) 1 log( ) ( ) log( )i i i i ip y n p y This procedure helps us to test coeffi cients for significan ce. The logistic regression is almost identical to a linear re gression. The main advantage of logistic regression is that the logit transformation of the probabi lities to odds allows to limit the dependent variable to be a 0/1 or success/fail ure response. The next section will illustrate the application of these concepts to st udy the relationship betw een the independent variables (gender, income, arri val time, and price) versus th e dependant variable (parking lot choice). 5.4.1 Logit Model Results The logistic regression m odel described in the previ ous section was applied to study the relationship among the variables gend er, age, income, arrival time and price with the selection of a parking facility. The objective is to find what factors influence drivers behavior at the time of selection among a set of parking alternatives. Most

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53 importantly, it is important to demonstrate that the arrival time factor is significant on the selection process. Table 5 presents the results of the logit model implemented in R2.3.1. The results show the probability of selecting th e parking lot with the lo west price (Lot B). The results show that gender, arrival time, and price are signif icant at the time of selecting a parking lot. It is important to note that the age and income factor are not significant. However, these factors are no t significant because the majority of the participants have the same age and income. Table 5: Logit Model Results Coefficients Estimate Std. Error z value Pr(>|z|) Intercept 1.13E+011.49E+007.583.46E-14 *** Gender -8.44E-013.17E-01-2.6660.00768 ** Age 5.61E-024.92E-021.1390.25463 Income -2.52E-051.84E-05-1.3730.16972 Arrival Time -3.14E-013.55E-02-8.819<2e-16 *** Price -9.81E-011.11E-01-8.846<2e-16 *** Significant Codes 0 '***' 0.001 '**' 0.01 '*' Null Deviance 533.33 Residual Deviance 314.72 The estimated values show that choice is relatively inelastic with respect to distance and more elastic with respect to pr ice. Furthermore, the significant negative coefficient of arrival time in Table 4 indicates that when the arrival time is small; drivers choose the parking lot closer to the destination. This he lps to support the previous statement that drivers are willing to pay hi gher parking rates when they are under a time constraint.

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54 CHAPTER 6 PARKING DEMAND FORECASTING MODELS 6.1 Introduction Accurate forecasts are extremely important to estimate quantities such as demand, price sensitivity, and number of bookings in a particular market and for a particular type of passenger. If the demand for each type of customer was known with certainty, the problem of optimally allocati ng capacity would be easy to solve. However, demands for each type of customer are never known with certa inty. Historical data would help us to estimate future demand. The performance of the revenue management system depends significantly on the accuracy of the forecast of future demand. Parking managers/planners need to be aware that forecasts are not always accurate; therefore, it is important to estimat e not only the expected value of the forecast, but also a measure of the forecast error. Fu rthermore, short-term and aggregate forecasts are usually more accurate than long-term and disaggregate forecasts. There are two different approaches for aggregating fo recasting: top-down and bottom-up. In the top-down approach the total number of customer who will use the service/product is predicted a nd this number is divided into the demand for different parts of the facility. For example, a hotel may estimate the total number of customer who will book in a particular day and classify them into different segments, and estimate length of stay and type of room to be used.

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55 The bottom-up approach is performed at a more detailed level. The end forecast is assembled by aggregating these de tailed forecasts. This approach takes the lowest level unit and predicts the demand for it. For example, a hotel may predict the demand for a particular room. Then, it w ill aggregate the forecast of all rooms to construct the end forecast (t otal demand of customers). The most appropriate strategy usually depends on the type of data available or the type of outcome desired. There is a risk on both approaches of losing accuracy; however, the degr ee of accuracy tends to be better when using the top-down approach. The forecasts can be estimated using qualitative or quantitative methods. Qualitative methods rely on expert opinion. This approach is useful when the data available is limited or when the experts have a critical knowledge of the market that is essential for the accuracy of the forecast. Quantitative methods can be based on the assumption that historical trends will conti nue on the future (i.e. Time Series methods: Moving Average, Simple Exponential Smoothing, Holts Model, Winters Model, etc), or causal models which assume that the demand fo recast is correlated with certain factors in the environment (i.e. Linear Regression, Non-Li near Regression, Neural Networks, etc). Predicting parking demand is a very comp lex task since it can be influenced by many factors. The relation among these factors is often non-lin ear which provides a challenging task for computational purpos es. Previous park ing demand modeling approaches have considered how parking demand (drivers) w ould react to changes in the availability or location of th e parking facilities. Impact would be reflected on the day/time to do the trip or even changing des tination or discarding the trip due to parking concerns. In Young, Thompson, and Taylor (1991) a comprehensive review of parking

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56 models is presented; however, most of the models discussed have found limited application by only adding an understanding of the traffic system, parking system and the interaction between them. That is, previous approaches have st udied parking demand trying to answer how drivers search for a parking space and how they will react to different parking scenarios, but they stop short when presenti ng an applicable solution to the specific cases. It is important to note that there are differences on the forecasting needs between the parking industry and other i ndustries such as airline and ho tel. In the airline and the hotel industry there is a broad range of forecasting requirements. For example, the airline industry requires forecasts for customer de mand; the way reservations for different customer types arrive during the booking period, and cancellation and no-show probabilities. In the case of the hotel indus try, forecasts requirements include the total number of guests who will book to arrive on each day in each rate category, the length of time that the customer will stay in the hotel, and room occupancy. The forecast requirements for the parking industry are closer related to those in the hotel industry. For example, the parking manager/planner needs to predict the total number of drivers who will reserve a parking space for each hour and for each rate. Also, it is necessary to predict parking lot occupancy. The objective of this chapter is to ev aluate different quantitative methods and select the best technique to forecast pa rking demand and parking space occupancy. Traditional forecasting method including moving average, simple exponential smoothing, Holts model, and Winters model are comp ared against a non-trad itional forecasting technique: neural networks. The next secti ons provide an introduction to the theory and

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57 mathematics of the models utilized followed by an evaluation of the models in terms of their performance using parking demand data ob tained from a major airport. The quality of forecasting results is measured through the mean square error, mean absolute error, mean absolute percentage error, and root mean square error. 6.2 Time Series Forecasting Methods Time series forecasting methods assume that historical data is a good indicator of future demand. These models are typically used in revenue management because they are easy to understand, simple to code, pe rform well, and maintenance is relatively simple. Before proceeding to the theory of the models, it is important to define the following terminology. LevelIt is the typical or average demand TrendIt is a decrease or increase in the data values over time Seasonality-It is a repeating pattern in the data values over time (i.e. day of the week, hour of the day, month of the year, etc) 6.2.1 Moving Average The moving average method is based on a we ighted average of past values. It represents the average of the N most recent data points. The following is the moving average formula: N D D D FN t t t t) .... (1 1 The forecast for the period 1 tand for the kperiod are given by: N D D D FN t t t t) .... (2 1 1

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58 K k F Ft k t,...., 2 ,1 tF number of empty spaces predicted for period t tD actual demand of empty spaces for period t N number of periods averaged The moving average method is simple and fast. The fundamental idea is that the most recent observations are better predictors than older observations. As seen in the formula above, the idea is to drop the oldest observation and add the latest. The number of periods averaged Nhas to be determined by the analyst. It is important to note that the smaller value given to N represents a more responsive forecast. However, a value that is too small might result in a more vol atile forecast. In ge neral, the value of N ranges from 3 to 15, but this value depends on the characteristics of the data. It is recommended to use the mo ving average method when demand has no observable trend or seasonality. The moving average is not adequate when the data exhibits upward and downward trend because it might under or ove r forecast (Chopra and Meindl, 2004). 6.2.2 Simple Exponential Smoothing Simple exponential smoothing is very similar to the moving average. It estimates future forecasts based on a weighted averag e of past observations of demand. This technique weights recent observations more heavily than older observations. The exponential smoothing formula for period 1 is given by: n t tD n F1 11

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59 The one step ahead exponentially smoothed forecast is given by: t t tF D F ) 1 (1 1FForecast for period 1 (average of all demand periods) 1tF One step ahead forecasted demand tD Actual demand of empty spaces for period t Smoothing constant for the level (1 0 ) The value of has to be determined before starting the forecast. A high value of represent more weight assigned to more r ecent observations; therefore, the model is more responsive to change, but it is also more susceptible to noise. In contrast, a small value of represents a smoother forecast; therefore, the model represents a more stable forecast, but it is less responsive to change. The exponential smoothing method is appropriate when demand has no observable trend or seasonality (Chopra and Meindl, 2004). 6.2.3 Holts Model The Holts model is also known as Trend Corrected Exponential Smoothing. It is appropriate when demand presents either upward or downward trends (Chopra and Meindl, 2004). To account for these trends, Holts model decomposes the systematic component of demand into a level and a tre nd when making the forecast. To find the initial level 0L and initial trend0T it is necessary to run a linear regression between demandtD and time period t of the form b at Dt where 0L = b and 0T = a. The forecast for period 1 tand k t is given by: t t k t t t tkT L F and T L F 1

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60 Before using the formula to find the forecast for period k t it is necessary to revise the level and trend by using the following formulas: ) )( 1 (1 1t t t tT L D L t t t tT L L T ) 1 ( ) (1 1 Smoothing constant for the level (1 0 ) Smoothing constant for the trend ) 1 0 ( 6.2.4 Winters Model Winters model, also known as Tre nd and Seasonality Corrected Exponential Smoothing, is appropriate to forecast data se ries that exhibit seas onality (i.e. hourly, daily, monthly, etc), level, and tr end (Chopra and Mein dl, 2004). Assume p represents the periodicity of the demand. The periodic ity represents the number of periods after which the seasons repeat. For example, if the seasonality is by month, 12 p or by hour, 24 p. The first step is to determine the estimates of the initial level0L initial trend0T and seasonal factors ) ,..., (1 pS S To obtain these values, it is necessary to deseasonalize the demand data which represent the demand without seas onal fluctuations. The next step is to run a linear regression of the form kT L Dk where kD represents the deseasonalized demand. After the initial le vel and trend has b een found, then the seasonal factor (Sk) can be calculated by: k k kD D S The forecast for period k t and t 1is given by: 1 1) ( t t t tS T L F k t t t k tS kT L F ) (

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61 and the level, trend and seasonality are updated as follows: ) )( 1 (1 1 1 t t t t tT L S D L t t t tT L L T ) 1 ( ) (1 1 1 1 1 1) 1 ( t t t p sS L D S Smoothing constant for the level (1 0 ) Smoothing constant for the trend ) 1 0 ( Smoothing constant for the seasonal factor ) 1 0 ( 6.3 Causal Models Causal models assume that the demand fo recast is correlated with certain factors in the environment. This makes them app licable to model park ing problems since the relationship among different factor s is often non-linear. In this section, neural networks would be introduced, and parking demand woul d be predicted using this model. 6.3.1 Introduction to Neural Networks Neural network is an e ffective tool at trend pred iction, pattern recognition, modeling, control, signals filtering, noise reduction, image analysis, classification, and evaluation (Landau and Taylor, 1998). The neural networks are quantitative models that link together inputs and outputs adaptively in a learning process similar to that used by the human brain (Abdi, Valentin, and Edelma n, 1999). The human brain consists of hundreds of billions of neurons which are connected together in a complex form. Neurons send information back and forth to each other through a seri es of connections.

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62 Neurons and connections are refe rred as a network. This ne twork can perform intelligent functions such as learning, anal ysis, prediction, and recognition. Neural networks consist of an input layer, an output la yer and one or more hidden layer as seen in Figure 12. The nodes or neurons of the network are arranged in consecutive layers (hidden laye rs) and the arcs are directed from one layer to the next from left to right. Figure 12: Neural Network Model This type of neural networks is calle d feed-forward networks or perceptrons. Basically, neural networks ar e built from simple units (neurons). These neurons are interlinked by a set of weighted connections (w). Each node or neuron is a processing unit that contains a weight and a summation function. A we ight returns a mathematical value for the relative strength of connections to transfer data from one layer to the next. On the other hand, a summation function ycomputes the weighted sum of all input

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63 elements entering a neuron. In Figure 12, each neuron in the hidden layer computes the summation jy using the following formula: 2 13 2 1i ij i jj w x y Furthermore, a sigmoid function Tyis used to transform the output so that it falls into an acceptable range (between 0 and 1). The objective is to prevent the output from being too large. The sigmoid f unction is of the following form: y Te y 1 1 As previously described, neural networks consist of neurons or nodes organized in different layers: input, hidden, and output. The input layer co rresponds to the factors that would be feed into th e network. The information is propagated through the weighted connections to the hidden layers where it is an alyzed. Then, the result of this processing is propagated to the next layer and eventually, to the output layer. The output is obtained by the following function: 3 1j kj jw y Y 6.3.1.1 Training After the network architecture has been de fined, the next step is to train the network. A training data set is feed forward into the network to calibrate the weights and values of the threshold functi ons. In the forward pass the output are calculated as well as the errors of the output compared to the or iginal values. After the forward pass, the errors of the output are back propagated and the weights are altered. This is called training the network. The goal of the netw ork is to learn some relationship between

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64 input and output patterns. This learning pro cess is achieved through the modifications of the connection weights between neurons. There are several learning algorithms that are commonly used such as the Widrow-Hoff Learning Rule, the Hebbian Learning Rule, and the backpropagation algorithm (Abdi, Valentin, and Edelman, 1999). The most popular algorithms used for training purposes is the latter, error back-propagation method. The backpropagation al gorithm objective is to mini mize the mean square error function: 2)] ( [i approx i ix F y E This error functions tells us how good an approximation to the real function F is. The idea of the backpropagation algorithm is to minimize this error (threshold) by adding for each training period, small changes in the di rections that minimize the error function. This minimization method is called the steep est descent method. The general learning process is described in the following steps: 1. Random numbers are assi gned to the weights 2. For all data points in the data set, calculate the output using the summation functions of each neuron as described in section 7.3.1 3. Compare estimated output with actual values 4. If the results from 3 do not meet a th reshold value, repeat steps 2 and 3. 6.3.1.2 Overfitting and Generalization During the last years, many researcher s have taken advantage of powerful and efficient computer systems. Neural Networ ks is one of the fiel ds that have taken advantage of such advancements in technology. Its applications have increased to

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65 numerous fields. For example, neural networ ks have been used by Air Canada for airport scheduling, reducing delays from flight re-sched uling, cutting fuel and other direct costs, and shortening the idle time of aircraft. Neur al networks have also been used for pattern recognition, classification, r econstruction, biology, comput er game playing and time series forecasting (Talluri and Van Ryzin, 2004). However, a common problem that may o ccur when fitting the neural network to training data is overfitting. Overfitting occurs when the error of the training set is minimized to a very small value. As a result, when new data is introduced into the network the error becomes very large. In this situation th e network has memorized the data set, and it is not able to generalize when new data is introduced into the network. Generalization refers to the ability of the m odel to perform well on data that has not been used to train the network. There are two strategies that can be us ed to avoid overfitti ng: regularization and early stopping. Regularization involves m odifying the performance function. Early stopping involves dividing the data set into two subsets. The first subset is the training set and the second subset is the validation set. At the beginning of the training process the error for the validation and testing sets tends to decrease; however, when the network starts to overfit the data both errors will increase. When the error for the validation set continues to increase for a specific number of iterations, then training is stopped. This research applies neur al network as a tool to predict parking demand. The traditional backpropagation algorithm is used as the learning method for our network and early stopping criteria is used to avoid overfit ting. The next section describes the neural network model developed for the prediction of parking demand.

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66 6.4 Parking Demand Predictor Model The objective of the predictor models is to give managers a useful insight by setting up a real time mechanism of clusteri ng the day patterns and predicting parking demand. Neural networks have proven to be an efficient tool to predict future states of a system given several relationships. Figure 13 shows an overvie w of the prediction model developed and the inputs that would be re quired. Many of these inputs have been obtained from data provided by a major airp ort in Florida. Th e data provided was analyzed using the neural network f unctions and tools provided in MatLab. Figure 13: Neural Network Parking Model

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67 The predictor model would be a helpful t ool for managers that must, on a daily basis, be able to recognize the conditions th at will prevail in the system to pick the appropriate strategy to implement. The de sign and implementation of such management plans requires the predictor m odel to have the following cap abilities: distinguish between long, medium and short stay parkers, classi fy typical and a-typical conditions (e.g., special events), and identify daily hourly, and monthly patterns. Time series data used for this study were collected at a major airport. The data obtained a four week period of demand for two parking facilities. The data obtained were studied using the layered neural network with a backpropagation least mean square error learning algorithm. To predict parking de mand, a neural network with 3 input nodes (month, day, and hour), a singl e output node (number of cars that would enter the parking facility), and a one-layer backpropagation ne twork has been used. There is no standard formula to calculate the num ber of nodes needed in the hidden layer (Wang and Sun, 1996). Basically, the number of hidden laye rs may be tested by trial and error. Figure 14 shows the graphical represen tation of the neural networ k used in this study. Figure 14: Neural Network Architecture The neural network developed is act ually a mapping function representing the relationship between the month, day, hour a nd number of cars that enter the parking garage. The output obtained from the neural network is used to predict the availability at different time frames. In the next sections the results from the study are presented and

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68 compared versus other traditional prediction techniques used to estimate demand. The comparison would be based on several performa nce measures that would be introduced in the next section. 6.5 Performance Measures Forecast errors are extremely useful to determine if the forecasting model is accurately predicting demand. They can help to determine if the model is overpredicting or underpredicting. There are several perfor mance measures of forecast error such as Mean Absolute Percentage Error (MAPE), Absolute Deviation (MAD), Mean Square Error (MSE), Root Mean Square Error (R MSE), Tracking Signal (TS), and the Mean Error. In the following secti ons, each one of these performance measures are describe. 6.5.1 Mean Absolute Percentage Error (MAPE) The mean absolute percentage error (MAPE) is the average absolute error as a percentage of demand and is given by 100 11 n t t tD e n MAPE In practice a MAPE between 10% and 15% is excellent while a MAPE between 20% and 30% is average. 6.5.2 Mean Absolute Deviation (MAD) The mean absolute deviation (MAD) is the average of the absolu te deviation over all periods. MAD measures the average distance of the sample errors from the mean of the error values. If the value of MAD is large, it is reasonably to say that the errors in the data set are spread out (variabl e). In contrast to MSE, th e MAD is very good at detecting

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69 overall performance of the model. It doe s not concentrate largely on the error of individual observations The MAD is given by n t te n MAD11 MAD is appropriate to use when the numeri cal difference between the forecast value and the actual value is important. 6.5.3 Mean Square Error (MSE) The Mean Square Error (MSE) can be relate d to the variance of the forecast error. This is extremely useful since it can be used to measure the variability or dispersion of the error. The forecast e rror for a particular period t is given by t t tD F e where tF is the forecasted or estimated value at time t and tD is the actual value at time t. The Mean Square Error is given by n t te n MSE1 21 MSE penalizes large errors for a singl e observation, and it is very good at detecting if a few observations have large e rrors. The smaller the value of the MSE the closer the fit is to the data. 6.5.4 Root Mean Square Error (RMSE) The Root Mean Square Error (RMSE) is just the square root of the MSE. The RMSE is the distance on average of a data point from the fitted line, measured along a vertical line. The RMSE is given by

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70 n t te n RMSE1 21 This statistic is very easy to interpret since it has the same units as the values plotted in the vertical axis. 6.5.5 Tracking Signal (TS) The tracking signal (TS) is used to m onitor forecast bias. If the TS exceeds a predetermined bound, this indicates an alert that the forecast is being bias one way or the other. In general, the bound of the TS is between 6 units from the mean. If the TS is below -6 then the model is underforecasting. On the other hand, if the TS is above +6 then the model is overforecasting. This w ould indicate an alert for analysts who may have to decide on using another mode l. The TS is defined as follows N N t t NMAD e TS0 6.5.6 Mean Error The mean error is an estimate of the forecast bias. The mean bias should converge to zero as N increases if the forecasting is not biased one way or the other. The mean squared error is defined as follows N t t Ne N E01 6.6 Comparison of Forecasting Techniques Five forecasting models, namely moving average (ma=4), simple exponential smoothing ( = 0.7), Holts model ( =0.5, = 0.1), Winters model ( =0.05, = 0.1), and neural networks were used to for ecast parking occupancy at a major airport.

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71 The data provided represents the number of cars per day that occupied the parking facilities (parking occupancy) at each hour fo r a period one month (the peak month), see Figure 15. There are several peak periods which make it challenging for any forecasting method to accurately predict future values of demand. Daily Parking Occupancy0 100 200 300 400 500 123456789101112131415161718192021222324 Time (Hour) Demand Figure 15: Raw Data for Parking Occupancy The data was analyzed using the four traditional methods using Microsoft Excel, and the neural network was developed using tools and functions provided by MatLab and NeuroSolutions for MatLab (Appendix D and E). Figure 16 shows the results obtained for each forecasting method. The data plotted in this graph corresponds to one day forecast. Graphical Representation of Different Forecasting Methods 0 100 200 300 400 500 123456789101112131415161718192021222324 Time (Hour) Original Data Moving Average (4) Exponential Smoothing Holt's Model Neural Network Winter's Model Demand Figure 16: Graphical Representations for Different Forecasting Methods

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72 As seen in Figure 16, the neural network mimics the original data better than the other models. The neural network is able to capture more accurate ly the changes from peak to low periods. It is important to not e that the other traditional models overforcast for periods of low demand while the neural netw ork is able to capture very accurate this changes. The above representation gave us a good indication of the performance of each model. However, a more detailed study was conducted using each performance measure previously described. Table 6 summarizes the results obtained for each one of the performance measures. Table 6: Performance Comparison for the Various Forecasting Models Method MAPE (%) MAD MSE RMSE TS Mean Error Neural Network 18.31 31.11 1,483.68 38.52 -0.000016 -0.0000014 Winter's Model 22.82 40.80 3,032.33 55.07 -1.17 -0.06 Holt's Model 70.89 70.74 8,058.62 89.77 -4.25 -0.40 Exponential Smoothing 78.23 61.39 6,191.81 78.69 -2.64 -0.22 Moving Average 106.96 84.64 11,124.65 105.47 3.53 0.40 Experimental results in Table 6 reveal that the parking occupancy estimated by a neural network is very close to the actual values. This indicates that the estimated outputs of the neural network are very accurate with a relatively small amount of error. The low MAPE indicates that the discrepa ncies between the forecasted values by the neural network and the actual values are very small. The MAPE performance measure is useful for comparing performance among differe nt time series because the errors are measured relative to the data values (T alluri and Van Ryzin, 2004). The MAPE of 18.31% obtained for the neural network is slightly over the 10%-15% range which indicates an excellent forecast; therefore, th e neural network forecasts are said to be

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73 above average. The results indicate that the MAPE values tend to in crease linearly as the model complexity decreases as seen in Figure 17. MAPE 0.00 20.00 40.00 60.00 80.00 100.00 120.00 Neural Network Winter's ModelHolt's ModelExponential Smoothing Moving Average Modelr Error Figure 17: Relationships among Performance Measures The reason may be that Holts m odel, exponential smoothing, and moving average are not able to capture the seasonality and trend of the data. On the other hand, the Winters model performs relatively well comp ared to the neural network. The reason is that this method takes into account th e trend and the seasona lity of the data. It is important to note that the exponential smoothing m odel is performing relatively well taking into account all the performance measure. The reason can be attributed to the large value of9 0 which makes the forecast more responsive to changes in level but more susceptible to noise which in the future may lead to large forecasting errors. Previously, the models have been compared using the MAPE performance measure. The root mean square error (R MSE) is probably the easiest performance measure to interpret since it has the same units as the demand plotted in the vertical axis (parking occupancy). In table 1, we can se e that the RMSE for th e neural network is 38.52. This indicates that on average the distance of the forecasted value with respect to

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74 the actual values is 38.52 units (number of cars in the parking lot). The RMSE is an excellent performance measure for the for ecast since it provides information easy to interpret that can be used for managers that can take this error into account for planning purposes. The mean error is another important performance measure that should be discussed. The mean error is an estimate of the forecast bias. If the forecasting model is not biased, the mean bias s hould converge to zero as N increases. In Figure 18, it can be seen that mean error for the neural network is extremely close to zero, which indicates that the neural network model is unbiased. The Winters model, Holts model, and simple exponential smoothing have a tende ncy to underforecast while the moving average have a tendency to overforecast. Mean Error -0.6000000 -0.4000000 -0.2000000 0.0000000 0.2000000 0.4000000 0.6000000 Neural Network Winter's Model Holt's ModelExponential Smoothing Moving Average ModelErro r Error Figure 18: Mean Error As well as measuring forecast performance, managers need a tool that constantly monitors the forecast bias. The tracking signal (TS) is a method used to accomplish this monitoring process, see Figure 19. If the TS at a ny period is outside the range6 this indicates a signal that the forecast is overforecasting or underforecasting.

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75 TRACKING SIGNAL (TS) -8 -6 -4 -2 0 2 4 6 8 Neural Network Winter's ModelHolt's ModelExponential Smoothing Moving Average ModelErro r Upper Bound Lower Bound TS Error Figure 19: Tracking Signal Figure 19 indicates that none of the m odels fall outside the upper and lower bound. However, the neural network is at zero which indicates that the model is unbiased. 6.7 Discussion As shown in the previous section, neur al networks outperfor ms moving average, simple exponential smoothing, Holts model, and Winters model in forecasting parking demand and utilization. A paired T-test was conducted on the Mean Square Error to determine if the performance difference between the utilized models was statistically significant (Appendix F). The test statistics revealed that the difference in performance between the neural networks and the other models is st atically significant (low p -value). This validates the use of neural networks as an efficient tool to predict parking demand. One advantage that neural networks ha ve over these other methods is that its architecture does not require developing algorithms specific to problems. That is, the architecture can be easily adapted for diffe rent parking facilitie s where demand patters may vary. For example, although the parki ng demand characteristics and the interaction among factors at a University are different to those at a major Airpor t, the neural network

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76 architecture is flexible and can be modified to represent both environments. Another advantage of neural networks is that they ca n easily handle nonlinea r functions. This is an advantage over other traditional methods since to analyze a non-linear relationship using linear regression analysis it is necessary to first analyze the nonlinearity of the system and determine whether some input need to be squared or two input variables need to be combined. This analysis is overcome by the neural networks capabilities.

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77 CHAPTER 7 CAPACITY CONTROL MODEL 7.1 Introduction In parking terms, capacity control can be defined as the science of predicting the quantity and specific attributes of parking facilities and sp aces needed to satisfy the forecasted demand. Currently, capacity cont rol methods do not provide efficient results because most of the time the huge amount of dy namic input data is ignored. In addition, even when high uncertainty in the forecas ts typically exists, not sufficient demand scenarios are considered. In this chapter, a model that optimally allocates parking spaces to different fare classes of demand is presented. According to basic economic theory, it is more profitable to have more than one fare class in the same market provided that the inventory can be managed properly. The results from the parking survey discussed in Chapter 5, help to demonstrate that the introduction of more than one fare class increases revenue. As seen in Figure 20, if a space is sold at an original price P0 of $6, its revenue is P0D0 or ($6*35spaces) $210. Demand Curve for Closest Parking Lot-Early0 10 20 30 40 50 60 $5$6$7$8$9$10 Price Demand Figure 20: Revenue Generated for One Segment

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78 Figure 21 presents the revenue generated for two fare classes where P1>P0 and P2
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79 7.2 Capacity Control Model This section provides some important defi nitions that will be carried out through this chapter. There are different strategies th at can be used to cont rol the availability of parking spaces. Examples of these strate gies include booking limits, protection levels, bid prices, standard nesting, and theft nesting. In this research, booking limits and protection levels are explored to develop strategies for the capacity control model. These strategies are discussed in more detail next. Booking Limits are used to control the amount of parking spaces that may be sold to any particular class of customer at a given point in time (Talluri and Van Ryzin, 2004). For example, a booking limit of 20 spaces for low fare drivers indicates that at most 20 spaces of the total capacity will be sold to low fare drivers. Therefore, the booking limit is the maximum number of spaces that may be sold at the lowest fare. The remaining of the spaces will be sold at a full price. There are two types of booking limits: partitioned and nested o Partitioned booking limits split the total capacity into blocks (one for each class), and then each block can be sold at a particular rate. For example, we have 100 parking spaces to sell. The booking limit for full fare is 20 spaces; therefore, the remaining 80 spaces will be reserved for the low fare drivers. Let say that we receive a reservation request for a full fare space and all 20 spaces previously reserved are sold (full fare is closed). Therefore, the revenue from the full fare will be lost because the booking limit fo r the full fare was closed. To

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80 prevent full fares to be unavailable nested booking limits could be used. o Nested booking limits make the already allocated spaces for low fare available for the full fare. This is accomplished by having the high fare class access to all the capacity reserved for the low fare class. Figure 3 illustrates this method. Consider the previously described example (total capacity = 100 spaces, 80 reserved for low fare, and 20 reserved for high fare). The high fa re is allocated 80 spaces, when in reality its demand could exceed th at number. A nested booking limit prevents rejecting any excess of full fare demand. In Figure 22, we can see that the nested booking limit of the full fare is 100 spaces (the total capacity), and the nested booki ng limit for the low fare would be 80 spaces. Therefore, we will accept at most 100 booking for full fare and discount fare, and at most 80 fo r low fare. The idea is that any left over capacity for the low fare becomes available for the full fare (Talluri and Van Ryzin, 2004). Figure 22: Example of Nested Booking Limits Low Fare = 80 Spaces Full Fare = 100 Spaces

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81 Protection Levels is the number of spaces that will be reserved for a particular class. The relationship of protection levels and booking limits could be described as follows. Let say that we have i classes of demand, then the booking limit (ib ) is: n i y Capacity bi i,..., 21 where iy the amount of capacity to save for 1 ,..., 1 i icombined. This is for classes i and higher. For example, let say that there are two fare classes and a capacity of 100 spaces, then the protecti on level is the number of spaces that will not be sell to low fare customers becau se of the probability that full fare customers may book latter in time. The ne w challenge is on how to determine the optimal protection levels for each cl ass. In the next section, the singleresource model for determining protecti on levels is presented. Furthermore, two traditional heuristics used in revenue management will be discussed. 7.2.1 Expected Marginal Revenue Model The basic trade-off that a parking reservat ion system has to c onsider is between selling a space at a low fare or waiting for a fu ll fare driver to arrive later on. There are two risks that have to be considered in this situation: spoilage and spill. Spoilage occurs when the capacity reserved for the full fare drivers is wasted because the demand for this class does not materialize. Spill occurs if full fare drivers have to be rejected because the capacity has already been committed to low fare drivers. Therefore, the objective is to determine the protection level for the full fare drivers so as to minimize the expected cost of spoilage and spill (Chopra and Meindl, 2004). If the demand for each fare is known with certainty then the problem would be eas ily solved. Unfortunately, the demands for

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82 each fare are never known with certainty. However, historical data can provide good estimates for the demand of each fare. From historical data a dist ribution function of the demand for each class can be described. These demand distributions will be later used in the model to determine the optimal protection levels. 7.2.1.1 Littlewoods Two Class Model Littlewoods two class model is a well-known method used in revenue management to address the problem of optimally allocating capacity to different classes. The model assumes the following: Two product classes with associated prices 2 1p p No cancellations and no overbooking Demand for the low fare arrives before the demand for the high fare The demand for class i is denoted by iD and its distribution is denoted by ) ( iF The total capacity is denoted by C. The problem is to determine how many of the low fare drivers to accept before seeing the reali zation of demand for the high fare drivers. To illustrate this concept, assume that a re quest for a low fare space is received and the reservation system has to decide whether to accept or reject the request. As seen in Figure 23, the request can be e ither accepted or rejected. If the request is accepted then the gain in revenue is2p (low price). On the other hand, if the request is rejected, there are two possibilities. The first is that space will be sold at the full fare; therefore, the actual revenue will be1p (full price). The second possibili ty is that the space will not be requested by a full fare; therefore, the revenue will be zero. In other words, the decision to stop selling low fares depend on the conditiona l probability of selling more full fare,

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83 which depends on the number of seats alread y sold and the accuracy of the forecasted demand (Talluri and Van Ryzin, 2004). Figure 23: Decision Tree The solution to this problem can be de rived using simple marginal analysis. Suppose that there are x units of capacity rema ining and a request from a low fare driver is requested. If the request is not accepted, the x unit will be sold at the high fare if and only if demand for high fare is x or higherx D1. A request from a low fare driver should be compared with the expected revenue from waiting for a high fare driver. The expected marginal revenue from the higher fare driver is given by) (1 1x D P p The request for the low fare driver should be accep ted if the expected revenue from the higher fare driver is lower than the revenue from the lower fare driver. The following equation illustrates this concept. ) (1 1 2x D P p p The reserved number of spaces for the high fare driver should be chosen such that the expected marginal revenue from the highe r fare driver equals the current marginal

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84 revenue from the low fare driver ) (1 1x D P p =2p. In other words, the number of spaces x* reserved for the full fare drivers should be such that ) (1 1x D P p = 1 2p p If the demand for the full fare drivers is normally distributed, then the optimal protection level for the high fare drivers is ) 1 ( *1 2 1 1p p F x This equation is known as Littlewoods rule. It provides the optimal booking limit for the high fare drivers. Then, the booking limit for the low fare drivers is *1 2x Capacity b Lets consider an example where the de mand for the high fare drivers is normally distributed with mean 1Dand standard deviation1 Using the previously described concepts, the reservat ion quantity would be 1 1 2 1 1* 1 p p NORMINV D x Therefore, enough capacity will be re served to meet the mean demand 1D plus or minus a factor that depends both on the re venue ratio and the standard deviation1 In general, the lower the ratio 1 2p p the more capacity we reserve for the high fare. Consider the following cases: 8 0 8 $ 10 $1 2 2 1 p p p p Versus 2 0 2 $ 10 $1 2 2 1 p p p p Case 1 Case 2

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85 For case 2, more spaces will be reserved for the full fare drivers than in case 1. The reason is obvious since we should be willing to reserve low prices only when the chances of selling full fare spaces are lower. This m odel will be used latter on in this chapter to optimally allocate spaces for two classes. 7.2.1.2 Expected Marginal Seat Revenue-version a (EMSR-a) Littlewoods two class model has prove n to provide optimal protection and booking levels. Although the implementation of optimal policies is not complex, in practice most revenue management systems prefer to use heuristics to allocate spaces to more than two fare classes. The reason is that the optimality of Littlewoods model for more than two classes was prove n after heuristics were introduced. Therefore, heuristics gained popularity, and at that point, it wa s hard to convince airline management to redesign their reservation systems. Manage rs preferred to have a solution that was approximately right rather than havi ng one that was precisely wrong. There are two heuristics commonly used in revenue management introduced by Belobaba in 1987: Expected Marginal Seat Revenue-version a (EMSR-a) and Expected Marginal Seat Revenue version b (EMSR-b). The idea of EMSR-a is to apply Littlew oods rule to successive pairs of classes and then add the protection levels produced. The following procedure is based on the one outlined by Talluri and Van Ryzin, 2004. Consider stage j+1 where demand arrives with price pj+1. We want to determine the protection level yi for classes j and higher ( j, j1,) Consider a single fare class k among the remaining classes j, j-1, and compare k and j+1 in isolation. Taking into account these two classes, L ittlewoods rule is used to reserve capacity 1j ky for class k, where

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86 1 ,..., 1 ) (1 1 j j k p p y D Pk j j k k Therefore, the capacity for each class will be computed in isolation. Then, each one of these individual protection levels are added up to approximate the total protection level yi for classes j and higher. The protection level yi is j y yj k j k j 1 1 This heuristic is easy to implement. The problem is that by adding individual protection levels; it ignores the pooling e ffect produced by aggregating demand across classes. To avoid this probl em, Belobaba introduced EMSR-b. 7.2.1.3 Expected Marginal Seat Revenue-version b (EMSR-b) EMSR-b uses the same principle as EMSR-a of reducing the problem at each stage to a two class in order to apply Littlewoods rule. To avoid the pooling effect of EMSR-a, this heuristic approximates the prot ection levels by aggregating demand rather than aggregating protection leve ls. Therefore, the demand from future classes is added and treated as revenue equal to the weighted-average revenu e. The following procedure is based on the one outlined by Talluri and Va n Ryzin, 2004. The heuristic works as follows. Consider that we are given estimates of the mean and standard deviation for each fare class j then the protection level yi for class j and higher is given by Littlewoods rule so that j j j jp p y S P1) ( where Sj is the aggregate future demand for classes j,j-1,

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87 j k k jD S1 And let the weighted-average revenue jp from classes 1,,j be defined by j k k j k k k jD E D E p p1 1] [ ] [ Assuming that Sj is a normal random variable with mean j k k1 and variance of the aggregated demand isj k k1 2 2 Therefore, the protection level yi for class j and higher is defined as z yi where j jp p z1 11. This heuristic is easy to implement and it extremely popular in many revenue management implementations. The next sect ion will show an application of the three previously discussed capacity contro l methods to the parking problem. 7.3 Application to the Parking Industry This section adapts the models discussed in the previous section to the parking problem by computing the protection levels and calculating the number of spaces that should be reserved for each fare. The results obtained from the parking survey distributed are used as input data for the models. The parking survey was distributed to 51 subjects. Table 7 shows the demand data obtained from the parking survey. The demand is assumed to be normally distributed. It also shows the optimum pr otection levels for 51 parking spaces. The

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88 optimum protection levels were obtained usi ng Littlewoods two class model described in section 8.2.1.1. Table 7: Protection Levels for Two Classes Class P(j) (j) (j) Opt. Protection Level Revenue 1 $7 23.0 5.8 19.7 $ 294.43 2 $5 28.0 2.4 31.3 The results indicate that twenty spaces should be re served for the full fare segment and thirty one for the lowest fa re. Littlewoods model provided optimal protection levels for two fare classes. For more than two classes, EMSR-a and EMSR-b heuristics are used to analyze the impact on revenue by adding more than two fare classes. The heuristics implemented in Excel ar e discussed in more de tail in Appendix G. Table 8 shows the protection levels for three fare classes implementing EMSR-a and EMSR-b heuristics. As the results indi cate the addition of a fare classes increased revenue from $294.43 to $330.32 or 11 percent. It is important to note that there is not a significant discrepancy among the computed protection levels from the heuristics. Table 8: Protection Levels for Three Fare Classes Class p(j) (j) (j) EMSR-a EMSR-b Revenue 1 $9 10.0 2.4 8.16 8.16 $ 330.32 2 $7 23.0 5.6 29.50 30.53 3 $5 18.0 3.2 13.34 12.30 Table 9 illustrates the option of adding a fourth fare class. The results show that the addition of the fourth fare classes in creased revenues from $330.32 (for three fare classes) to $354.65 or by 7 percent.

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89 Table 9: Protection Levels for Four Fare Classes Class p(j) (j) (j) EMSR-a EMSR-b Revenue 1 $11 5.0 2.3 2.91 2.91 $ 354.65 2 $9 10.0 2.5 12.29 12.98 3 $7 23.0 5.8 34.63 35.93 4 $5 13.0 4.6 1.17 1.00 Figure 24 summarizes the results previously discussed. It shows the relationship between the number of fare classe s and the total expected revenue. Number of Fare Classes vs. Total Revenue $$100.00 $200.00 $300.00 $400.00 $500.00 1234 Number of Fare ClassesReven u Revenue Figure 24: Number of Fare Classes vs. Total Revenue As can be seen in this figure, an increase in number of fare classes leads to an increase in total revenue. However, it is important to note that the increase in revenue can only be accomplished if the interactions among classes are minimized. This means that it is recommended that there is a significant difference in price that induces drivers to discriminate among classes. The results obtain ed from the parking survey show that a 20 percent difference in prices produ ces a more balanced demand. The results of the scenarios using both he uristics for three and four classes are shown in Table 10. The capacity is varied from 50 parking spaces to 140 spaces. This variation on capacity illustrates how capacity will vary on a parking facility during a normal day. The results corroborate the previ ous conclusion that the addition of an extra

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90 fare class increases to tal revenue. However, this study shows that the in crease in revenue is more significant as capacity increases. Table 10: Simulation of Revenue Performance Revenue EMSR-a % Revenue EMSR-b % Capacity 3-classes 4-classes Increase 3-classes 4-classes Increase 50 $325.32 $349.65 7% $327.39 $353.64 7% 60 $375.32 $399.65 6% $377.39 $403.64 7% 70 $425.32 $452.39 6% $427.39 $453.78 6% 80 $475.32 $522.39 9% $477.39 $523.78 9% 90 $539.13 $600.62 10% $539.13 $600.62 10% 100 $609.13 $690.62 12% $609.13 $690.62 12% 110 $679.13 $780.62 13% $679.13 $780.62 13% 120 $749.13 $870.62 14% $749.13 $870.62 14% 130 $825.40 $977.40 16% $825.40 $977.40 16% 140 $879.40 $1,043.40 16% $879.40 $1,043.40 16% This study shows how revenue manage ment techniques increase revenues by increasing the number of fare classes. Howe ver, the objective of a parking manager is not only to increase revenue but also to maximize utilizati on. During low-periods of demand, parking manager could decrease prices to attract drivers during these periods. On the other hand, higher pri ces could be applied during peak periods of demand. This strategy is illustrated in Table 11 where Littlewoods two class model is used to optimally allocate parking spaces to two fare classes. The demand data is normally distributed. The next analysis uses the results of the ne ural network model to forecast parking space availability. During low demand periods (Hour s 0-9) more spaces are reserved for low fare drivers. On the other hand, all spaces are sold at the higher price during peak hours (Hours 10-17).

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91 Table 11: RM Capacity Control Example LITTLEWOOD'S TWO CLASS MODEL Hour Forecasted Availability OPT CLASS1 OPT CLASS2 Expected Revenue 0 421 14 406 2131 1 442 14 428 2238 2 447 14 433 2265 3 442 14 428 2236 4 393 14 379 1994 5 246 14 232 1259 6 172 14 158 890 7 270 14 256 1377 8 243 14 229 1241 9 163 14 149 844 10 89 89 0 626 11 89 89 0 626 12 89 89 0 626 13 56 56 0 394 14 25 25 0 178 15 25 25 0 177 16 56 56 0 395 17 56 56 0 395 18 101 14 87 532 19 192 14 178 989 20 198 14 184 1019 21 212 14 198 1088 22 221 14 207 1132 23 311 14 297 1581 Total Revenue $26,232.68 7.4 Summary Revenue Management is the use of di fferential pricing over time or customer segments to maximize profits from a limited capacity of resources. (Chopra and Meindl, 2004). This chapter has illustrated this concept by introducing different prices for multiple fare classes. It has been demonstrated that an increase in the number of fare classes increases revenue. The idea of balance demand and supply has also been illustrated. Littlewoods two class model has been used to optimally allocate parking

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92 spaces for two fare classes. Furthermore, tw o traditional heuristics, EMSR-a and EMSRb has been used to allocate parking spaces for three and four fare classes.

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93 CHAPTER 8 CONCLUSIONS AND FUTURE RESEARCH The research methods used for modeli ng parking systems have varied in complexity, ranging from simple empirical st udies and heuristics to advanced techniques for mapping complex parking non-linearity. Mo st parking related literature reviewed appears to have several gaps that present oppor tunities associated w ith integration, and incorporation of technology into the approach es used for modeling. Although the models presented in the literature have a strong t echnical foundation, they have found limited application. Therefore, there is a need in the parking literature to provide managers and planners with tools that can be used to control parking demand. Each advance in information technology provides an opportunity for more innovative and comprehensive solutions, and greater integration with other important tran sportation functions. The parking problem possesses distin ctive characteristics where revenue management techniques may be employed fo r better allocation of limited resources and evaluation of issues such as parking fees. In this thesis, the traditional methodology of revenue management has been adopted and appl ied to the parking problem. First, market segmentation was studied through a stated pref erence survey. The results of the survey indicate that drivers are willing to pay higher fares under a time constraint situation. This demonstrates the concept that a parking spac e can be sold at different price rates. Furthermore, the parking survey helped to identify that a 20 percent difference in prices

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94 induces drivers to change their parking ch oice from long walking distance to short walking distance. The next step in the revenue management methodology is to forecast parking demand. This thesis compared neural networ ks versus traditional time series methods. The results show that Neural Networks are an efficient tool to predict parking demand. The major advantage of neural networks is that it is not necessary to pay major attention to nonlinearity included in the problem. Furthermore, the neural network architecture provides a framework that can be adapted to different case scenarios, and it is not necessary to develop new algorithms for specif ic problems. Neural networks allow to easily study complex relationship of factors which may have been difficult or impossible to model. In this thesis, parking spaces were optimally allocated to two fare classes by Littlewoods two class model. Furthermore, two traditional heuristics, EMSR-a and EMSR-b, were used to allocate parking spaces to three and four fare classes. The results show that an increase in the number of fare classes increases tota l revenue. Littlewoods two class model was also used to optimally allocate parking spaces using the forecasted results from the neural network. The resu lts show how revenue management techniques are effective to increase revenue and diversify demand. The parking problem provides the opport unity for researchers to explore the creation of dynamic programming revenue ma nagement to identify optimal parking pricing strategies with real-time information. This may lead to the creation of more sophisticated information systems for drivers who will be able to know in advance where to find an available parking space. The ul timate objective should be to create an

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95 intelligent system that allows drivers to rese rve in advance where they will park and how much they are going to pay. This will provide a better balance of parking supply and demand and as a result will incr ease available parking inventor y without the need to build additional facilities. Some of the extensions to this research include: To develop an online parking reservation simulation system. This system will allow drivers to reserve a parking space in advance. The simulation will help to de termine demand distributions for different drivers segments. The second extension of th is thesis is to dynamically recalibrate the protection levels taking into account on-time reservations. It is important to further study the potential to introduce overbooking models. The stated parking survey distributed in this thesis should be applied on different demographi c populations. This population should include older adults, and different in come levels. There are some cases where owners of parking facility have a network of parking facilities. Therefore, it is necessary to apply the models to optimally allocate parking spaces to different fare classes for a network of parking facilities. More importantly, this thesis provides the opportunity for interdisciplinary collaboration among industr ial engineering, transportation engineering and computer science. The collaboration of these disciplines will provide a more robust framework for solutions to the parking problem.

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96 REFERENCES Alstrup, J., Boas, S., Madsen, G., B., O., Vidal, R., and Victor, V. (1986). Booking Policy for Flights with Two Types of Passengers. European Journal of Operations Research, 27, 274-288. Arnott, R. and Rowse, J. (1999). Modeling Parking. Journal of Urban Economics 45. 97-124. Axhausen, K. W. and Polak, J. (1991). Choice of Parking: Stated Preference Approach. Transportation 18 59-81. Beckmann, J., M., and Bobkoski., F. (1958) Airline Demand: An Analysis of Some Frequency Distributions. Naval Res. Logistics Q, 5, 43-51. Beckmann, M., J. (1958). Decision and Team Problems in Airline Reservations. Econometrica, 26, 134-145. Beloba, P., P. (1987). Air Travel Dema nd and Airline Seat I nventory Management. Ph.D. Thesis, Flight Transportation Laboratory. Massachusetts Institute of Technology: Cambridge, MA. Belobaba, P., P. (1987). Airline Yield Management: An Overview of Seat Inventory Control. Transportation Science, 21, 63-73. Ben-Avika, M. (1987). Improving Airline Passenger Forecasting Using Reservation Data. ORSA/TIMS Proceedings. St. Louis, MO. Biffulco, N. G. (1993). A Stochastic User Equilibrium Assignment Model for the Evaluation of Parking Policies. European Journal of Operations Research, Vol. 71, 269-287. Brumelle, S., L., and McGill, I., J. ( 1993). Airline Seat Allocation with Multiple Nested Fare Classes. Operations Research, 41, 127-137. Calthrop, E., Proost, S., and Dender, K. (2000). Parking Policies and Road Pricing. Urban Studies, Vol. 37. No. 1, 63-76. Cassady, C. R., and Kobza, J. (1998). A Probabilistic Approach to Evaluate Strategies for Selecting a Parking Space. Transportation Science, Vol. 32, No 1 30-42.

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97 Centeno, G., and Rojas, D. (2005). Predicting Parking De mand Using Neural Networks. Proceedings IIE Annual Conference, Atlanta. Chatwin, R.E. (1998). Application of a pr obabilistic decision mo del to airline set inventory control. Operations Research, 37 183-197. Chopra, S., and Meindl, P. (2004). Suppl y Chain Management: Strategy, Planning and Operation. Pearson Prentice Hall: Upper Saddle River, NJ. Curry, E., R. (1990). Optimal Airline S eat Allocation with Fare Classes Nested by Origins and Destinations. Transportation Science, 24, 193-204. Dana, J., D. (1996). Peak-Load Pric ing when the Peak Time is Unknown. Working Paper, General Motors Research Cent er for Strategy in Management, Kellog School. Northwestern University: Evanston, IL. Feeney, B. P. (1989). A Review of the Impact of Parking Policy Measures on Travel Demand. Transportation Planning and Technology, 13 229-244. Gallego, G. (1996). A Dema nd Model for Yield Management. Technical Report Columbia University: New York, NY. Hess, S., and Polak, W. J. (2004). Mi xed Logit Estimation of Parking Type Choice. 83rd Annual Meeting of the Tr ansportation Research Board. Washington, DC. Hunt, J. D., and S. Teply (1993). A nest ed logit model of parking location choice. Transportation research 27 B(4), 253-265. Innovative mobility. http://www.innovativemobility.org, 2004. Intelligent Transportation Systems Journal. http://www.tandf.co.ok 2002. Intelligent Vehicle Initiative. http:www.dot.gov, 2000. Lam, W. H. K., Li, Z. C., Huan, H. J ., and Wong, S. C. (2006). Modeling time-dependent travel choice problems in road networks with multiple user classes and multiple parking facilities. Transportation Research Part B: Methodological. Vol. 40, No. 5 368-395. Landau, L. J., and Taylor, J. G. (1998). Concepts for Neural Networks: A Survey. Springer-Verlag Berlin Heidelberg: New York Lee, Y., and Young, W. (1998). Mode ling Shopping Centre Traffic Movement (1): Model Validation. Transportation Planning and Technology, Vol. 21, 203-233.

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98 Lee, Y., and Young, W. (1998). Mode ling Shopping Centre Traffic Movement (1): Model Validation. Transportation Planning and Technology, Vol. 21, 203-233. Littlewood, K. (1972). Forecasting and Control of Passenger Bookings. AGIFORS Symposium Proc. 12. Lyle, C., (1970). A Statisti cal Analysis of the Variabili ty in Aircraft Ocuupancy. AGIFORS Symposium Proceedings, 12. Maccubbin, A. R., and Hoel, A. L. (2000) Evaluating ITS Management Strategies: A Systems Approach. Center for Transportation Studi es at the University of Virginia. McGill, I., J. (1995). Censored Regression Analysis of Multiclass Demand Data Subject to Joint Capacity Constraints. Ann. Operations Research, 60, 209-240. Miller, G. K., and Everett, C.K. ( 1982). Raising Commuter Parking Prices-An Empirical Study Transportation, 11 105-129. National Parking Association. http://www.npa.org 2005. Polak, J. W. (1990). Parking Guidance and Information Systems : Performance and Capability. Traffic engineering & control. Vol. 31, no. 10 519-524. Polak, J., Vythoulkas, P., and Chatfield, I. (1991). Behavioral Impact of A Broadcast Parking Information Service in Nottingham. Proceedings of Seminar E: PTRC Transport, Higways and Planning, P345. Rothstein, M. (1968). Stochastic Models for Airline Booking Policies. Ph. D. Thesis, Graduate School of Engineering and Science. New York University: New York, NA. Sa., J. (1987). Reservations For ecasting in Airline Yield Management. Masters Thesis, Flight Transportation Institute. Massachusetts Institu te of Technology: Cambridge, MA. Sattayhatewa, P., and Smith, L., R. (2003). Development of parking choice models for special events. Transportation research record. No. 1858 31-38. Scholefield, G., Bradley, R., and Skinner, A. (1997). Study of Parking and Traffic Demand: A Traffic Restrain t Analysis Model (TRAM). Transportation Planning Methods, Vol. P414. Shlifer, R., and Vardi, R. (1975). An Airline Overbooking Policy. Transportation Science, 9, 101-114.

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99 Shlifer, R., and Vardi, Y. (1975) An Airline Overbooking Policy. Transportation Science, 9, 101-114. Shoup, C., D. (1995). An Opportunity to Reduce Minimum Parking Requirements. Journal of the American Pl anning Association, Vol. 61 No. 1. Tallury, T., K., and Van Ryzin, J., G. (2004). The Theory and Practice of Revenue Management. Klumer Academic Publishers: Norwell, MA. Taneja, K., N. (1978). Airline Traffic Fo recasting: A Regression Analysis Approach. Lexington Books, Lexington, MA. Taylor, J., C. (1962). The Determination of Passenger Booking Levels. AGIFORS Symposium Proceedings, 2. Fregene, Italy. Thompson, R., H. (1961). Statistical Pr oblems in Airline Reservation Control. Operations Research Q, 12, 167-185. Thompson, R. G., Takada, K., and Koba yakawa, S. (1998). Understanding the Demand for Access Information. Transportation research. Part C, Emerging technologies, Vol. 6C, No. 4. 231-245. U.S. Department of Transportation Intelligent Transportation Systems. http://www.its.dot.gov 2002. United States Department of Transportation. http://www.dot.gov 2002 Van der Waerden, P., Borges, A., and Timm ermans, H. (1998). The Impact of the Parking Situation in Shopping Cent ers on Store C hoice Behavior. GeoJournal, Vol. 45, No. 4 309-315. Verhoef, E., Nijkamp, P., and Rietveld, P. (1995). The Economics of Regulatory Parking Policies: The (im)possibilities of Parking Policies in Traffic Regulation. Transportation Research -A, 29, 141-156. Visser, J., Van der Mede P. (1986). Th e Effects of Parking Measures on Traffic Congestion. Proceedings of the 1986 PTRC Summer Annual Meeting Brighton England. Weatherford, R., L. (1994). Optimizati on of Perishable-Asset Revenue Management Problems that Allow Prices as Decision Variables. Working Paper. University of Wyoming, Laramie, WY. Williamson, L., E. (1992). Airline Netw ork Seat Inventory Control: Methodologies and Revenue Impacts. Ph.D. Thesis. Flight Transportation Laboratory. Massachusetts Institute of Technology: Cambridge, MA.

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100 Willson, W., R., and Shoup, C., D. (1990) Parking Subsidies and Travel Choices: Assesing the Evidence. Transportation, 17, 141-157. Wollmer, D., R., (1992). An Airline Seat Management Models for a Single Leg Route when Lower Fare Classes Book First. Operations Research, 40, 26-37. Yang, Z., H. Liu, and Wang, H. (2003). The Research on the Key Technologies for Improving Efficiency of Parking Guidance System. Proceedings of the 2003 IEEE International Conference on In telligent Transportation Systems 1177-1182. Young, W. (1986). PARKSIM/1: A Netw ork Model for Parking Facility Design. Traffic Engineering and Control, Vol 27, 606-613. Young, W., and Taylor, M. (1991) A Parking Model Hierarchy. Transportation, 18, 37-58. Young, W., Thompson, R. G., and Taylor, M. A. P. (1991). A Review of Urban Car Parking Models. Transport Reviews 11 63-84. Wang, Q., and Sun, X. (1996). Enhanced Ar tificial Neural Network model for Chinese Economic Forecasting. Proceedings of the International Conference on Management Science and the Economic Development of China. Vol. 1 30-36.

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101 APPENDICES

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102 Appendix A: Stated Preference Survey DYNAMIC PARKING PRICING SYSTEM SURVEY Project Description: Parking plays an important role in the traffi c system since all vehi cles require a storage location when they are not being used to transport passengers. Most major cities continually struggle with parking limitations, violations and cost. Parking facilities experience peak and low demand periods. Th e problem increases during peak periods when it becomes challenging to find an ava ilable parking on a particular parking lot location. One alternative to this problem is to stimulate and dive rsify the demand with the introduction of pricing strate gies. The goal of this survey is to identify how you as a driver would react to changes on prices and which parking facility would be selected for various set of scenarios and circumstances. Instructions: In the next pages you will find 12 questions. For each question, you will have the options to park on either LOT A or LOT B. K eep in mind the following assumptions when answering the questions: (1) Weather condition is about 75 degrees Fahrenheit and it is not raining. (2) When walking to destination, the walking pace is fixed and the same for all individuals -that is, you wont be ab le to walk faster in order to arrive earlier. Walking time accounts for the time it takes from the parking lot of your choice to the indicated destination. (3) Arrive time indicates how early you are for your meeting/class or activity on a given scenario. For exampl e indicates that you arrived 15 minutes early to your m eeting/class or activity. (4) Time to Destination(time to destination = walking time + driving time) indicates the time that will take to reach your final destination. NOTE: The majority of the time to reach your destin ation will be spend walking rather than driving An example: In Figure 1, you will position yourself in the on the left side of the picture. Then you will check for the sign that indicates the time you have available from the parking lot you choose to the final destination. Sometimes you will be 15 minutes early, some others you might be 5 minutes early In the example, the sign shows that you ARRIVED 15 minutes EARLY Next, you will compare parking LOT A versus parking LOT B in terms of price and time to destination. In this example, if you park in Lot A you will have 10 minutes to reach your destinati on (you will arrived 5 minutes early to your destination). The cost to park in lot A is $5. To park in Lot B you will have 5 minutes to reach your destination (you will be 10 minutes early), but you will have to pay $10. If you would prefer to pay less, then you w ill circle Lot A (as shown in the Figure). If you ra ther walk less time and cost is not of concern, you would choose Lot B. Remember that you have to take all the factors (arrival time, price, and time to destination) into consideration before selecting either Lot. ARRIVED 15 minutes EARLY ARRIVED 15 minutes EARLY START

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103 Appendix A: (Continued) Figure 25: Survey Case Scenario Sample Lot A selected

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104 Appendix A: (Continued) Figure 26: Case Scenario # 1 Figure 27: Case Scenario # 2 Figure 28: Case Scenario # 3 Figure 29: Case Scenario # 4 Figure 30: Case Scenario # 5 Figure 31: Case Scenario # 6

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105 Appendix A: (Continued) Figure 32: Case Scenario # 7 Figure 33: Case Scenario # 8 Figure 34: Case Scenario # 9 Figure 35: Case Scenario # 10 DESTINATION START ARRIVED 5 minutes EARLY TIME TO DESTINATION = 10 min PRICE = $ 5 LOT A LOT B TIME TO DESTINATION = 5 min PRICE = $ 7 Figure 36: Case Scenario # 11 Figure 37: Case Scenario # 12

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106 Appendix A: (Continued) Please answer the following questions: 1. What is your gender? Male Female 2. How old are you? Less than 20 20 29 30 39 40 49 50 59 60 or older 3. Are you employed? Yes Full-time Part-time No 4. What is your income? Less than $15,000 $15,000 $19,999 $20,000 $29,999 $30,000 $39,999 $40,000 $49,999 $50,000 $59,999 $60,000 $69,999 $70,000 or more 6. Would you pay more for a guaranteed parking space close to your destination? Yes No 7. Would you reserve a parking space in advance (on-line or by phone)? (Similar to the way you reserve an airline ticket) Yes No 8. Please rank which factor was most important to you when making your selection in the previous scenarios. Please write 1, 2 or 3 next to the factor. (1=very important, 2 important, 3 less important) Time to Destination (walking time + driving time) = Arrival time (being early or late) = Price ($) =

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107 107Table 12: Survey Raw Data Results OT = On Time MTTD = Minimum Time to Destination MC = Minimum Cost Sc1 to Sc6= Scenario 1 to Scenario 6 = On Time (Time is not a constraint) Sc7 to Sc 12= Scenario 7 to Scenario 12 = Late (Time is a constraint) A = Parking Lot Further Away to the destination (Minimum Cost) B = Parking Lot Closest to the Destination (Hi ghest Cost and Minimum Time to Destination) Appendix B: Stated Pr eference Survey Raw Data 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Sc 1 A A A A A A A A A A A A A A A A A A A B B A B A A A Sc 2 A A A A A A A A A A A A A A A B B A A B B A B B A A Sc 3 A A A A A A A A A A A A A B A B B A A B B A B B A A Sc 4 B A A A A A A B B B A A A B A B B A A B B A B B A B Sc 5 B A A B A B A B B B A B B B A B B A B B B A B B A B Sc 6 B B B B B B B B B B B B B B B B B B B B B B B B B B Sc 7 A B B B A B B B B B A A A B A B A B B B B A B A A A Sc 8 B B B B A B B B B B B A B B A B B B B B B A B B A A Sc 9 B B B B A B B B B B B B B B A B B B B B B B B B A A Sc 10 B B B B A B B B B B B B B B B B B B B B B B B B A B Sc 11 B B B B B B B B B B B B B B B B B B B B B B B B B B Sc 12 B B B B B B B B B B B B B B B B B B B B B B B B B B # OT 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 # MTTD 2 0 0 1 0 1 0 2 2 2 0 1 1 3 0 4 4 0 1 5 5 0 5 4 0 2 #MC 3 5 5 4 5 4 5 3 3 3 5 4 4 2 5 1 1 5 4 0 0 5 0 1 5 3 # OT 4 5 5 5 1 5 5 5 5 5 4 3 4 5 2 5 4 5 5 5 5 3 5 4 1 2 # MTTD 4 5 5 5 1 5 5 5 5 5 4 3 4 5 2 5 4 5 5 5 5 3 5 4 1 2 #MC 1 0 0 0 4 0 0 0 0 0 1 2 1 0 3 0 1 0 0 0 0 2 0 1 4 3 Appendix B: Stated Preference Survey Raw Data

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108 Appendix B: (Continued) Table 12: (Continued) 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 MTTD MC Sc 1 A A A A A A A A A A A A A A A A A A A A A A A A A 3 48 Sc 2 A A A A A A A A A A A A A A A A A A A A A A A A A 6 45 Sc 3 A A A A A B A A A A A A A A A A A A A A A A A A A 8 43 Sc 4 A A B A A B A A B B B B B A A A A A A A B A B B B 23 28 Sc 5 B A B A B B B A B B B B B A B B B A B A B A B B B 35 16 Sc 6 B B B B B B B B B B B B B B B B B B B B B B B B B 51 0 Sc 7 B A A A B B B B A B B B B B B A A A B B A A B B B 31 20 Sc 8 B A A B B B B B B B B B B B B A B A B B A B B B B 40 11 Sc 9 B A A B B B B B B B B B B B B B B A B B A B B B B 43 8 Sc 10 B B B B B B B B B B B B B B B B B A B B B B B B B 48 3 Sc 11 B B B B B B B B B B B B B B B B B B B B B B B B B 51 0 Sc 12 B B B B B B B B B B B B B B B B B B B B B B B B B 51 0 OT 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 255 100% MTTD 1 0 2 0 1 3 1 0 2 2 2 2 2 0 1 1 1 0 1 0 2 0 2 2 2 75 29% MC 4 5 3 5 4 2 4 5 3 3 3 3 3 5 4 4 4 5 4 5 3 5 3 3 3 180 71% OT 5 2 2 4 5 5 5 5 4 5 5 5 5 5 5 3 4 1 5 5 2 4 5 5 5 213 84% MTTD 5 2 2 4 5 5 5 5 4 5 5 5 5 5 5 3 4 1 5 5 2 4 5 5 5 213 84% MC 0 3 3 1 0 0 0 0 1 0 0 0 0 0 0 2 1 4 0 0 3 1 0 0 0 42 16% OT = On Time MTTD = Minimum Time to Destination MC = Minimum Cost Sc1 to Sc6= Scenario 1 to Scenario 6 = On Time (Time is not a constraint) Sc7 to Sc 12= Scenario 7 to Scenario 12 = Late (Time is a constraint) A = Parking Lot Further Away to the destination (Minimum Cost) B = Parking Lot Closest to the Destination (Hi ghest Cost and Minimum Time to Destination) 108

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109 Appendix C: Scenario Results Scenario 10 20 40 60 # MTTD#MC Factor# Answer s Figure 38: Case Scenario 1 Results Scenario 20 10 20 30 40 50 # MTTD#MC Factor# Answer s Figure 39: Case Scenario 2 Results Scenario 30 10 20 30 40 50 # MTTD#MC Factor# Answer s Figure 40: Case Scenario 3 Results Scenario 40 10 20 30 # MTTD#MC Factor# Answer s Figure 41: Case Scenario 4 Results Scenario 50 10 20 30 40 # MTTD#MC Factor# Answer s Figure 42: Case Scenario 5 Results Scenario 60 20 40 60 # MTTD#MC Factor# Answer s Figure 43: Case Scenario 6 Results Scenario 70 10 20 30 40 # MTTD#MC Factor# Answer s Figure 44: Case Scenario 7 Results Scenario 80 10 20 30 40 50 # MTTD#MC Factor# Answer s Figure 45: Case Scenario 8 Results Scenario 90 10 20 30 40 50 # MTTD#MC Factor# Answer s Figure 46: Case Scenario 9 Results Scenario 100 20 40 60 # MTTD#MC Factor# Answer s Figure 47: Case Scenario 10 Results Scenario 110 20 40 60 # MTTD#MC Factor# Answer s Figure 48: Case Scenario 11 Results Scenario 120 20 40 60 # MTTD#MC Factor# Answer s Figure 49: Case Scenario 12 Result

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110 Appendix D: Forecasting Models Results MOVING AVERAG E 0 100 200 300 400 5005 24 43 62 81 100 119 138 157 176 195 214 233 252 271 290 309 328 347 366 385 404 423 442 461 480 499 518 537 556 575 594 613 632 651 670 689 708 727HOUR Figure 50: Moving Averag e Forecasting Results EXPONENTIAL SMOOTHING0 100 200 300 400 5001 20 39 58 77 96 115 134 153 172 191 210 229 248 267 286 305 324 343 362 381 400 419 438 457 476 495 514 533 552 571 590 609 628 647 666 685 704 723 742HOU R DEMA N Figure 51: Exponential Smoothing Forecasting Results 110

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111 Appendix D: (Continued) Appendix D: Forecasting Models Results HOLT'S MODEL0 100 200 300 400 5001 20 39 58 77 96 115 134 153 172 191 210 229 248 267 286 305 324 343 362 381 400 419 438 457 476 495 514 533 552 571 590 609 628 647 666 685 704 723 742HOU R DEMA N Figure 52: Holt's Model Forecasting Results WINTER'S MODEL0 100 200 300 400 500 6001 20 39 58 77 96 115 134 153 172 191 210 229 248 267 286 305 324 343 362 381 400 419 438 457 476 495 514 533 552 571 590 609 628 647 666 685 704 723 742HOU R DEMA N Figure 53: Winter's Mode l Forecasting Results 111

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112 Appendix D: (Continued) 112 NEURAL NETWORK0 100 200 300 400 5001 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172 181 190 199 208 217 226 235 244 253 262 271 280 289 298 307HOU R DEMAN D Figure 54: Neural Network Forecasting Results

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113 Appendix E: Neural Network Code in MatLab %################################################################# %###NEURAL NETWORK TO FORE CAST PARKING DEMAND########### %################################################################# %The following code forecast the parking demand using a Neural Network %The model is tested with data provided from a major airport %STEP 1 %The data needs to be separated into two subsets: testing data %and validation data %The testing data would be used to train the network and the validation %data would be used to test network %###################CREATES INDEX FOR DAYS %################### g=(unidrnd(2,31,1));% CREATES INDEX FOR SUBSAMPLING k=0; for i=1:31 for c=1:24 k=k+1; vec(k)=i; vec2(k)=g(i); end end data=[d vec' vec2']; for i=1:1 %FOR EACH VALIDATION SET valid=data(find(data(:,5)==i),1:3); clear tdata z=0; for j=1:3%TRAINING DATA SET if i ~=j z=z+1; if z==1 tdata=data(find(data(:,5)==j),1:3); else tdata=[tdata;data(find(data(:,5)==j),1:3)]; end end end

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114 Appendix E: (Continued) %NN HERE####################################### p=tdata(:,2)'; t=tdata(:,3)'; val.P=valid(:,2)'; val.T=valid(:,3)'; net=newff(minmax(p),[3,1],{'tansig','purelin'},'trainlm'); net.trainParam.show = 25; net.trainParam.epochs = 300; net = init(net); [net,tr]=train(net,p,t); %END NN#########################################

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115 Appendix F: Statistical Test of MSE NEURAL NETWORK VS MOVING AVERAGE Paired T-Test and CI: NN, MA Paired T for NN MA N Mean StDev SE Mean NN 24 749.5 78.2 16.0 MA 24 10513.2 173.4 35.4 Difference 24 -9763.7 168.3 34.3 95% CI for mean differenc e: (-9834.8, -9692.7) T-Test of mean difference = 0 (vs not = 0): T-Value = -284.28 P-Value = 0.000 NEURAL NETWORK VS EXPONENTIAL SMOOTHING Paired T-Test and CI: NN, ES Paired T for NN ES N Mean StDev SE Mean NN 24 749.5 78.2 16.0 ES 24 5883.1 99.8 20.4 Difference 24 -5133.7 128.8 26.3 95% CI for mean differenc e: (-5188.0, -5079.3) T-Test of mean difference = 0 (vs not = 0): T-Value = -195.23 P-Value = 0.000

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116 Appendix F: (Continued) NEURAL NETWORK VS HOLT'S METHOD Paired T-Test and CI: NN, Holts Paired T for NN Holts N Mean StDev SE Mean NN 24 749.5 78.2 16.0 Holts 24 8023.3 130.9 26.7 Difference 24 -7273.9 134.2 27.4 95% CI for mean differenc e: (-7330.5, -7217.2) T-Test of mean difference = 0 (vs not = 0): T-Value = -265.54 P-Value = 0.000 NEURAL NETWORK VS WINTER'S MODEL Paired T-Test and CI: NN, Winters Paired T for NN Winters N Mean StDev SE Mean NN 24 749.5 78.2 16.0 Winters 24 2635.9 61.9 12.6 Difference 24 -1886.5 49.0 10.0 95% CI for mean differenc e: (-1907.2, -1865.8) T-Test of mean difference = 0 (vs not = 0): T-Value = -188.60 P-Value = 0.000

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117 Appendix G: Capacity Control Models Table 13: Littlewood's Two Class Model Results Class p(j) (j) (j) OPT Revenue 1 7 23.0 5.8 19.7 $ 339.43 2 5 28.0 2.4 31.3 Table 14: Three Classes Data Class p(j) (j) (j) 1 9 10.0 2.4 2 7 23.0 5.6 3 5 18.0 3.2 Table 15: Four Classes Data Class p(j) (j) (j) 1 11 5.0 2.3 2 9 10.0 2.5 3 7 23.0 5.8 4 5 13.0 4.6 Table 16: EMSR-a for Three Classes EMSR-a j k = 2 k = 1 y(j) 219.83 9.66 29.50 1 8.16 8.16 Table 17: EMSR-b for Three Classes EMSR-b j P(j) y(j) 233.0 6.09 7.61 30.53 110.0 2.40 9 8.16 Table 18: EMSR-a for Four Classes EMSR-a j k =3 k = 2 k = 1 y(j) 3 19.72 9.65 5.26 34.63 2 8.09 4.20 12.29 1 2.91 2.91

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118 Appendix G: (Continued) Table 19: EMSR-b for Four Classes EMSR-b j P(j) y(j) 3 38.00 6.72 8.05 35.93 2 15.00 3.40 9.67 12.98 1 5.00 2.30 11.00 2.91