1 ENHANCEMENT AND EVALUATION OF DYNAMIC PRICING STRATEGIES OF MANAGED TOLL LANES By DIMITRA MICHALAKA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2012
2 2012 Dimitra Michalaka
3 I dedicate this dissertation t o my amazing mom, dad, sister, and grandparents, who have always given me so much love, support and advice.
4 AC KNOWLEDGMENTS I t is with great pleasure to first acknowledge my advisor, Dr. Yafeng Yin for his guidance insight support and patience throughout my graduate studies Dr. Yin is an outstanding professor and person. He has been my greatest advisor and me ntor and he has significantly influenced my life. E ach day I am grateful for being his student I also would like to thank Dr. Lily Elefteriadou for all of her advice and support She is an exceptional female professor who has greatly inspired me. In addi tion I wish to thank the remaining members of my dissertation committee, Dr. Siriphong Lawphonpanich Dr. Sivaramakrishnan Srinivasan and Dr. Scott Washburn for their assistance and input Overall, all the professors at the University of Florida (UF) T ransportation Research Center are outstanding and I want to express my sincere thanks to them for everything they have taught me and for letting me teach course It was then that I realized that teaching is one of my passio ns. Furthermore, I would like to thank Tom Simmerman and David Hale, programmers at the Mc Trans Center, who significantly contributed to the enhancement of CORSIM and Jie Lu who helped with the implementation of the genetic algorithm procedure in Matlab Importantly, I would like to thank my mother, who has always been there for me and has dedicated her life to me and my sister. Even when we are separated by thousands of miles, I feel her near me and I draw great strength from her. Also, I want to thank m y father whose teachings and values forged my personality and greatly influenced my character, and my sister, who is always supportive and willing to hear me
5 out whenever I need it the most. Moreover, special thanks to my grandmothers and my grandfather fo r their continuous love and the amazing conversations we have together. Also, I am greatly thankful to my undergraduate advisor, Dr. Matthew Karlaftis, who motivate d me and persuade d me to come to the Uni ted States for graduate studies. It was a move that changed my life forever. In clo sing, I would like to thank Debra Anderson, Ines Aviles Spadoni coordinator of STRIDE and Heather Hammontree and Hui Xiong for being the best officemates, plus all my friends within and outside the department who have made my life so special. Life during my graduate studies at UF was so much better than I could ever have imagined.
6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 9 LIST OF FIGURES ................................ ................................ ................................ ........ 11 LIST OF ABBREVIATIONS ................................ ................................ ........................... 13 ABSTRACT ................................ ................................ ................................ ................... 14 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 16 1.1 Background ................................ ................................ ................................ ....... 16 1.2 Problem Statement ................................ ................................ ........................... 17 1.3 Research Objectives, Supporting Tasks and Validation ................................ ... 19 1.4 Document Organization ................................ ................................ .................... 19 2 LITERATURE REVIEW ................................ ................................ .......................... 21 2.1 Congestion Pricing ................................ ................................ ............................ 21 2.2 HOT Lanes ................................ ................................ ................................ ....... 24 2.2.1 HOT Lane Concept ................................ ................................ .................. 24 2.2.2 HOT Lane Benefits and Risks ................................ ................................ 25 2.2 .3 Current Practice of HOT Lanes in the U.S. ................................ .............. 27 2.3 Determination of Dynamic Pricing Strategies ................................ .................... 30 2.3.1 Bottleneck Models ................................ ................................ ................... 30 2.3.2 Network Models ................................ ................................ ....................... 36 2.3.3 Self learning Control Approaches for Dynamic Tolling ............................ 38 2.4 Lane choice Models ................................ ................................ .......................... 40 2.5 Value of Time ................................ ................................ ................................ .... 46 2.6 Traffic Simulation Software ................................ ................................ ............... 55 2.7 Software to Simulate HOT Lanes ................................ ................................ ..... 56 2.7.1 AIMSUN ................................ ................................ ................................ .. 57 2.7.2 DynaMIT and MITSIMLab ................................ ................................ ....... 57 2.7.3 TransModeler ................................ ................................ .......................... 59 2.7.4 DYNASMART P ................................ ................................ ...................... 59 2.7.5 DynusT ................................ ................................ ................................ .... 59 2.7.6 Paramics ................................ ................................ ................................ 60 2.7.7 VISSIM ................................ ................................ ................................ .... 60 2.8 Summary ................................ ................................ ................................ .......... 61 3 ............... 63
7 3.1 GA Procedure ................................ ................................ ................................ ... 63 3.1.1 Ini tialization ................................ ................................ .............................. 63 3.1.2 Selection of Parents ................................ ................................ ................ 64 3.1.3 Crossover ................................ ................................ ................................ 65 3.1.4 Mutation ................................ ................................ ................................ ... 65 3.1.5 Stopping Criteria ................................ ................................ ...................... 66 3.2 Optimizing the 95 Express Tolling Algorithm ................................ .................... 66 3.2.1 The 95 Express Dynamic Tolling Algorithm ................................ ............. 66 3.2.2 Parameter to be Optimized ................................ ................................ ...... 70 3.2.3 Optim ization Objective ................................ ................................ ............. 70 3.2.4 GA Procedure ................................ ................................ .......................... 73 184.108.40.206 Initialization ................................ ................................ .................... 73 220.127.116.11 Selection of parents ................................ ................................ ....... 74 18.104.22.168 Crossover ................................ ................................ ....................... 74 22.214.171.124 Mutation ................................ ................................ ......................... 75 126.96.36.199 Stopping criteria ................................ ................................ ............. 76 3.2.5 Optimized DST ................................ ................................ ........................ 76 188.8.131.52 Base demand scenario ................................ ................................ .. 76 184.108.40.206 Increased demand scenario ................................ ........................... 77 3.2.6 Conclusions ................................ ................................ ............................. 77 4 PRICING OF MULTI SEGMENT HOT LANE FACILITIES ................................ ..... 80 4.1 Multi Segment HOT Lanes in the U.S. ................................ .............................. 81 4.1.1 Toll Structures ................................ ................................ ......................... 81 220.127.116.11 Zone based tolling ................................ ................................ .......... 82 18.104.22.168 Origin specific tolling ................................ ................................ ...... 84 22.214.171.124 OD based tolling ................................ ................................ ............ 84 126.96.36.199 Distance based tolling ................................ ................................ .... 85 4.1.2 Summary ................................ ................................ ................................ 86 4.1.3 Pros and Cons of Toll St ructures ................................ ............................. 86 4.2 The Future 95 Express ................................ ................................ ..................... 89 4.3 Recommendations for Pricing the Future 95 Express ................................ ....... 91 5 ENHANCEMENT OF CORSIM ................................ ................................ ............... 97 5.1 Introduction ................................ ................................ ................................ ....... 97 5.2 Pricing Strategies ................................ ................................ .............................. 9 8 5.2.1 Responsive Pricing ................................ ................................ .................. 98 5.2.2 Closed loop control based Pricing Algorithm ................................ .......... 98 5.2. 3 Time of day Pricing Scheme ................................ ................................ ... 99 5.3 Lane Choice ................................ ................................ ................................ .... 100 5.4 Toll Structures ................................ ................................ ................................ 102 5.5 Summary ................................ ................................ ................................ ........ 103 6 EVALUATION OF THE ENHANCED CORSIM ................................ ..................... 104
8 6.1 Simulating the Current 95 Express ................................ ................................ 104 6.2 Evaluation of Optimized DST for 95 Express Tolling Algorithm Using CORSIM ................................ ................................ ................................ ............ 106 6.3 Simulating the Future 95 Express ................................ ................................ ... 107 6.3.1 Zone based Toll Structure ................................ ................................ ..... 108 6.3.2 Origin specific Toll Structure ................................ ................................ 110 6.3.3 OD b ased Toll Structure ................................ ................................ ........ 113 6.3.4 Distance based Toll Structure ................................ ............................... 113 6.3.5 Toll Variation ................................ ................................ ......................... 113 6.4 Summary ................................ ................................ ................................ ........ 115 7 SUMMARY AND CONCLUSIONS ................................ ................................ ........ 116 APPENDIX: SIMULATING HOT LANES IN CORSIM ................................ ........... 118 A.1 Coding HOT Lane Network ................................ ................................ ............ 119 A.2 Setting the Pricing Algorithm ................................ ................................ .......... 123 A.3 Lane Choice Parameters ................................ ................................ ................ 128 A.4 Toll Structures ................................ ................................ ................................ 129 A.4.1 Zone based Tolling ................................ ................................ ............... 130 A.4.2 Origin based Tolling ................................ ................................ .............. 131 A.4.3 Distance based Tolling ................................ ................................ .......... 131 A.4.4 OD based Tolling ................................ ................................ .................. 132 A.5 Example ................................ ................................ ................................ ......... 132 A.5.1 HOT Lanes Charge Individually ................................ ............................ 132 A.5.2 Zone based Tolling ................................ ................................ ............... 133 A.5.3 Origin based Tolling ................................ ................................ .............. 133 A.5.4 Distance based Tolling ................................ ................................ .......... 133 A.5.5 OD based Tolling ................................ ................................ .................. 134 A.6 HOT Lane Simulation Outputs ................................ ................................ ....... 134 LIST OF REFERENCES ................................ ................................ ............................. 137 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 144
9 LIST OF TABLES Table page 2 1 VOT values for the different choice types ................................ ........................... 48 2 2 VOT estimates for user groups ................................ ................................ ........... 49 2 3 VOT by market segment ................................ ................................ ..................... 50 2 4 USDOT 2011 recomme nded VOTs ................................ ................................ .... 55 2 5 Most widely used traffic simulation software ................................ ....................... 56 3 1 Delta setting table of the 95 Express ................................ ................................ .. 68 3 2 Toll range for the 95 Express ................................ ................................ ............. 70 3 3 DST Parameters subject to fine tuning ................................ ............................... 71 3 4 Performance measures for base demand scenario ................................ ............ 76 3 5 Optimized DST for base demand scenario ................................ ......................... 78 3 6 Performance measures for increased demand scenario ................................ .... 78 3 7 Optimized DST for increased demand scenario ................................ ................. 79 4 1 Summary of multi segment HOT facilities in t he U.S. ................................ ......... 87 4 2 Pros and cons of toll structures ................................ ................................ .......... 89 4 3 Toll ranges for the zones of future 95 Express ................................ ................... 94 4 4 Future 95 Express zoning performance measures ................................ ............. 95 6 1 Comparison of performance statistics for northbound PM peak period ............ 105 6 2 Comparison of optimized and original DSTs ................................ .................... 107 6 3 Value of time ($/hr) ................................ ................................ ........................... 111 6 4 Perf ormance measures of Future 95 Express under zone based tolling .......... 111 6 5 Performance measures of Future 95 Express under origin based tolling ......... 111 6 6 Performance measures of Future 95 Express under OD based tolling ............ 112 6 7 Performance measures of Future 95 Express under distance based tolling .... 112
10 A 1 HOT output explanation ................................ ................................ .................... 135
11 LIST OF FIGURES Figure page 2 1 Optimal congestion toll. ................................ ................................ ...................... 23 2 2 Dynamic Pricing Simulation using MITSIM and DynaMIT ................................ .. 58 2 3 VISSIM HOT lane modules ................................ ................................ ................. 61 3 1 GA Procedure Flowchart ................................ ................................ .................... 64 3 2 Representation of price jump points ................................ ................................ ... 75 4 1 Example of a multi segment HOT lane facility ................................ .................... 82 4 2 Map of the 95 Express after Phase 1 completion; left is southbound, right is northbound ................................ ................................ ................................ ........ 90 4 3 Completed 95 Express. Left is southbound, right is northbound. ....................... 91 4 4 Potential zoning for the 95 Express. Left is southbound, right is northbound. .... 93 5 1 Drive e choice in CORSIM ................................ ................................ ....... 101 6 1 Entrances and exits of the Future 95 Express northbound direction ................ 109 A 1 HOT lane simulation in CORSIM ................................ ................................ ...... 118 A 2 HOT/HOV lane use codes ................................ ................................ ................ 120 A 3 Toll paying vehicles ................................ ................................ .......................... 121 A 4 Free usage vehicles ................................ ................................ ......................... 122 A 5 Specifying network properties in TSIS Next ................................ ..................... 123 A 6 Transponder and registered percentage inpu t ................................ .................. 123 A 7 Pricing algorithms available in CORSIM ................................ ........................... 124 A 8 Delta settings table for responsive pricing ................................ ........................ 125 A 9 Minimum and maximum toll values for responsive and closed loop control based pricing algorithms ................................ ................................ ................... 126 A 10 Model parameters for pricing algorithms ................................ .......................... 127 A 11 Time of day pricing ................................ ................................ ........................... 128
12 A 12 FRESIM calibration ................................ ................................ ........................... 129 A 13 Value o f Time Tab under FRESIM Setup ................................ ......................... 130 A 14 HOT lane output. A) Summary of Inputs B) Output ................................ ....... 136
13 LIST OF ABBREVIATION S AVC Average Variable Cost DST Delta Settin gs Table FHWA Federal Highway Administration GA Genetic Algorithm GP General Purpose HOT High Occupancy/Toll HOV High Occupancy Vehicle ITS Intelligent Transportation Systems LOS Level of Service SOV Single Occupancy Vehicle SRMC Short Run Marginal Cost TD Traffic Demand TTS Travel Time Savings VOT Value of Time
14 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ENHANCEM ENT AND EVALUATION OF DYNAMIC PRICING STRATEGIES OF MANAGED TOLL LANES By Dimitra Michalaka August 2012 Chair: Yafeng Yin Major: Civil Engineering H igh occupancy/toll (HOT) lanes are facilities that combine pricing and vehicle eligibility to maintain s uperior traffic conditions i n the HOT lanes while maximizing I deally tolls should vary in real time in response to traffic conditions in order to achieve the above objective S ince the first HOT lane s were implemented in 1995 the co ncept has become quite popular and widely accepted by many transportation authorities Currently, t here are a pproximately ten HOT lane facilities in operation in the United States Some of them are single segment facilities, that is they have essentially one entrance and one exit, plus one tolling point while others co nsist of multiple segments, that is they have multiple ingress or egress points that are located distantly from each other and more than one tolling point Depending on the toll stru cture i mplemented and where motorists enter or exit, they may pay different tolls. T his dissertation enhances and evaluates dynamic pricing algorithms for HOT lane facilities that consist of a single or multiple segments First, a genetic algorithm optimization procedure to enhance pricing strategies that are already implemented in practice is developed The procedure is demonstrated on 95 Express in S outh Florida
15 which is currently a single segment facility The experiments show that the procedure can yield imp rove ments to the HOT lane operations. Then, the tolling practice for the multi segment HOT lane facilities is outlined and recommendations for the future 95 Express which will be expanded in to a multi segment facility, are made T his research also include s the enhancement of a microscopic simulation tool, CORSIM, to simulate HOT lane operations. T hree main modeling c omponents a re developed, including three pricing strategies, a lane choice module, and four toll structures for multi segment HOT facilities The enhanced software is demonstrated by simulating the current and future 95 Express. T he result is that CORSIM enhancements are able to capture the primary characteristics of HOT lane operations and management.
16 CHAPTER 1 INTRODUCTION 1.1 Background Tr affic congestion has become a severe problem in many societies According to a well cited report (Schrank et al., 2010 ), United States ( U.S. ) congestion levels nationwide have risen significantly since 1982. As travel demand increases, existing infrastruct ure become s more congested and alternative methods are required to manage the traffic flow The construction of new facilities is very difficult due to environmental constraints and limited funding. This has le d transportation agencies to explore other alt ernatives to manage traffic demand Some of them include lane management strategies that can regulate demand, separ at e traffic streams, and utilize available but unused capacity on existing transportation facilities. In recent years, these operational stra tegies have come to be known as The Federal Highway Administration (FHWA) defines managed lanes as highway facilities or a set of lanes in which operational strategies are implemented to respon d to changing conditions in real time Managed lanes include high occupancy vehicle (HOV) lanes, high occupancy/toll (HOT) lanes priced and special use lanes such as express, bus only, or truck only lanes (Obenberger, 2004). HOT lanes are facilities that combine pricing and vehicle eligibility to m aintain free flow conditions on the HOT lanes while maximizing a T hey provide a travel time saving s incentive for high occupancy vehicles (HOVs) as these are allowed to enter the lanes at no monetary cost HOV and special use lanes h ave been used for decades but HOT lanes were implemented much later t he first in December, 1995 on California State Route 91 C urrently, there are more than ten HOT lanes in operation in the U.S Among other
17 factors, the popularity of the HOT lane concep t is due to the underutilization of HOV lanes and the additional option it provides to motorists. Many have expressed concern about the wasted capacity resulting from a low utilization of HOV lanes (Dahlgren, 2002). Thus, converting underutilized HOV lanes to HOT lanes is likely to create a win win situation for both HOT and regular lane users. Moreover, managed lanes provide motorists with the lane operator must ensure a superior level of servic e in order to attract motorists to pay and use the lanes. I deally tolls should vary in real time in response to changes in traffic conditions in order t o achieve the aforementioned objective Currently, there are at least six authorities pricing their to ll lanes dynamically the California Department of Transportation (Caltrans) on Interstate 15, the F lorida Department of Transportation (F DOT ) on Interstate 95, the Minnesota Department of Transportation (MnDOT) on Interstate 394 the Washington Department of Transportation (WSDOT) on S tate R oad 167 the Utah Department of Transportation (UDOT) on Interstate 15 and the Georgia State Road and Tollway Authority (SRTA) on Interstate 85 O ther HOT lane facilities such as Interstate 10 in Houston, Texas impleme nt time of day tolls. More specifically, the tolls vary by the time of day according to a predetermined schedule, which is usually designed based on historic traffic data. 1.2 Problem Statement Many HOT lane facilities are single segment facilities while others consist of multiple segments. A single segment HOT facility has essentially one entrance and one exit. So metime s more than one entrance or exit exist s but they are very close to each other and motorists still pay the same amount in toll s to use th e facility no matter where
18 they enter or exit. In contrast, a multi segment HOT lane has multiple ingress and egress points that are located distantly from each other and there are multiple tolling points in the facility. Depending on the toll structure im plemented and where they enter or exit, motorists may pay different amounts in toll s Similar to the pricing of a single segment facility, the pricing approach for a multi segment HOT facility should provide superior traffic services on the HOT lanes whil e maximizing the utilization of the available capacity of the lanes. Moreover, the approach should avoid creating too much inequality between motorists entering at different points For example, if not priced properly, those who access the HOT lanes via a n entry point further downstream could end up paying much higher tolls for less time savings. In the literature, many studies have been conducted to determine optimal dynamic tolls for congested freeway facilities but many of them focus on idealized and h ypothetical situations to derive solutions while others require too many resources (e.g., much computational time) to be applied in practice Conversely the methods implemented in the field may not give the optimal toll rates for best managing a certain HOT lanes facility. Th us the pricing strategies implemented in practice should be enhanced to be more robust. Also, there are no studies on how to price multi segment HOT lane facilities. In order t o evaluate a proposed pricing scheme or the operation of managed lanes, m icroscopic simulation is very useful (e.g., Zhang et al., 2009). Unfortunately, few traffic simulation programs are able to simulate managed lanes especially HOT lanes and even those that do suffer limitations For example, there are no s oftware tools that
19 can simulate different toll structures for multi segment HOT lanes. Th erefore th ere is a need to enhance the existing simulation software. 1.3 Research Objective s Supporting Tasks and Validation The objective s of this research are firs t to enhance and evaluate dynamic pricing algorithms implemented in practice for single segment and multi segment HOT lane facilities then to present the different toll structures that can be implemented on multi segment HOT lanes and finally t o enhance a microscopic traffic simulation software to simulate HOT lanes operations The enhanced software will be validated by simulating a n existing HOT lane facility. The tasks conducted to achieve the objective are as follows: Conduct a thorough literature revie w in order to identify existing methods and procedures for managed lane operations Develop a procedure to enhance pricing strategies that are already implemented in practice. This procedure is demonstrated by optimizing the pricing algorithm currently imp lemented on the 95 Express in S outh Florida. Outline the tolling practice for the multi segment HOT lane facilities Make recommendations of how to select a tolling structure for a m ulti segment HOT lane facility like the future 95 Express. Enhance the m icroscopic simulation tool, CORSIM, to simulate HOT lane operations. Validate the enhanced software by simulati ng the operations of the current 95 Express. the differen t toll structures for multi segment HOT lanes b y applying all the structures on the future 95 Express. 1.4 Document Organization Chapter 2 presents a literature review of the HOT lanes including the pricing algorithms and current practice for singe segment and multi
20 segment HOT l anes facilities Chapter 2 also reviews the lane choice models used to determine the number of drivers that will choose to travel on the HOT lanes versus the general purpose (GP) lanes. One of the most important component s that affect travelers lane choic e between HOT and GP lanes is the value of time (VOT) L iterature on VOT is also provided Also, Chapter 2 reviews simulation software used to simulate HOT lanes. Chapter 3 describes an optimization procedure to enhance pricing strategies for HOT lanes and then as a case study, it presents the fine tuning of parameters of the pricing algorithm that is currently implemented on the 95 Express in S outh Florida Chapter 4 presents the toll structures for multi segment facilities and recommends one to be implem ented on the future 95 Express. Chapter 5 describes the new components incorporated into CORSIM that enable it to simulate HOT lane operations Chapter 6 focuses on the evaluation of the CORSIM enhancements by simulating the current and future 95 Express a nd it validates the optimized 95 Express tolling algorithm using the enhanced CORSIM. Chapter 7 summarizes the research and presents some concluding remarks Appendix A provides a user guide on how to simulate HOT lanes in the enhanced CORSIM.
21 CHAPTER 2 LITERATURE REVIEW This literature review focuses on methodologies and procedures used or proposed for HOT lane operations It consists of four different sections: introduction to congestion pricing and HOT lanes practice pricing models for determin ing to ll rate s, lane choice models predicting the number of users who will choose to travel on the HOT lanes versus the GP lanes and simulation software that can be used to simulate HOT lane operations 2.1 Congestion P ricing I n many countries, including the U S ., t oll roads, with fixed toll rates that every traveler has to pay, date back at least to the late eighteenth century At that time, t he purpose of tolling was to recover the construction cost or to gain revenue. In the early 1920s, economists and trans portation researchers started to consider tolling as a measure to manage traffic demand and reduce congestion that ha d started to increase in many places (Morrison, 1986). C ongestion pricing or value pricing is a tool for mitigating traffic congestion b ecause it has been observed that people tend to make more socially efficient choices when they face the cost of their actions and the social benefits (Lindsey and Verhoef, 2000). Co ngestion pricing usually leads rush hour travel ers to shift to off peak per iods or to other transportation modes. R emoving even a small percentage of the p eak period volume from a congested facility through value pricing allows the system to perform much better (FHWA, 2006 a ). Congestion pricing involves setting tolls depending on real time traffic conditions This implies that tolls must vary according to time, location, vehicle type, occupancy of the vehicle and current circumstances such as bad
22 weather, accidents and special events Congestion pricing is also used in other pr actices besides traffic, such as determining rates for telephone lines travel hotels electricity, other utilities, and other public services and facilities The U.S. Federal Highway Administration ( FHWA 2006 b ) refers to four types of variable pricing s trategies. The first involves priced lanes with variable tolls on separated l anes within a highway, such as express toll l ane s and HOT lanes while the second includes var iable tolls on entire roadways (i.e. on toll roads, bridges, and existing toll free roads ) during rush hours. The third pricing strategy is applying cordon charges to drive into a congested area within a city and the fourth is implementing area wide charges which are charges per mile on all roads within an area that vary by the level of congestion. The basic theoretical approach to congestion pricing was developed by Pigou (1920) and Knight (1924) who were the first people to propose pricing as a measure to alleviate congestion. Morrison (1986) further developed t he theory of optimal con gestion tolls based on Pigou and Knight work by us ing the speed flow curve to derive the relationship between flow and cost per user. T he most significant effect of congestion was considered to be the cost associated with increased trip travel times wi th an assumed VOT If speed is inverted on the speed flow curve, time per mile is obtained. Multiplying the VOT by the time per mile and adding operational vehicle costs gives the average variable cost (AVC). The extra cost of adding a vehicle t o the flow is the shor t run marginal cost (SRMC). The c ost curves a nd the demand curve that represent the willingness to pay for various quantities of trips are shown in F igure 2 1. In this figure the backward bending portion of the AVC curve is not illus trated because the
23 optimal flow will never occur in this region due to the fact that the same flow can be achieved at a lower cost. Figure 2 1. Optimal congestion toll (Morrison,1986). If there are no tolls ( ) equilibrium will occur at which is the intersection point of the demand and AVC curves. At this point, the additional cost incurred from considering other users exceeds the benefit derived by the last traveler. This happens for all trips beyond point The amount by which the extra cost of these exceeds the additional benefits represents the loss from non optimal pricing. In order to have equilibrium a toll, must be added to the optimal quantity This toll is equa l to congestion externality, which is the difference between the cost a travele r affords (AVC) and the cost he imposes on the society (SRMC). In other words, externality is the congestion cost that each additional user of a congested road or other facility imposes
24 on other users, by slowing down, increasing the risk of accidents, and the like (Carey and Srinivasan, 1993). Kraus et al (1976) and Keeler and Small (1977) further analyzed the congestion problem from a long run pers pective. They argue d that, in a long run analysis, optimal tolls depend on highway capacity cost s due to the fact that optimal highway capacity and congestion depend on the cost of the additional capacity. Kraus et al estimated long pseudo expressway. They found that tolls vary according to the capital cost and with t he location of th e expressway. Keeler and Small took into consideration speed flow relationships for uninterrupted flow condi tions and highway construction costs for the San Francisco Bay Area T heir results indicated that peak tolls vary greatly among the different types of roads. 2.2 HOT Lanes In this section, the general principles of HOT lanes including definition, purpose, objectives, motivation and current practice are summarized 2.2 .1 HOT Lane C oncept HOT lanes are facilities that combine pricing and vehicle eligibility to maintain free flow conditions while still provi ding a travel time saving s incentive for HOVs (Oben berger, 2004). This allows additional HOV lan e capacity to be used while acting as a stimulant for mode shifting. HOT lanes were first advocated by those who believed that congestion pricing can reduce the congestion levels on freeway s because drivers have to pay a specific amount of money in order to use the congested facility. They posited that HOT lanes are the first step for more widespread pricing of congested roads (Dahlgren, 1999).
25 Dahlgren (2002) investigated when to implement HOT, HOV and GP lanes then suggested that a HOT lane seemed to perform as well as or even better than a HOV lane in any circumstance. More specifically, HOT lanes may offer a solution to the issue of under utilization of HOV lanes. The concept of HOT lanes combines two ver y eff ective highway management tools: lane management and value pricing. L ane management includes limited access to designated highway lanes depending desirable level of traffic service is maintained by limiting th e number of vehicles on the designated lanes. The lane management can promote a range of policies such as car pools and transit vehicles to encourage higher occupancy or low emission vehicles to improve air quality or vehicles equipped for electronic to ll collection to improv e operational efficiency (FHWA, 2006 b ). Value pricing includ es the introduction of road user charges that vary over the time of day and according to the congestion leve l. During the peak periods when the volumes are high, even the sh ift of a small number of vehicles can reduce the overall congestion levels significantly and lead to more reliable travel times (FHWA, 2006 b ). 2 .2 .2 HOT Lane Benefits and Risks The implementation of HOT la nes is appealing to transportation authorities beca use it results in many advantages to traffic networks First of all implementing HOT lanes is a n effective way to manage traffic demand during peak periods (FHWA, 2006 a ) and mitigate congestion by giving drivers a financial incentive to seek alternative m odes of transportation, such as carpooling and public transit or to drive during off peak hours (Replogl e, 2008 ). Second HOT lanes offer travel options for saving time and enhance travel time reliability (Obenberger, 2004). Third they improve transit sp eeds and service
26 reliability and prevent the loss of vehicle throughput that comes from a breakdown of traffic flow Also, they help commercial vehicles deliver more products per hour to the ir market s (FHWA, 2006 a ). In addition, converting HOV lanes that are underu tilized to HOT lanes often reduce s traffic in the free lanes by more efficiently utilizing the (Replogle, 2008 ). Furthermore, HOT lanes can decrease turbulence among vehicles because they separate traffic streams reducing the possibility of accidents (Sisiopiku and Cavusoglu 2007). Another important benefit of congestion tolling is that it can take into consideration not only congestion at traffic peak hour s, but also congestion that is caused by such special events as accid ents, sport ing events, parades, construction, maintenance and severe weather conditions (Halem et al, 2007). Another significant benefit of imposing tolls on congested roads is the improvement of the quality of transportation services without an increase in taxes or large capital expenditures by providing additional revenues for funding transportation (FHWA, 2006 b ). The implementation of HOT lanes has many advantages but, as in other traffic manage ment strategies the re is always a risk of ineffective ope ration if tolls are not set appropriately, for instance, in the case of inaccurate traffic forecasts. If inaccurate traffic models are used to predict the tolls, the expectations of toll roads will not be met (Replogle, 2008 ). In accurate t raffic forecasts were used, for instance at Dulles Greenway in Virginia (U.S. DOT, 2006) creating problems in the toll s In addition, the construction of HOT toll collection infrastructure requires funding resources Moreover, consumers view tolls as a direct additional cost or tax, for using the roads spurring many of them to oppose the implementation of HOT
27 lanes (Smith, 2007). How much consumers are affected by the toll payment depends on the ir VOT and the travel time savin gs. 2. 2 .3 Current Practice of HOT Lanes in the U.S. Currently, there are approximately ten HOT lanes constructed in six different states in the U.S. One of them will open by the end of 2012. Each HOT lane facility is briefly described below : The State Rou te (SR) 91 HOT lanes in Orange County California opened in December 1995 and were the first ones implemented in the U.S. T he facility is a four lane, ten mile toll r oad located on the median of SR 91 (OCTA, 2012). The tolls vary over the day to meet the tr affic pattern and ensure that the toll lanes operate under free flow conditions. The exact toll amount is set from a time of day toll schedule that include s the price for each hour on a particular day or holiday. HOVs with three or more commuters are allow ed to use SR 91 for free during mos t hours, except between 16:00 and 18: 00 on weekdays when the y pay half of the posted toll. Priced lanes are separated from free lanes with plastic pylons on SR 91. Sullivan (2000) conducted a study to evaluate the impacts of the value pricing on SR 91. Some of his findings include that the toll lanes attracted a substantial share of the traffic using the SR 91 corridor the congestion in the free lanes was reduced and new trips mostly for non work purposes were induced by the better travel conditions on the facility Furthermore, the number of accidents in the express lanes decreased significantly after the implementation of the tolling. I n San Diego the I 15 HOT lanes opened in December 1996. The facility is sixteen mi les long and has n ine entrances and eight exits in the northbound direction and nine entrances and nine exits in the southbound direction. The facility was initially barrier separated HOV lanes but then solo drivers were allowed to gain unlimited access b y p urchasing a monthly permit ( initially $50, then $70). In March 1998, time of day pricing was implemented. In March 2009, dynamic pricing was implemented on I 15 Express Lanes. Every few minutes, the system will recalculate the per mile toll rate based o n the traffic demand in the corridor, ensuring free flow traffic conditions in the HOT lanes. When a motorist enters the facility, he or she needs to pay the minimum toll, regardless of his or her eventual exit location. I n Houston, Texas, the Katy manage d lanes on the I 10 corridor replaced the HOV lanes in 1998 and be came fully operational in 1999. They are thirteen miles long and consist of two lanes in each direction separated by barriers from the GP lanes. As specified by the Harris County Toll Road A uthority (HCTRA), there are five entrances and three exits westbound and three entrances and five exits eastbound. In addition, there is one e ntrance and one exit to a park and ride lot in each direction where buses can enter and exit the managed lanes (HC TRA, 2010).
28 Vehicles with two or more people and motorcycles can enter the lanes for free from 5:00 to 11:00 and 14:00 to 20:00. For other times, all vehicles must pay a toll to access the managed lanes. The tolls are determined by a toll schedule and vary b y time of day, tolling zone vehicle occupancy and axle count Commercial vehicles with 3+ axles and vehicles towing trailers are allowed to use the HOT lanes by paying $7.00 for each zone regardless of the time of day and the traffic condition s (HCTRA 2010). In November 2000, tol ling was also implemented o n US 290 HOV lanes in Houston. The average number of trips on the HOT lanes increased and the main source of the travelers on toll lanes were those who used to travel in single occupancy vehicles ( SO Vs ) in regular lanes (FHWA, 2006 a ). In Minnesota in May 2005, the MnPass program converted the HOV lanes on I 394 in Minneapolis into HOT lanes. The MnPass HOT lanes consist of three miles of re versible lanes that are barrier separated and eight miles of previously HOV lanes that are separated with double white lines. The tolls vary dynamically every three minutes to maintain the target speed of 50 55 mph on the HOT lanes. The tolls are usually between $0.25 and $4.00, but sometimes can be as high as $8.00 The average price during the peak period is $1.00 to $4.00. The reversible lanes are always tolled, running east between 6 :00 and 1 3:00 and west between 14:00 and 5 :00 The tolls on the HO T lanes are in effect between 6:00 to 10 :00 and 14:00 to 19:00 Mo nday through Friday. For the other hours, HOT lanes are open to all traffic (MnDOT, 2010). In order t o maintain the target speed for all vehicles, the algorithm that adjusts the toll rates is based on the detected traffic density on the HOT lanes, the leve l of service HOT lanes operate at during a certain time, the section type ( diamond or reversible ) and the time of day. When a change in the density is detected by the road table and adjusted (Halvorson e t al., 2006). The toll rates are calculated at each entry point according to the maximum traffic density downstream of each entry point. The rate calculation interval is adjusted so that traffic conditions that change rapidly can be measured. High differen ces between the toll rates in a single calculation interval are avoided. HOT lanes have also been implemented on I 35W in Minnesota. I n Denver Colorado, t he I 25/US 36 managed lane facility opened i n June 2006 It is a two lane, seven miles long facility Solo drivers have to pay a toll to use these lanes while carpools, buses, and motorcycles do not. Prices vary by the time of day based on a predetermined toll schedule One month after its opening, t he usage of this facility had increased by more than 4 6% (Colorado Department of Transportation, 2006). I n Salt Lake City, Utah the I 15 express lanes opened in September 2006 ( by converting HOV to HOT). The facility is forty miles long. There are two entrances and one exit in each direction, and eighteen ac cess points in between where drivers can enter, exit, or over take a slow moving vehicle. Those access points, separated by white dotted striping from the GP lanes, are 3,000 to 9,000 feet long and located at each I 15 interchange (UDOT, 2010a). Vehicles wi th two or more passengers, buses, clean fuel vehicles and motorcycles are allowed to use the
29 HOT lanes for free. Vehicles with a gross weight of 12,000 pounds or more ar e not allowed to use the lanes or the adjacent passing lane to the express lanes. When this system first opened, the SOVs had to buy a monthly decal for $50 for unlimited access to the HOT lanes In August 2010, the express lanes were divided into four payment zones and dynamic pricing was implemented. The Washington State Department of Tr ans portation (WSDOT) opened the SR 167 HOT lanes in May 2008. The HOT lanes are ten miles long and separated by double white lines from the GP lanes. There are six access points northbound and four access points southbound where drivers can either enter or exit (WSD OT, 2008) SR 167 HOT lanes are designed to make the most efficient use of HOV lane capacity while providing fast and reliable trips for buses and carpools. Vehicles with two or more people, vanpools, transit and motorcycles are a llowed to trave l for free on SR 167 HOT lanes. Vehicles that weight more than 10,000 pounds and slow moving vehicles are not al lowed to enter the HOT lanes. On SR 167, the tolls are adjusted every five minutes based on real time traffic condition s to ensure that the traf fic in the HOT lanes always flows smoothly and the speed does not drop below 45 mph. The toll ranges from $0.50 to $9.00. If the traffic on the HOT lanes increases significantly, the signs at the entrances of the HOT lanes ing access of all SOVs In 2008, t he Florida Department of Transportation (FDOT) opened the 95 Express in the Miami area by co n verting about seven miles of the HOV lanes on I 95 into HOT lanes The HOT lane system is planned to be approximately twenty two miles long, extending from the I 95 interchange at SR 112 north to the Broward Boulevard Park and Ride lot (FDOT, 2008) and constructed in two phases. The current 95 Express extends from SR 112/I 195 to the Golden Glades Interchange and has two HOT lanes i n each direction separated from the local traffic lanes with pylons. The northbound express lanes opened to traffic on July 11, 2008 and tolling began on December 5, 2008. The southbound express lanes opened to traffic in late 2009 and tolling began on Ja nuary 15, 2010. Phase 2, currently under construction, will expand the HOT lanes from the Golden Glades to Broward Boulevard in Broward County. The tolls o n the first part of 95 Express depend on traffic conditions and range from $0.25 to $2.65 during the average traffic conditions. During peak hours, tolls can be up to $ 7.25 in order to provide oper ating speeds between 45 50 mph in the HOT lanes. In Georgia, I 85 HOV lanes in the northeast Atlanta area were converted to HOT lanes in October 2011. They are about sixteen miles long and have one lane per direction The toll changes dynamically about every fifteen minutes to ensure uncongested traffic conditions on the HOT lanes Transit vehicles, carpools with three or more occupants, motorcycles, emergency v ehicles and alternative fuel vehicles can access the lanes for free. All vehicles willing to use the HOT lanes should register with SRTA There are five entries and six exits on the northbound direction and four entries and four exits on the southbound di rection
30 In northern Virginia b y the end of 2012, t he Capital Beltway HOT lanes on the 495 Express lanes will ope n on the I 495/Capital Beltway. The y will consist of two lanes in each direction and they will be fourteen miles long. There will be several ac cess points to the lanes. More precisely, there will be six entry and seven exit points on the northbound direction and eight entry and nine exit point s on the southbound direction. Vehicles with three or more occupants will use the lanes for free. Dynamic pricing will be applied on the HOT lanes to control the demand and to keep free flow conditions. The prices will mainly be based on the traffic conditions but it is expected that the toll rate will be from about $0.20 to $1.25 per mile with an average to tal trip cost between $5.00 and $6.00 (VDOT, 2012) More HOT lanes are planned for Texas, California, Oregon, and North Carolina 2.3 Determination of Dynamic Pricing Strategies In this section the models that have been developed over the years to deter min e dynamic pricing strategies are summarized More specifi cally, bottleneck, network and self learning control models are presented 2.3 .1 Bottleneck Models The bottleneck model was introduced by Vickrey (1969) and further developed by Arnott et al. (19 93). It focuses on the time at which motorists want to depart Motorists in this model travel along a single road with a bottleneck or bottlenecks downst ream of certain flow capacity. The b ottleneck model often does n o t take into consideration route choice Vickrey (1969) was the first t o consider trip costs with respect to desired arrival times T ravelers arriving later or earlier than the desired arrival time experience not only the travel ti me costs but also schedule costs The simple bottleneck model i s dynamic, deriving the time pattern of congestion over the peak hour ( Arnott et al, 1999 ; Arnott, 199 8 ). It assumes that every morning a fixed number, of individuals living in the suburbs would like to travel from home, which is the origin, to work, which is the destination, at the same time Each person travels in his own car along a single
31 road connecting the origin and destination whi ch has a bottleneck downstream. Traffic conditions are uncongested except at the bottleneck that has a deterministic capacity of s cars per unit time. Due to the motorists to be at their destination at the same time. As a result, travelers arrive at work at different times, some early and others late Early or late arrivals entail a cost of delay. Furthermore, travelers incur expenses including a fixed component which can be set equal to zero f or comp utational simplification and a variable component which depends on the time spent waiting at the bottleneck. The bottleneck model addres ses of departure from their homes. The basic insight is that the total trip cost including the travel cost, the delay cost and the toll must be constant over the departure interval under equilibrium. For analysis simplification, in the model total trip cost is assumed to be linear in its components as in equation 2 1 : (2 1) where is is the shadow value of queuing time is the shadow value of time early and is the shadow value of time late According to empirical results, (Small, 1982). It is also assumed that a ll individuals have the sa me desired arrival time, (Small, 1982). Let denote the time at which the first traveler arrives to wor k, the time at which the last traveler arrives at work and the variable travel time. During the peak hour the capacity throughput of the bottleneck must be used because in any other case, a traveler could depart in the middle of the peak hour incurring zero queuing cost and less delay cost than either the
32 first or the last person to arrive for the equilibrium consistency. This implies that which means the first individual to arrive does no t face a queue and experience s only a delay cost equal to and the last individual to arrive who also does no t face a queue experiences only a delay cost equal to Under equilibrium, delay costs of the first and last person to arrive must be equa l so the equilibrium price, is equal to Therefore, the travel cost function without toll is If a dynamic toll that equals the queuing cost component in the equilibrium without toll is introduced the queu e will be eliminated without changing the rush hour interval. In this case, every traveler has the same trip cost as before (equilibrium without toll) and as the trip costs have become equ al, no one wants to change his behavior. By i mposing this toll the social optimum is decentralized, the delay cost is minimized, the queuing costs are eliminated and the bottleneck is used at capacity during the peak hour. The amount of travel does no t change while the total social cost is reduced by reallocating the tr affic over the peak hour. The bottleneck model presented above is simple and limited to homogeneous commuters Therefore, many extensions are needed in order to make it more realistic. Over the years, many studies, have consider ed elastic demand, heterogen eous individuals, stochastic capacity and demand, simple networks and alternative congestion treatments, to improve the simple bottleneck model. Arnott et al (1993) also used determ ine the time varying tolls on the traffic ne twork used by Vickrey (1969) They assumed individuals who travel through the network and all want to be at work at the same time but because
33 the bottleneck limits the network capacity, this is not possible and d elay costs are unavoidable. In this model, the social optimum and the distribution of travel delays, the scheduling costs at the peak period, and the duration of the peak are determined endogenously. The optimal toll depends on time and has its maximu m value when drivers arrive at the desired arriv al time. The most important thing in this approach is that private costs of the road use which include the toll, the travel time cost and the delay cost, should be constant over the peak period. Iryo and Kuwahara (2000) considered that travelers choose t heir departure times to minimiz e their travel cost which included the queuing delay at a bottleneck and schedule delay at the destination. They developed a mathematica l model to analyze the traveler s decision assuming one bottleneck with constant capaci ty and FIFO service between a residential area and a working area that must be used by all the commuters. At first, they derived the model without considering the congestion toll and then they applied it to evaluate a dynamic pric e The ir goal was to creat e a tool that can evaluate policies that have been proposed to mitigate congestion such as Traffic Demand Management (TDM) po licies. Specifically, they considered a policy that disperses travel demand over time because individual variation s in time are ver y important when a road pricing scheme is analyzed. Their conclusions after the application of the ir method to road pricing were that dynamic congestion tolls that reduce the waiting time are not proportional to waiting time without the existence of the to lls. Moreover, commuters are likely to change their departure times and that can cause different travel costs for them. This case will not be true if all travelers have the same willingn ess to pay. Finally, they concluded that even though individual s can h ave different VOTs there is a dynamic
34 congestion toll that can reduce queuing delay to zero. In this case, a toll changes Although the single bottleneck model that Vickrey (1969) used gives good insight for travel time s, the optimal toll and its benefits it has an important deficiency. It does no t consider the spatial extent of queues which is a significant aspect in the analysis of extended networks because it gives more realistic patterns to avoid congestion. Yperm an et al (2005) followed the same procedure as Vickrey (1969) but replaced the simple bottleneck model by a traffic flow model in order to take into consideration the road space that is occupied by the queues. Specifically, they used the Lighthill, Whith am and Richards ( LWR ) traffic flow model which considers the spatial extent of queues and at the same time is not a very complicated model. The LWR model assumes that traffic is behaving as in a kinematic wave model. Yperman et al (2005) used a simple multi destination network in their study and tried to determine the advantages of congestion pricing and understanding the mechanisms of congestion equilibrium and system opt imum network conditions using the LWR traffic model. After the analysis, they concluded that congestion can be mitigated if an optimal toll is imposed and that the benefits of introducing this time varying optimal toll are higher than those expected by con ventional point queuing bottleneck models. The toll must be equal to the delay costs that commuters would experience if there were no toll. After imposing the toll, commuters who travel through the bottleneck have the same travel costs as would be the c ase without toll s but their total travel time is less than when there was no toll imposed T he commuters that do not want to use the
35 bottleneck but experience queue s that spill over from the bottleneck have reduced trip costs. Thus, travel demand will in crease without an increase in congestion. Therefore, optimal tolling can lead to reduced trip costs for the travelers, more efficient use of the transportation network and extra revenue for the government. Verhoef (1997) considered a dynamic model of roa d congestion for the determination of time varying tolls. T he model is based on the bottleneck approach but considers elastic demand for the morning peak road usage. Such elasticity of demand could come from the presence of different transport modes. In th is case, the optimal time varying toll should include a time invariant component when drivers share the same desired arrival time. This means that the regulator should have information about set the optimal tolls, because the underlying reason of the time invariant component is the assumption that desired travel times are equal among the users. This time invariant component is relevant only in studies of road traffic congestion with elastic de mand. In this approach, the optimal toll is greater than zero even in the case where congestion, in terms of travel time delays, has been reduced Although bottleneck models that tak e into consideration real world complications give good insight into the amount of tolls to introduce for mitigating congestion levels they do no t incorporate route choice and they always consider a bottleneck on the road. Therefore, bottleneck models cannot be applied to large networks. That problem led researchers to develop models called network models that can include more parameters with regard to individual choices and can be used t o determine pricing strategies o n networks.
36 2.3 2 Network Models In recent literature network models have also been examined to find policie s to alleviate the problem of congestion that is present on most transportation facilities. Network models in contrast to bottleneck models encompass the mode, departure time route choice and longer run choices. The traffic models must be as realistic as possible in order to derive logical and effective poli cies. T here are many types of network models, some of them consider fixed departure times, others variable demand, others many alternative modes, others destination choice route choice or combinati on s of the factors afore mentioned. Some of them are presented in the next paragraphs. De Palma et al. (1997) focused on the efficiency of use of private toll roads assuming a simple ne twork with two parallel routes that can have different free flow travel times and capacity which connect s one origin and one destination. In addition, they assumed that congestion takes the form of queuing and that every traveler has three options: whether or not to travel by car, and if by car, which route and what time to travel. For the analysis, they considered three cases: free access on one of the routes and a privat e road with tolls on the other private roads on both routes and a public road with tolls competing with a private road. In each case, they measured the ef ficiency gain by determini ng the social surplus relative to the efficiency gain if both routes had first best optimal tolls. The conclusion of the study was that the efficiency gain is much higher if to lls are imposed dynamically rather than using a fixed toll in each assumed case Time dependent tolls on a general network are determined by Joksim ovic et al (2005a) using a dynamic traffic model to describe the network performance. They determined the time varying road prices that minimize the total travel time in the
37 network, taking into account the time changes of the route and departure as a respon se to the prices with the formulation of a network design problem. For the analysis, they considered dynamic traffic flows and dynamic road pricing strategies T hey formatted the problem using m athematical p rogramming with e quilibrium c onstraints and analyzed a small and simple network. In their research, they demonstrated that dynamic pricing can lead to savings in the total travel time in the network. F inally, they concluded that it wa s very difficult to find any simple solution to the dyna mic toll design problem in real size dynamic traffic networks because the objective function is non linear and non convex Therefore, it is difficult to find a global optim al solution and optimal toll values T hey suggested that in order to find a global solution to large networks, a global search algorithm should be developed. That was the reason they considered a small hypothetical network to analyze uniform and var iable pric ing. Joksim ovic et al (2005b) considered elastic demand and applied second best tolling scenarios only to a subset of links on the network. They used the same methodology as Joksim ovic et al (2005a) in order to determine the optimal toll. Friesz et al (20 06) introduced a d ynamic o ptimal t oll p roblem with user e q uilibrium constraints (DOTPEC). T hey further presented and tested two algorithms for solving the optimal control representations of the DOTPE C. First they studied a d ynamic e fficient t oll p roblem b y employing a form of dynamic user equilibrium model to compare the efficient tolls with DOTPEC which is not equivalent to dynamic generalization of the static efficient toll problem. Then, they formulated DOTPEC in two different ways and solved it using both a descent in Hilbert space without time discretization and a finite dimensional approximation solved as a nonlinear program algorithm I n their approach
38 t he mathematical representation is detailed enough to capture the behavioral and technological co nsiderations about dynamic tolling and it is considered as a computable theory. 2. 3 .3 Self l earning Control A pproaches for Dynamic T olling The models developed in previous studies always assume that the travel demand is known. These models are often not a pplicable for managing a HOT lane facility. Yin and Lou (2009 ) proposed two practical approaches for the determination of pricing strategies for operating managed lanes. They considered dynamic tolls that change according to traffic conditions in order to maximize the throughput of a freeway and keep superior free flow conditions for travelers. The first approach is a feedback control approach where one loop detector station located downstream is required to detect the traffic condition along a facility se gment. The second approach is a reactive self learning approach that calibrates the willingness to pay using revealed preference information and then determines the optimal toll rate using the approaching flow rates, the estimated travel time and the cali brated willingness to pay. For the implementation of this approach, two loop detectors ar e required, one before the toll entrance to detect approaching flows and one after the entrance to detect the flows on both the managed and the regular lanes. For the conducted. The conclusions of this research were that although both approaches are simple and easy to implement, they may lead to drastically varying toll pattern s that can cause unstable traffic con ditions. Moreover, the toll price is determined for each entry point without considering other entries which may create inequality among motorists that enter the managed lane from different points.
39 Lou et al. (2011) further expanded the approach proposed by representing traffic dynamics more realistically and with an explicit formulation t o optimize tolls. The impacts of the lane changing before the entrance to the toll lanes on the freeway and the travel time s are considered using the multi lane hybrid tr affic flow model that was proposed by Laval and Daganzo (2006). The optimal tolls we re determined for specific throughput and to ensure that the density of HOT lanes w ill not exceed the desired HOT lane operation density. They also further examined the conversion of HOV lanes to HOT lanes and presented some extensions to the approach that they proposed considering more realistic cell representations for differences in H OT lane slip ramp configurations. For the validation and demonstration of the approach, simulation experiments were conducted using data from loop detectors. The self learning framework proposed by Yin and Lou (2009) and Lou et al. (201 1 ) is reactive in na ture and may perform unsatisfactorily if there are substantial fluctuations in traffic demand. For this reason, Michalaka et al. (2012) enhanced that framework by developing a robust scenario based toll optimization model that determines a proactive dynami c pricing strategy to accommodate traffic demand uncertainty and effectively manage HOT lanes under various conditions. The toll s we re optimized to ensure free flow conditions on HOT lanes while maximizing a freeway throughput. Simulation experiments wer e conducted to validate the proposed approach Then, the robust scenario based approach was compared with the one currently implemented on the 95 Express It was observe d that the new, more robust model operates effectively on the HOT lane facility and pro duces a smoother toll pattern and better system performance
40 than the current 95 Express approach. Moreover, the robust approach responded more adaptively when there was a sudden demand surge. Zhang et al. (2008) also developed a feedback based dynamic tol ling algorithm for HOT lane operations. They used a second order control scheme to relax the complexity of the calculations. First, the optimal flow ratio for the HOT lanes was calculated using feedback control logic with an increment piecewise optimal fun ction of traffic speed measured from the GP and HOT lanes. Then, the toll was estimated using a discrete route choice logit model. By decomposing the calculations, the tolling algorithm becomes more practical and effective. An external HOT lane module in M icrosoft Visual Basic and VISSIM were used to examine the performance of the proposed algorithm. Five HOT lane sections on the southbound SR 167 corridor in Washington State were simulated and the results showed that the proposed method performs well under various traffic demand scenarios. Currently, the approaches that are used to determine dynamic tolls depend on the availability of data, modeling software, model structure and the objective of the study. 2.4 Lane choice M odels In the areas where HOT la nes exist, motorists have the choice of traveling on either the HOT or the GP lanes. Choosing the HOT lanes means that they have to carpool or pay a toll but at the same time they will save some travel time and their trip will be more reliable Sometimes the choice between HOT and GP lanes is referred to as a route choice because HOT lanes are basically a n alternative parallel route to the GP lanes with different cost and travel time. Knowing how many vehicles will choose to travel on the HOT lanes in the presence of a specific toll and the factors that affect
41 choice is very important for effective HOT lane operation. F ollowing are some s between HOT and GP lanes. Sullivan (2000) conducted an extensive stud y to evaluate the impacts of the implementation of HOT lanes on SR 91 in California. This study analyzed many aspects of travel behavior o n the corridor including traffic trends, driving conditions, transit, corridor travel behavior, assessing public opin ion, modeling of travel choice and elasticities, collision trends and characteristics and others. Here, the three models related to travel choice are presented. The first travel choice model included the route choice only assuming other factors such as t ransponder choice exogenous T he second one included route choice, mode choice and transponder choice T he third one included route choice, transponder choice and time of day. Many variables about travelers and trip characteristics were included in each model. The route choice model was a conditional multinomial logit model that showed that women, people 30 to 50 years old and professional s are more likely to use the express lanes. The route choice, mode choice and transponder model was a nested logit model with mode choice in the upper nest and joint transponder and route choic e at the lower nest. That model indicated that getting a transponder in order to use the express lane was a barrier for male s people with lower education, and people younger tha n 30 and older than 50 years of age The results were consistent with the route choice model. The route choice, transponder choice and time of day model was also a nested logit model with time of day in the upper nest and joint transponder and route choic e again in the lower nest. The results of this model were comparable with the results of the other models An additional result was that travelers do not very commonly shift to traveling during
42 different times of day The travel choice models described abo ve are also published by Yan et al. ( 2002 ) Lam and Small (2001) also modeled the route choice on SR 91 in Orange County, California collecting data from surveys and traffic loop detectors. They developed a route choice only model and a route choice, mode l choice and transponder choice as Sullivan (2000 ) as well as models for route and time of day, route choice and mode choice, and route choice and transponder choice. Each model include d many socio economic and trip characteristics variables More specifi cally, it was assumed that a traveler, chooses route by maximizing the conditional utility function 2 2 : (2 2 ) where and are the measures of travel time, variability in travel time and cost, respecti vely for each route and traveler is a vector of observable socio economic characteristics such as age, gender, annual household income, language spoken at home, wage rate, education, and other characteristics like flexibility of work arrival times and car occupancy ; and is a random utility component. The model s with the route choice only were binomial logit models and suggested that people, who l ive in a high income household, speak English at home do not have route options other t han SR 91, and females are more likely to use the HOT lanes. For the route and the time of day to work choice combination, multinomial and logit models were run. The models showed that males and older workers are more likely to arrive early at work. For t he models of route and mode choice carpooling was assumed to be an endogenous factor and travelers could choose between three modes: driving alone, carpooling with one other person (HOV2) and carpooling with more than one other
43 person (HOV3+) In th ese c ase s three models were run; one with mode choice alone and two with mode and route choice, a logit and a nested logit. The models indicated that long distance trips, foreign language speaking, and a large workplace favor HOV3, while low car ownership and low education levels favor HOV2. For the case of route and transponder choice, a transponder choice model a transponder and route choice logit model and a transponder and route choice nested logit model were estimated. The results showed that income, gen der, and language influence the transponder choice more than the route choice. At the last logit model transponder, route carpool choice, gender, the distance of the trip, the number of worker s in the household and the number of cars shared by the househ old seem ed Li (2001) also used survey data from SR 91 trying to explain the factors that influence motorists to use the HOT lanes. For this purpose, Li examined five nested multivariate logistic regression models. The first mod el tested the effects of travel characteristics like trip purpose, trip length, vehicle occupancy, and travel frequency on SR 91 financial capability, that is, level of household income in addition to the variables in the first model D emographic characteristics such as gender, number of children in the household (indicating the household type) household size, and age were added to the variables of the first and second model The fourth an d fifth models included various variables representing different trip purposes. The only differen ce between the last two models wa s that the fourth model uses home to work trips as the reference category as oppo sed to the fifth model that uses work to home as the reference category. The results showed that as the age of the travelers increases so does the probability of them
44 choosing the HOT lanes I ncome significantly influenced lane decision with people with higher income being more inclined to use the H OT lane s I n teresting finding s were that trip length, gender, household size, and household type did not seem to affect the lane decision and the fact that motorists were more likely t o use the HOT lanes in the work to home trip than the home to work or an unrelated trip. Small et al. (2005a ) also on SR 91 using both state and revealed preference data from three different surveys conducted in the area T he data included d hypothetical choices motorists could make between express and GP lanes under different travel conditions. Small et al. simultaneously examined three choices motorists had to make. The first one was whether or not someone will install a transponder to hav e access to the express lanes, the second was to whether they will use the express lanes or the GP lanes and the third was whether they will travel with one, two, three or more people in the vehicle For the analysis, discrete choice modeling was applied indirect utility assume d to be random and equal to: (2 3) where indicates the alternative, the traveler, and the attributes associated with alternative includin g the toll, travel time, and trip rel iability is a vector of preferences, is a vector of explanatory variables of traveler including age, sex, household size, per capita income, and trip distance is a vector of the parameters to be estimated statistically is a vector o f random variables of traveler and is the error term. Small et al. (2005a ) examined more explanatory
45 traveler variables like occupation, education, workpl ace size, and arrival time flexibility but they proved not to have much explanatory power. The multinomial logit model results showed that toll, travel time and reliability aged women and all commuters were mo re likely to get a transponder and middle aged women with large families were more likely to carpool which make sense as many family members may travel together. Another finding was that women, middle aged motorists, and motorists in small households were more inclined to choos e the express lanes. Bro wnstone et al. (2003) studied travelers choice s of driving alone on the GP lanes, driving alone i n the express lanes, and carpooling using revealed preference panel survey data at the I 15 in San Diego around the Express lanes area Their model was a conditional logit model with all the choices available to all travelers. The results showed that households with income greater than $100,000, women, persons 35 to 44 years old, persons with a graduate degree, and homeowne rs we re more likely to choose the express lanes. Also, it seemed that the express lanes were chosen both for commut ing and long distance trips. A s the number of wo rkers in the vehicle increased for long trips, for non commuting trips and when the re was a carpool bypass on ramp available carpooling was preferred Burris and Xu (2006) conducted a study on the potential SOV demand for traveling on HOT lanes using state and revealed preference data from the travelers on the GP lanes at the Katy Free way and Northwest Freeway corridors in Texas. Discrete choice modeling was implemented to analyze the data and more specifically a nested s Nine potential
46 mode choices were assumed. Each of them was a combination of mode (SOV, HOV2, HOV3, transit), lane (GP, HOV) and on off peak period choice s For example, one mode was SOV on the HOV lane in the off peak period. Some of the variable s used in the model were travel time savings, toll divided by the income, household size, vehicle indicated that people with high income are more likely to use the HOT lanes and that motorists traveling on the Katy F reeway were willing to pay more than the ones tra veling on the Northwest F reeway. This fact may be based on the difference s i n income level s As it can be seen from the above studies, there are many models that can be used to model travelers' la ne/route choice s In addition, the factors that affect each choice are equally numerous al though not all of them are included in every model. However, travel time and cost are always considered in the lane choice models. These two factors indicate how muc h motorists value their time and how much they are willing to pay to switch lanes. A literature review on how much drivers value their travel time is presented in the following section. 2. 5 Value of T ime Value of time (VOT) often used in transportation studies and economics, is the cost traveler s are willing to pay to save time or the amount of money they would accept for lost time ; it is usually expressed in dollars per hour highly affected by their VOT. There are several studies that examine the factors that influence it. It should be mention ed that VOT can be different among roadway users and vehicle groups; SOVs HOVs and commercial vehicles. The following literature mostly focuses on studies examining
47 Small (199 2) used discrete choice modeling to specif y a utility function that enables VOT calculation to include such socioeconomic characteristics as income Then he applied a technique to find the conditional indirect util ity function and estimate VOT as the marginal rate of substitution between cost and time without having to solve the entire choice model. In the model, he assumed that the average VOT for work travel is 50% of the gross wage rate but he mention ed that it can vary from 20 to 100% depending on the city and population group. It was concluded that the VOT is affected by the trip purpose, income or wage rate and where the time is spent (in a vehicle or walking or waiting) T he average estimated VOT was equal to $4.80 per hour. Brownstone et al. (2003 ) from a congestion pricing project on I 15 in San Diego California The data used were obtained from a panel survey and loop detectors and includ ed such trip characteristics as travel time, toll, mode choice and trip type, demographic characteristics by mode choice such as age, gender, education level, reason for travel, household income, home and vehicle ownership and number of workers in the hou sehold. Assuming that each traveler had three mode alternatives: solo driving on GP lanes, solo driving on express lanes, and carpooling they estimated a conditional logit model and computed the VOT using equation (2 4) : (2 4) where is the co effic ient of the travel time savings, is the coefficient of the toll value on the express lanes, and is the reduction in variability of time savings from express lane use measured as the difference between
48 the 90 th percentile and median time savings. They found that the median VOT is $30 per hour with the upper quartile of the distribution equal to $43 per hour and the lower equal to $23 per hour. In their study, VOT is not reported as a percentage of an hourly wage because individual income data were not available. Lam and Small (2001) studied VOT using actu al travel behavior data from SR 91 in Orange County, California. The data including both socio economic and travel characteristics such as age, gender, income, education, flexibility of work arrival time route, mode and transponder choice travel time and toll per person were collected from mail surveys and traffic loop detectors Using the available data, they examined five choice combinations and for each combination they estimated three to four different models. The VOT was computed using formula (2 5) : (2 5 ) w here indicates the traveler, the utility, the cost The computed VOT for the best fitting model in each of the five choice categories is presented in Table 2 1 Table 2 1 VOT values for the different choice types Type of choice VOT ($/hr) Route 19.22 Route and time of day 4.74 Route and mode 24.52 Route and transponder 18.40 Route and transponder and mode 22.87 The route and ti me of day model s gave much lower VOTs than the other models which as they claimed, cou ld be a result of either upward biased VOT estimation s from the other models or inaccurate assumptions for a trip outside the study range. The other
49 models gave VOT s fr om $18.40 to $24.52 per hour. The best fitting model was the one that gave a VOT equal to $22.87. Small et al. (2005a ) also used data from SR 91. The data, however, included not only actual travel behavior data but also stated preference data. A s mention e d in the previous section, a multinomial logit model was developed to try to examine the factors s between the express lanes and the GP lanes; obtaining a transponder or not; and how many people w ould travel in the vehicle. For this model, the VOT was computed for all road users and for the express lane user s and free lanes users separately by dividing the coefficient of travel time by the coefficient of the cost for each group The median VOT estimates as well as the 5 th and 9 5 th percentile s for a 90% confidence level are presented in Table 2 2 The median VOT value was $19.63 per hour which was about 85% of the wage rate. The average wage rate estimated to be equal to $23 was obtained by matching the data from the U.S Bure au of Labor Statistics for 2000 Small et al. (2005b) in another study using the revealed preference data from Small et al. (2005a) found that the median VOT is $21.46 per hour or about 93% of the wage rate Table 2 2 VOT estimates for user groups VOT ($/h) 90% confidence interval Median 5 th percentile 95 th percentile All users 19.63 8.75 34.61 Express l ane users 25.51 11.50 39.99 GP lane users 18.63 7.76 29.08 Outwater and Kitchen (2008) used Global Positional System (GPS) data collected from the Puget Sound Regional Council (PSRC) for 275 households to derive the revealed VOT for different auto market segments. The auto market segments under
50 analysis included single occupancy vehicles, carpool s, vanpools and trucks. During the survey, participants were given a financial incentive t o avoid routes with high tolls so their choices between paths with short travel time s but high tolls and paths with longer travel times but lower cost could be o bserved. The paths with short travel times and high tolls were defined as control paths while the others as actual or experimental paths. The VOT for each market segment was calculated as: (2 6 ) where is the difference between the experimental and the actual toll in cents and is the difference between the experimental and the control travel time in minutes. Table 2 3 summarizes all the VOT results. Tabl e 2 3 VOT by market s egment (Outwater and Kitchen, 2008) Vehi cle type Income VOT ($/h) SOVs Low Income 9.52 Home based w ork SOVs Low medium i ncome 17.65 Medium high i ncome 26.09 High i ncome 33.33 Non w ork SOVs All i ncome groups 15.68 Carpool and Vanpool AM Peak Midday PM Peak Evening Night HOV2 All i ncome groups 30.33 19.34 23.00 20.56 26.66 HOV3+ All i ncome groups 38.34 21.35 27.01 21.35 34.57 Vanpools All i ncome groups 102.49 37.38 59.08 37.38 88.02 Trucks Light trucks 40.00 Medium trucks 45 .00 Heavy trucks 50.00 From Table 2 3 it can be seen that VOT varies significantly across the different auto market segments, income groups and time of day.
51 In this paragraph, two VOT studies conducted in Sweden are presented. First, A lgers (1995) exam ined the national Swedish VOT t aking into consideration that the VOT may vary with the user, mode and trip characteristics. H e calculated the VOT for different modes ( cars, air, long distance using regional train, and long distance using regional bus ), trip type (business or priv ate), household type (singles, two employed with children, and two employed without children) where the time is spent (in vehicle, transfer or frequency for the bus and train modes and delay for long distance tr ain only ) and the trip distance (under and over 50 km) He analyzed state preference data collected as part of the 1994 Swedish VOTs study by phone survey using multinomial logit models. The VOT values in the original paper are given in Swedish kronos (SE K) so they are not presented here. Nonetheless the VOT varied from approximately $3.8 0 per hour for a non commuting trip less than 50 km long to $28.8 0 per ho ur for high income households with two employed people and children when traveling for 50 km or more. Second, Algers et al. (1998) developed eight logit models to compute the VOT for long distance car trips using the same data as Algers (1995) Their focus was to examine how VOT varies if instead of a traditional multinomial logit model, a mixed logi t model is used. The difference between these two models was that in the mixed logit model, the user specific parameters can vary across the population Three main explanatory variables were used: cost, in vehicle time and an alternative specific constant for the base alternative By allowing possible combinations of normal and fixed parameters for the explanatory variables, eight different logit models were developed From the results, t hey observed that VOT is highly dependent on how the models are speci fied and more specifically the values are lower when the model coefficients are
52 assumed to be normally distributed rather than fixed. In their best model, the median VOT was about $7.96 per hour However, w hen the parameters were fixed, the VOT was about $12.4 0 per hour. The findings of Algers et al. (1998) differ from Brownstone and Train (1999 ) and Train (1998 ) both of who m found that the estimates in a mixed logit specification we re close to those in a traditional logit specification Brownstone and T rain (1999 ) stated that the insignificant difference s in their results m ight be because the standard logit model they used captured the coefficients well Sullivan (2000) also conducted a VOT study as part of S tudy to Evaluate th e I mpacts of the SR 91 Value SR 91 Express lanes which opened in 1995 in San Diego, w ere the fi r st HOT lanes to open in the U.S. Since the lanes opened, extensive amount s of data, including field observations, surveys and other sou rces, w ere being collected to examine changes in the traffic patterns, driver s behavior s, and public reactions. Five years later, the collected data were analyzed. The VOT was calculated in two ways. First, the travel time saving s on SR 91 and the amount of toll travelers paid were considered It was found that in 1997 the VOT per vehicle was at least $13.75 per hour during the peak hour but by 1999 only about $6.00 at the same peak hour. These values assume that the data derived from loop detectors and t he travel time savi ngs estimated by the travelers we re accurate. Next the VOT was calculated from several multinomial and nested logit lane choice models as the ratio of the cost and time coefficients. The first group of multinomial models considered many choice specific variables and traveler and trip characteristics including age, gender, number of children in the household, occupation type ( professional manager ial, or otherwise ) education, distance, time of
53 trip, flexibility in the working schedule and others but not income. These models gave VOTs from $15.98 to $17.16 per hour. Then, the income was added to the previously defined models to examine the e ffect s on the route choice and VOT The average VOT from $14.95 to $17.89 per hour included the VOT for the high income people which was from $22.32 to $29.22 per hour and the VOT for low income people which was from $10.20 to $11.49 per hour. Further, nested logit models were estimated to simultaneously model the mode, transponder and route cho ice. From these models, the VOT fell between $ 14.74 and $15.18 per hour. Also the time of day, transponder, and route were modeled and the subsequent VOT was between $13.31 and $15.77 per hou r. In the majority of the model estimates VOT varied between $1 3 .00 and $16 .00 per hour. In a ll the studies mentioned above discrete choice models were used to estimate travelers VOT. On the other hand, Ozb ay and Yanmaz Tuzel (2008) took an analytical approach. They used data from the New Jersey Turnpike where t im e of day pricing is implemented to s and/or mode and departure tim e choices under time of day pricing. In their model formulation, the objective function is to which includes the travel time, the tim e spent on other activities, travel cost, cost of other activities, income, available time, departure time, and early or late arrival time derivative of the objective function with respect t o travel time and the partial derivative of the objective function with respect to travel cost Twelve models were estimated; six for the travelers using electronic device (in this case E Zpass users) and six for the ones paying by cash. For each of these traveler group s the models developed were based
54 on three departure time periods (pre peak, peak, post peak) and two trip purposes (work and leisure) The VOT was computed only for the E Zpass holders because the toll related parameters proved to be statis tically insignificant for the cash users. For each individual, VOT was affected by the trip purpose, departure time choice, travel time, toll income, departure time and desired arrival time I ts average varied from $15.33 to $19.72 per hour across the di fferent models It is worth not ing that the highest average VOT was for travelers who depart ed at the peak period and mad e work trips while the lowest VOT was for travelers who depart ed after the peak period and we re going for leisure. In 1997, t he U.S. Department of Transportation (USDOT) de veloped and published its first manual for the valuation of travel time in economic analysis to be used by analysts in studies related to travel time and cost. In the manual, it is mentioned that each VOT estimation d epends on a large number of factors. Some of the factors can be measured and others not. Thus in a study not every parameter can be controlled Some of the parameters included trip purpose which was di vided in to business personal or leisur e and personal characteristics like age, sex, education, employment, hourly income, and mode characteristics like comfort, privacy, travel time, and travel cost The manual recommend ed different VOTs for different trip purposes, transportation modes, trip lengths and vehicle operators (e.g., car/SUV drivers, truck drivers, bus drivers, transit rail operators, locomotive engineers, and airline pilots and engineers). These VOTs were updated in 2003 and in 2011. In summary, Table 2 4 provides the recommended VOTs and the ir plausible ranges as presented in th e latest version of the manual.
55 Table 2 4 USDOT 2011 r ecommended VOTs Recommended Hourly VOT Savings (2009 U.S. $ per person hour) Category Surface m odes (except high speed r ail) Air and high speed rai l t ravel Low Recommended High Low Recommended High Local t ravel Personal 8.40 12.00 14.30 Business 18.30 22.90 27.50 All purposes 8.90 12.50 14.90 Intercity t ravel Personal 14.30 16.70 21.50 27.40 31.90 41.00 Business 18.30 22.90 27.50 45.80 57.20 68.60 All purposes 15.20 18.00 22.80 34.80 42.10 52.20 Truck d rivers 19.80 24.70 29.60 Bus d rivers 19.60 24.50 29.40 Transit rail o perators 32.30 40.40 48.50 Locomotive e ngineers 27.40 34.40 41.20 Airline pilots and e ngineers 60.90 76.10 91.30 From the literature review on VOT, we can see that there is high variability in the VOT estimations. D epending on and even the modeling procedure, VO T can vary from a few dollars to more than $70 per hour 2.6 Traffic S imulation S oftware Traffic simulation is very useful in design ing and /or evaluat ing pricing schemes and other managed lane operation al strategies (e.g., Zhang et al., 2009). The followin g paragraph s review the current practice of simulating HOT lane operations using traffic simulation softwar e. Traffic simulation software is a tool used by transportation engineers and planners to replicate real world transportation situations and test dif ferent design and operation
56 strategies. There are three types of traffic simulation models based on the scale used to describe traffic conditions: microscopic, mesoscopic and macroscopic. Any of these can be used for the simulation of traffic conditions. I n the transportation field, there are many simulation programs developed to accommodate the needs of the transportation industry However, only a few of these programs are capable of simulat ing certain aspects of the HOT lane operations Table 2 5 shows th e most widely used traffic simulation software, the company / university where they were developed the scale used to describe the traffic conditions and their ability to simulate HOT lane operations. Table 2 5 Most widely used traffic simulation softwar e Software name Developer Scale Ability to simulate HOT lanes AIMSUN 6.1.3 Transport Simulation Systems (TSS) Microscopic/ Mesoscopic / Hydrid Yes TSIS 6.2 ( CORSIM ) Mc Trans Microscopic No DynaMIT MIT Microscopic Under development DYNASMART P UMD Limite d DynusT DynusT Team Microscopic Yes MITSIMLab MIT Microscopic Under development Paramics The Edinburgh Parallel Computing Centre and Quadstone Ltd Microscopic Limited Synchro/ SimTraffic Trafficware Microscopic No TransModeler Caliper Corporation Mic roscopic/ Mesoscopic/ Macroscopic Yes VISSIM 5.4 PTV System Software and Consulting GMBH Microscopic Yes WATSIM KLD Associates Microscopic No 2.7 S oftware to S imulate HOT Lanes This section describes the software programs that are able to simulate HOT lane operations to some extent, the procedures used to accomplish that and also the software that the simulation of HOT lanes is under development
57 2.7 .1 AIMSUN AIMSUN is a traffic simulation program developed and distributed by Transport Simulation Syst ems (TSS). It contains mesoscopic, microscopic and hydrid components that allow for traffic simulation o n any scale and degree of complexity. According to TSS ( 2012), AIMSUN can be used for feasibility studies of HOT lanes. Unfortunately, a document that d escribes the components pertinent to HOT lane simulation could not be obtain ed 2. 7 2 DynaMIT and MITSIMLab DynaMIT is a real time traffic microscopic simulation program developed by the Massachusetts Institute of Technology (MIT) Intelligent Transportati on Systems (ITS) Program It is based on dynamic traffic assignment and has two versions: DynaMIT R and DynaMIT P version. It includes models of travel demand, travel behavior, netwo rk supply, and their interactions (Ben Akiva et al., 201 2 ). MITSIMLab is a simulation program, also developed by the MIT ITS Program to evaluate the impacts of alternative traffic management system designs at the operational level and to assist in designi ng a system (MITSIMLab, 2010). It consists of three modules: the Microscopic Traffic Simulator (MITSIM) that has the ability to represent the road network and its components in a microscopic scale, the Traffic Management Simulator (TMS) that mimics the tra ffic control and route guidance systems and Graphical User Interface (GUI) for demonstrating the simulated models through animation. I n a presentation by Rathi and Koutsopoulos ( 2007 ) it was described how to simulate dynamic pricing using MITSIM and DynaM IT. P ricing is one component of a
58 closed loop framework. This framework uses network state information from DynaM IT and provides information as an input to the MITSIM traffic simulator. After MITSIM runs, the output surveillance sensor data are then used b y DynaMIT to simulate the network stat e. This closed loop framework is illustrated in Figure 2 2 In the same presentation, Rathi and Koutsopoulos talked about the models and functionalities that should be implemented into DynaMIT and MITSIMLab in order to be able to simulate the operations of the HOT lanes. More precisely, they mentioned that models regarding the definition of classes of HOVs, the ability to specify HOV lanes in the network, the access type to HOT lanes (restricted or not), the pricing str ategy, the mode choice, both the pre trip and en pricing, the driving behavior ( concerning merging and lane selection ) and the availability of information to travelers should be incorporated into DynaMIT and MITSIM. Based on the information obtained from the MIT ITS Program website ( MIT 2011), all these model ing elements are not yet fully implemented within DynaMIT and MITSIMLab. Figure 2 2 Dynamic Pricing Simulation using MITSIM and Dyn aMIT ( Source: http://www.trb freewayops.org/sim_model/AnnualMeeting2007/HOT_Lanes_ MITSIMLab.pdf )
59 2. 7 3 TransModeler TransModeler is a traffic simulator devel oped by Caliper Corporations to simulate transportation networks in microscopic, mesoscopic and macroscopic scale (Caliper Corporation, 2011). It provides the functionalities to simulate many types of facilities, networks and applications including HOT la nes TransModeler can simulate pricing schemes that vary tolls based on vehicle occupancy, prevailing demand, and time of (VOT), cost sensitivity in route choice decision m aking, economic and operational impacts of various toll lane pricing strategies, HOT lane revenue, and HOT lane utilization under different scenarios ( Caliper Corporation, 2011 ). TransModeler has been used to simulate the HOT lane operations on the Capital Beltway (I 495) in Virginia. 2. 7 4 DYNASMART P DYNASMART P is the planning version of a dynamic network assignment simulation model that was previously developed by researchers at t he University of Maryland (UMD). I t is supported by the FHWA and distribu ted through Mc Trans It supports the evaluation of ITS options, network planning and traffic operations decisions, and production of policy relevant traffic assignment results for planning analyses (Mc Trans 2011). DYNASMART P can be used to simulate netwo rks with HOV lanes, HOT lanes, ramp metering, potential accidents and other operation strategies. Basically, it is able to evaluate HOT lane operations but it does not have any built in feature to simulate the behavior of the travelers in the presence of HOT lanes. 2.7.5 DynusT DynusT is a dynamic network assignment simulation model (DynusT, 2012 ). It can be used to simulate networks with HOV lanes, HOT lanes, ramp metering, potential
60 accidents, and other operational strategies. Regarding HOT lane simula tion, users have the cho ice of two different toll types : a distance based toll, and a link based toll. These tolls can be updated dynamically based on congestion levels by an iterative algorithm, whose objective is to maintain the HOT target speed. The dri GP and HOT lanes depends on congestion levels and their value of time, which is specified by the model user. This feature is useful for planning purposes but cannot be applied to simulate real time operations, because of its itera tive nature. 2.7.6 P aramics The commercial version of Paramics was developed by Quadstone, and is now maintained by Pitney Bowes Software. Paramics is capable of simulating HOT lanes with complex dynamic demand requirements or simple time based schedules ( Pitney Bowes Software, 2012 in route based on cost/benefit assessment. 2.7 .7 VISS IM VISSIM is a microscopic traffi c simulation tool part of the Vision Traffic Suite developed by the PTV Group. In the VISSIM product brochure, one of the features mentioned is the simulation of HOT lanes (PTV Vision VISSIM, 2012) Based on a presentation during the Transportation Resea rch Board ( TRB ) 86 th Annual Meeting (Dale, 2007) there we re three VISSIM HOT lane modeling options. The first is to define static routes between HOT and GP lanes prior to simulation; that is, the user predefines the demand percentage that will enter the H OT lanes at a specific time interval The second option is to allow dynamic choice based on the downstream section toll price T he third option allow s dynamic choice based on the downstream path cost. In the
61 second option, the user specif ies where the traf fic downstream of a HOT entrance would be monitored, the toll pri ce model, and the choice model However i n the third opti on where entire routes could be taken into account, HOT lane demand i s based on the path costs by assigning OD matrices. When using a dynamic option (option two or three), toll price depends on the current traffic density. The user has to set a toll price for a certain traffic density interval. Whenever a certain traffic density is realized, the toll applied is the one that was specifie d for that certain traffic density. For example, in Figure 2 3, the traffic density detected was 36.6 vehicles per mile per lane (vpmpl) so the toll for the density interval 35 vpmpl to 40 vpmpl was implemented which was equal to $3.50. VISSIM also provide s a component object model interface (COM), allowing users to expand on its main built in modules. For example, Zhang et al. ( 2009 ) built an external module in Microsoft Visual Basic, to enable the HOT lane simulation for evaluating the Washington State Ro ute (SR) 167 HOT Lane Pilot Project Figure 2 3 VISSIM HOT lane m odules ( Source: http://www.trb freewayops.org/ sim_model/AnnualMeeting2007/HOT_Lanes_VISSIM .pdf ) 2. 8 Summary T his literature review focuses on the different components of HOT lane operations and the tools that can be used to simulate them. Although a large number of studies
62 about HOT lanes that consider different aspects of dynamic tol ling ha ve been conducted, there are issues that have not yet been solved. For example, many studies consider idealized situations, make a large number of assumptions or require too much computational time to provide reliable and robust results. Therefore, the prici ng algorithms implemented in practice are generally heuristic in nature that includ e many parameters that are determined using trial and error or engineering judgment. These algorithms could be optimized to better manage the HOT lane facilities. Also, even though there is some information available explaining the toll structure of the already implemented HOT lanes, no research has been found on the issue of pricing multiple segments in the same HOT facility. Moreover, i n the literature, there are many stud HOT and GP lanes that show that motorists make their lane choice considering many factors such as the purpose of the trip, the travel time savings, the cost of the trip, and the reliability of the trip Furthermore, t he literature indicates VOT has high variability and d s characteristics Additionally among the existing traffic simulation programs, very few are capable of simulating certain features of HOT lanes. Therefore a dditional modeling components should be added in to the simulation software so that all the different characteristics of HOT lanes can be simulated. Overall, this literature review indicates that there is a need for both the development of a method to optim ize pricing strategies and more research on how to price mul ti segment facilities. Also, simulation programs should be enhanced to be able to simulat e all the functions of HOT lane operations
63 CHAPTER 3 ENHANCEMENT OF HOT L ANE FACILITIES PRICING STRATEG IES In this chapter, a procedure to optimize the pricing algorithm s implemented in practice is described. The procedure is based on genetic algorithms (GA s ) that mimic natural selection and are often used to generate optimal solutions to large scale probl ems. The procedure is validated by optimizing the pricing algorithm currently implemented on the 95 Express in S outh Florida 3.1 GA Procedure In this section, the GA procedure is presented. The evolution of the GA procedure maintains a population of indivi duals, each of wh om represents a potential solution to the optimization problem. Each potential solution is associated with a fitness value that is determined by the objective function value for that individual. The individuals with the highest fitnes s values are preferentially selected by a randomized algorithm to using different transformations like mutations and crossovers. After a number of iterations, the procedure converges and the optimal solution is obtained. The GA procedure is illustrated in Figure 3 1. In the next subsections, each major step of the GA optimization procedure is presented in detail. 3.1.1 Initialization An initial population of individual s is generated The initial population is usually created randomly. In the GA procedure, an individual needs to be represented by a string of binary symbols.
64 Figure 3 1 GA Procedure Flowchart 3.1.2 Selection of Parents After generating the initial population of individuals a number of iterations of GA operations is performed to obtain the optimal solution. At e ach iteration a new set of individuals are created by combining the best performing individuals with their offspring, which are formed using mutations and crossovers. The individuals are selected based on the ir fitness value s More precisely, the population is sorted in ascending order and the individuals with the highest fitness values are preferentially retained for the next generation. The number of selected individuals, who will become parents, can
65 be decided by the user. After all the parents are selected they are combined into pairs. For this procedure, a random number is generated to determine the mate of the first parent listed. For example, if six parents are selected, five intervals (0 0.1999; 0.2000 0.3999; 0.4000 0.5999; 0.6000 0.7999; 0.8000 0.9999) are created in order to pair off the first parent. If the random number is 0.1248, which falls into the 0 0.1999 interval, the first parent should be paired up with the first of the remaining fiv e parents. Then, to create the next couple, this procedure is repeated with four intervals rather than five and so on. 3.1.3 Crossover After the couples are created, there are several procedures used to create offspring for the next generation, including crossovers and mutations. For crossovers, when the two parents have the same feature of one gene, that feature will be transferred to the children. When the two parents have different features in one gene, the child will inherit that feature randomly. For instance, suppose that the two parents have the following genes: P1: 00111 and P2: 01011. In this case, the first, fourth and fifth digits are the same so the children will be C1: 0XX11 and C2: 0XX11, where X is an unknown digit. Random binary numbers ar e used to replace the unknown digits. 3. 1 .4 Mutation Next, mutation is used to finalize the genetic makeup of the offspring. The mutation occurs randomly by changing a small part of the genes thus help ing the optimization problem to avoid local optimum. However, the mutation rate of the GA should not be very great Otherwise, the GA would generate too many random genes, slowing convergence.
66 3. 1 .5 Stopping Criteria T he objective function value is recorded. When the value remains the sa me for several iter ations, it i s assumed that the objective function has reached its optimal value. The procedure can be terminated when the change in the objective value is under a particular number or when a certain number of iterations is reached. 3.2 Optimizing the 95 E xpress Tolling Algorithm In order to demonstrate t he GA procedure described above the 95 Express t olling a lgorithm is optimized Before the GA is applied, the parameters in the procedure that are going to be optimized and the measure that will indicate th e performance of the algorithm should be defined. 3. 2. 1 The 95 Express Dynamic Tolling Algorithm The GA procedure is used to fine tune the parameters of the 95 Express tolling algorithm. The 95 Express is one of the HOT lane facilities currently in operat ion in the U.S. It has two HOT lanes and it wa s implemented by FDOT on I 95 in S outh Florida. The primary goal of the 95 Express is to safely and efficiently maximize the throughput of the facility while providing free flow services on the HOT lanes. M ore specifically, the goal is to maintain travel speeds greater than or equal to 45 mph on the HOT lanes. To meet this goal, t he toll change s every 15 minutes varying from $0.25 to $7.25. The toll is determined by the traffic density currently detected on the HOT lane and the change in density from the previous interval. When an increase or decrease in the detected density occurs, the rate is adjusted upward or downward accordingly. The magnitude of the adjustment is based on called a Delta S ettings Table (DST), as reported in Table 3 1 Below is a description of the tolling algorithm of the 95 Express:
67 1) Calculate the average traffic density of the HOT lane segment, denoted as Adjust TD if necessary for specific geometric conditions, such as weaving areas. 2) Calculate t he change in traffic density where and are the traffic densities at time interval and respectively. 3) Determine toll adjustment, from the Delta Setting T able (D ST) ( Table 3 1 ) based on and 4) Calculate new toll amount as follows: where and are the toll amount for time interval and respectively. 5) Compare new toll amount with the minimum and maximum toll t hresholds in the level of service ( LOS ) setting table ( Table 3 2 ). If the toll is not within the toll thresholds corresponding to a specific either the maximum or minimum toll will be applied. It can be seen that t he toll at each time interval i s highly depend ent on drawn from DST. In other words, D S T plays a major role in determining the toll adjustment. Therefore, extra attention should be paid in designing the table and fine tuning its parameters. The current pricing algorithm is effective in managing the traffic demand on the HOT lanes but as t raffic condition s o n the I 95 corridor is expected to change in the future, the parameters will need to be updated. A macroscopic simulation tool developed in Matlab by Wu et al. (2011) will be incor porated in the GA procedure to compute the fitness values for the GA individuals. The simulation too l consists of two m ain modules: supply and demand The supply module mainly consists of a traffic flow model that represents the characteristics of the faci lity and describes traffic dynamics along the facility and the toll determination process implemented on 95 Exp ress, while t
68 Table 3 1 Delta setting table of the 95 Express (Source: FDOT, 2008) LOS Traffic d ensity Change in traffic d ensity (TD) 6 5 4 3 2 1 A 0 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 1 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 2 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 3 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 4 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 5 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 6 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 7 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 8 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 9 $0.25 $0.25 $0.25 $0.25 $0. 25 $0.25 10 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 11 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 B 12 $0.50 $0.50 $0.50 $0.25 $0.25 $0.25 13 $0.50 $0.50 $0.50 $0.25 $0.25 $0.25 14 $0.50 $0.50 $0.50 $0.25 $0.25 $0.25 15 $0.50 $0.50 $0.50 $0.50 $0.25 $0.25 16 $0.50 $0.50 $0.50 $0.50 $0.25 $0.25 17 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25 18 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25 C 19 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25 20 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25 21 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25 22 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25 23 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25 24 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25 25 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25 26 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25 27 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 28 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 29 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 D 30 $1.50 $1.25 $1.00 $0.75 $0.50 $0. 25 31 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 32 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 33 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 34 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 35 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 E 36 $1 .50 $1.25 $1.00 $0.75 $0.50 $0.25 37 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 38 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 39 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 40 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 41 $1.50 $1.25 $1.00 $0 .75 $0.50 $0.25 42 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 43 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 44 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 45 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25 F >45 $2.00 $2.00 $2.00 $2.00 $1.00 $0.50
69 Table 3 1. Continued LOS Traffic d ensity Change in traffic d ensity (TD) +1 +2 +3 +4 +5 +6 A 0 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 1 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 2 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 3 $0.25 $0.25 $0.25 $0.25 $0.2 5 $0.25 4 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 5 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 6 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 7 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 8 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 9 $0.25 $0.25 $0.25 $0.25 $0.25 $0.25 10 $0. 25 $0.25 $0.25 $0.25 $0.25 $0.25 11 $0.25 $ 0.25 $0.25 $0.25 $0.25 $0.25 B 12 $0.25 $0.25 $0.25 $0.50 $0.50 $0.50 13 $0.25 $0.25 $0.25 $0.50 $0.50 $0.50 14 $0.25 $0.25 $0.25 $0.50 $0.50 $0.50 15 $0.25 $0.25 $0.50 $0.50 $0.50 $0.50 16 $0. 25 $0.25 $0.50 $0.50 $0.50 $0.50 17 $0.25 $0.25 $0.50 $0.75 $1.00 $1.25 18 $0.25 $0.25 $0.50 $0.75 $1.00 $1.25 C 19 $0.25 $0.25 $0.50 $0.75 $1.00 $1.25 20 $0.25 $0.25 $0.50 $0.75 $1.00 $1.25 21 $0.25 $0.25 $0.50 $0.75 $1.00 $1.25 22 $0. 25 $0.25 $0.50 $0.75 $1.00 $1.25 23 $0.25 $0.25 $0.50 $0.75 $1.00 $1.25 24 $0.25 $0.25 $0.50 $0.75 $1.00 $1.25 25 $0.25 $0.25 $0.50 $0.75 $1.00 $1.25 26 $0.25 $0.25 $0.50 $0.75 $1.00 $1.25 27 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 28 $0.25 $0.50 $ 0.75 $1.00 $ 1.25 $1.50 29 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 D 30 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 31 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 32 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 33 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 34 $0.25 $0.50 $ 0.75 $1.00 $1.25 $1.50 35 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 E 36 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 37 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 38 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 39 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 40 $0.25 $0.50 $ 0.75 $1.00 $1.25 $1.50 41 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 42 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 43 $0.25 $0.50 $ 0.75 $1.00 $1.25 $1.50 44 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 45 $0.25 $0.50 $0.75 $1.00 $1.25 $1.50 F >45 $0.50 $1.00 $2.00 $2.00 $2.00 $2.00
70 Table 3 2. Toll range for the 95 Express (Source: FDOT, 2008) LOS Traffic d ensity (vpmpl) Toll r ange Min Max A 0 11 $0.25 $0.25 B > 11 18 $0.25 $1.50 C > 18 26 $1.50 $3.00 D > 26 35 $3.00 $5.00 E > 35 45 $3.7 5 $6.00 F > 45 $5.00 $7.25 3.2.2 Parameter to be Optimized The parameters in DST that are most influential in determining the toll amount are first identified. The paramet ers corresponding to the LOS A ( i.e., traffic density lower than 1 1 vpmpl ) do not play any role in determining the toll amount because they are always equal to $0.25 in accordance to Table 3 2. Also, when the traff ic density change is small, that is 1 and +1, the toll change is always the minimum, $0.25. When LOS F is reached, the toll usually reaches its highest value to discourage motorists from entering the HOT lanes. Consequently, fine tuning only the parameters associated with the LOS B to E and the change in traffic density ranging from 6 to 2 and from +2 to +6 is consi dered In Table 3 3 the cells with numbers followed by (*) represent the values that remain intact. 3.2.3 Optimization Objective To be consistent with the operating objective of the 95 Express, t he objective of the DST parameter optimization is to ma ximi ze the average speed on the GP lanes while ensuring the speed on the HOT lanes is higher than 45 mph.
71 Table 3 3. DST P arameters subject to f ine tuning LOS Traffic d ensity Change in traffic d ensity (TD) 6 5 4 3 2 1 A 0 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 1 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 2 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 3 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 4 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 5 $0.25* $0.25* $0. 25* $0.25* $0.25* $0.25* 6 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 7 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 8 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 9 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 10 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 11 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* B 12 $0.50 $0.50 $0.50 $0.25 $0.25 $0.25* 13 $0.50 $0.50 $0.50 $0.25 $0.25 $0.25* 14 $0.50 $0.50 $0.50 $0.25 $0.25 $0.25* 15 $0.50 $0. 50 $0.50 $0.50 $0.25 $0.25* 16 $0.50 $0.50 $0.50 $0.50 $0.25 $0.25* 17 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25* 18 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25* C 19 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25* 20 $1.25 $1.00 $0 .75 $0.50 $0.25 $0.25* 21 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25* 22 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25* 23 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25* 24 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25* 25 $1.25 $1.00 $0.75 $0.50 $0.2 5 $0.25* 26 $1.25 $1.00 $0.75 $0.50 $0.25 $0.25* 27 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 28 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 29 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* D 30 $1.50 $1.25 $1.00 $0.75 $0.50 $0. 25* 31 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 32 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 33 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 34 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 35 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* E 36 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 37 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 38 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 39 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 40 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 41 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 42 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 43 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 44 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* 45 $1.50 $1.25 $1.00 $0.75 $0.50 $0.25* F >45 $2.00* $2.00* $ 2.00* $2.00* $1.00* $0.50*
72 Table 3 3 Continued LOS Traffic d ensity Change in traffic d ensity (TD) +1 +2 +3 +4 +5 +6 A 0 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 1 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 2 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 3 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 4 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 5 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 6 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 7 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 8 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 9 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 10 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* 11 $0.25* $0.25* $0.25* $0.25* $0.25* $0.25* B 12 $0.25* $0.25 $0.25 $0.50 $0.50 $0.50 13 $0.25* $0.25 $0.25 $0.50 $0.50 $0.50 14 $0.25* $0.25 $0.25 $0.50 $0.50 $0.50 15 $0.25* $0.25 $0.50 $0.50 $0.50 $0.50 16 $0.25* $0.25 $0.50 $0.50 $0.50 $0.50 17 $0.25* $0.25 $0.50 $0.75 $1.00 $1.25 18 $0.25* $0.25 $0.50 $0.75 $1.00 $1.25 C 19 $0.25* $0.25 $0.50 $0.75 $1.00 $1.25 20 $0.25* $0.25 $0.50 $0.75 $1.00 $1.25 21 $0.25* $0.25 $0.50 $0.75 $1.00 $1.25 22 $0.25* $0.25 $0.50 $0.75 $1.00 $1.25 23 $0.25* $0.25 $0.50 $0.75 $1.00 $1.25 24 $0.25* $0.25 $0.50 $0.75 $1.00 $1.25 25 $0.25* $0.25 $0.50 $0.75 $1.0 0 $1.25 26 $0.25* $0.25 $0.50 $0.75 $1.00 $1.25 27 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 28 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 29 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 D 30 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 31 $0.25* $0.50 $0.75 $1.0 0 $1.25 $1.50 32 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 33 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 34 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 35 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 E 36 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 37 $0.25* $0.50 $0.7 5 $1.00 $1.25 $1.50 38 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 39 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 40 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 41 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 42 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 43 $0.25* $0.50 $0.75 $1 .00 $1.25 $1.50 44 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 45 $0.25* $0.50 $0.75 $1.00 $1.25 $1.50 F >45 $0.50* $1.00* $2.00* $2.00* $2.00* $2.00* Note: The values with (*) indicate the values that remain intact
73 Mathematically, the objective fu nction can be written as: (3 1) where is the tolling interval indicator; is the speed on the GP lanes at the tolling interval ; i s the speed on the HOT lanes at tolling interval and is a penalty parameter If the speed on the express lanes is below 45 mph, the second component in the objective function will become negative. The larger the is, the smaller the objective func tion value will be However, should not be too large Otherwise, the optimization would lead to prohibitively high toll amount s, which is not beneficial to the overall performance of the system. In this task, is set to be equal to100. 3 .2.4 GA Proce dure The steps of the GA procedure for the optimization of the 95 Express algorithm are explained in the following paragraphs. 3 .2.4 .1 Initialization A population of 10 different DSTs is randomly generated each of which represents in the p rocedure These 10 individuals are then evaluated using the macroscopic simulation toll in Matlab (Wu et al., 2011) and the corresponding fitness values, are subsequently calculated. In the GA procedure, each DST needs to be represented by a string of binary symbols. Instead of directly converting each parameter in the DST into a binary variable, which would lead to a prohibitively long string, only the points where the price changes ( or, in other words, jumps ) are captured From Figure 3 1, we observe that in the columns representing traffic density change from 6 to 3 and from +3 to +6, there are two price jump points, implying that each column can ha ve
74 three different prices. In the 2 and +2 columns only one price jump point exists and it yields two prices. In total, there are 18 price jump points. Optimizing DST is equivalent to optimizing the locations of these 18 price jump points. For the column s with one jump point, the location may be at any row from 14 to 45. For the columns with two jump points the first point is located at any row from density 13 to 44, while the second can be at any row between 14 and 45. In all case s there are 32 possibl e jump point locations. Thus, each location can take an integer value from 0 to 31 which can be represented as a five digit binary substring (gene). For each DST, the corresponding binary string contains 18 genes and is 90 bits long. The coding process is illustrated in Figure 3 2 where column +3 contains two price jump points X 1 and X 2 The first jump point is at density 17 where the toll increases from $0.50 to $0.75 (t he toll value is only allowed to change in increment s of $0.25 ) We thus have X1 = 1 7 13 = 4, and the substring or gene is coded as 00100. Similarly, the second jump point is at density 29 where the toll will change from $0.75 to $1.00. Therefore, X2 = 29 14 = 15 and the substring or gene is 01111. 3.2.4 2 Selection of p arents Afte r generating the initial population of 10 individuals 100 iterations of GA operations are performed to obtain the optimal solution. At e ach iteration a new set of 10 individuals is created by combining the best performing individuals with their offspring which are formed u sing mutations and crossovers. As mentioned earlier, t he individuals are selected based on the ir fitness value s 3.2.4 3 Crossover The crossovers are conducted to create the children or new individuals.
75 Traffic d ensity Change in traffic d ensity +3 12 $0.50 13 $0.50 14 $0.50 15 $0.50 16 $0.50 17 $0.75 18 $0.75 19 $0.75 20 $0.75 21 $0.75 22 $0.75 23 $0.75 24 $0.75 25 $0.75 26 $0.75 27 $0.75 28 $0.75 29 $1.00 30 $1.00 31 $1.00 32 $1.00 3 3 $1.00 34 $1.00 35 $1.00 36 $1.00 37 $1.00 38 $1.00 39 $1.00 40 $1.00 41 $1.00 42 $1.00 43 $1.00 44 $1.00 45 $1.00 >45 $2.00 Figure 3 2 Representation of price jump p oints 3 .2.4 4 Mutation There is a 10 % mutation probabilit y (flip the digit to the opposite value, for example, from 0 to 1) set in this model. X1 X2
76 3 .2.4 5 Stopping c riteria T he GA procedure was set to terminate after a total of 100 iterations so at that point t he optimal algorithm solution wa s obtained 3 .2.5 Optim ized DST T he DST parameters were optimized under two different traffic demand scenarios. Since the macroscopic traffic simulation tool used was calibrated against the traffic conditions on the 95 Express corridor in April 2010 by Wu et al. (2011), the trav el demand of April 2010 was used as the base demand scenario. T hen the demand was increased by 5% to create an increased demand scenario. 3 .2.5 1 Base demand s cenario Table 3 4 compares the performances of the original and optimized DSTs. The performanc e measures include the average spe ed of the HOT lanes ( HOT avg speed ), the average speed of GP lanes ( GP avg speed ), and the percent time that the express lanes operate at more than 45 mph (reliability). The reported values in Table 3 4 we re taken from the 95 Express performance report for April 201 0 (FDOT, 201 0a ) while the other values we re obtained from the macroscopic simulation tool. It can be observed that both the original and optimized DSTs provide satisfactory performance and the latter slightly ou tperforms the former. The optimized DST improves the speed reliability by 4.65%. A t test was conducted to confirm that the improvements are statistically significant. Table 3 4 Performance m easures for base demand s cenario Performance m easures Reported Original Optimized % Improvement HOT avg s peed (mph) 55.80 53.46 53.64 0.34% GP avg s peed (mph) 41.90 43.16 44.65 3.44% Reliability 94.40% 95.56% 100.00% 4.65%
77 The optimized DST for the base demand scenario is shown in Table 3 5 3.2.5 2 Increased de mand scenario The performance measures for the increase d demand scenario are presented in Table 3 6 and the optimized DST is illustrated in Table 3 7 Table 3 6 shows that the current DST does not yield satisfactory results when the re is a 5% demand incr ease Conversely the optimized DST improves the speed reliability by 16.60% without compromising the speed on the GP lanes. The above demonstrates that the proposed GA optimization framework is able to fine tune the DST parameters to adapt to the changes in traffic conditions. It should be noted that the GA procedure utilizes the macroscopic simulation tool due to its computational efficiency. 3.2.6 Conclusions The GA optimization procedure presented in this chapter can be used to optimize pricing algori thms that include a large number of parameters that are not produced from a closed form function. B efore applying the GA procedure the most critical steps are to identify the parameters to be optimized and define the objective function. In the process of demonstrating the procedure, the 95 Express pricing algorithm was optimized. The most influential of the toll calculation parameters of the DST were optimized under two different traffic demand scenarios. In both scenarios, the objective was to maximize th e speed on the GP lanes while maintaining speeds greater than 45 mph on the HOT lanes. The optimization of the 95 Express algorithm was conducted using Matlab and the results showed that the optimized algorithm gives much better network performance in the increased demand scenario. Overall, the proposed GA procedure provi des a sensible approach to fine tune the DST param eters, avoiding trial and error
78 The performa nce of the optimized algorithm was also tested using the enhanced CORSIM that is presented in Chapter 5. The results are provided in Section 6.2. Table 3 5. Optimized DST for base demand s cenario LOS Traffic d ensity Change in traffic d ensity (TD) 6 5 4 3 2 +2 +3 +4 +5 +6 B 12 $1.00 $0.75 $0.50 $0.25 $0.25 $0.25 $0.25 $0.50 $0.75 $1.0 0 13 $1.00 $0.75 $0.50 $0.25 $0.25 $0.25 $0.25 $0.50 $0.75 $1.00 14 $1.00 $0.75 $0.50 $0.25 $0.25 $0.25 $0.25 $0.50 $0.75 $1.25 15 $1.00 $0.75 $0.50 $0.50 $0.25 $0.25 $0.25 $0.50 $0.75 $1.25 16 $1.00 $0.75 $0.50 $0.50 $0.25 $0.2 5 $0.25 $0.75 $0.75 $1.25 17 $1.00 $0.75 $0.75 $0.50 $0.25 $0.25 $0.25 $0.75 $0.75 $1.25 18 $1.00 $0.75 $0.75 $0.50 $0.25 $0.25 $0.25 $0.75 $0.75 $1.25 C 19 $1.00 $0.75 $0.75 $0.50 $0.25 $0.25 $0.50 $0.75 $0.75 $1.25 20 $1.00 $1.00 $0.75 $0.50 $0.25 $0.25 $0.50 $0.75 $0.75 $1.25 21 $1.00 $1.00 $0.75 $0.50 $0.25 $0.25 $0.50 $0.75 $0.75 $1.25 22 $1.00 $1.00 $0.75 $0.50 $0.25 $0.25 $0.50 $0.75 $0.75 $1.25 23 $1.00 $1.00 $0.75 $0.50 $0.25 $0.25 $0.50 $0.75 $0.75 $1.25 24 $1.00 $1.00 $0.75 $0.50 $0.25 $0.25 $0.50 $0.75 $0.75 $1.25 25 $1.00 $1.00 $0.75 $0.50 $0.25 $0.25 $0.50 $0.75 $0.75 $1.25 26 $1.00 $1.00 $1.00 $0.50 $0.25 $0.25 $0.50 $0.75 $0.75 $1.25 27 $1.25 $1.00 $1.00 $ 0.50 $0.25 $0.25 $0.50 $0.75 $0.75 $1.25 28 $1.50 $1.00 $1.00 $0.50 $0.25 $0.25 $0.50 $0.75 $0.75 $1.25 29 $1.50 $1.00 $1.00 $0.50 $0.25 $0.25 $0.75 $0.75 $0.75 $1.25 D 30 $1.50 $1.00 $1.00 $0.50 $0.25 $0.25 $0.75 $0.75 $0 .75 $1.25 31 $1.50 $1.00 $1.00 $0.50 $0.25 $0.25 $0.75 $0.75 $0.75 $1.25 32 $1.50 $1.00 $1.00 $0.50 $0.25 $0.50 $0.75 $0.75 $0.75 $1.25 33 $1.50 $1.00 $1.00 $0.50 $0.25 $0.50 $0.75 $0.75 $0.75 $1.25 34 $1.50 $1.00 $1.00 $0.50 $0 .25 $0.50 $0.75 $0.75 $0.75 $1.25 35 $1.50 $1.00 $1.00 $0.50 $0.50 $0.50 $0.75 $0.75 $0.75 $1.25 E 36 $1.50 $1.00 $1.00 $0.50 $0.50 $0.50 $0.75 $0.75 $1.00 $1.25 37 $1.50 $1.00 $1.00 $0.50 $0.50 $0.50 $0.75 $0.75 $1.00 $1.2 5 38 $1.50 $1.00 $1.00 $0.50 $0.50 $0.50 $0.75 $0.75 $1.25 $1.25 39 $1.50 $1.00 $1.00 $0.50 $0.50 $0.50 $0.75 $0.75 $1.25 $1.25 40 $1.50 $1.00 $1.00 $0.50 $0.50 $0.50 $0.75 $0.75 $1.25 $1.25 41 $1.50 $1.00 $1.00 $0.75 $0.50 $0.5 0 $0.75 $0.75 $1.25 $1.25 42 $1.50 $1.00 $1.00 $0.75 $0.50 $0.50 $0.75 $0.75 $1.25 $1.50 43 $1.50 $1.00 $1.00 $0.75 $0.50 $0.50 $0.75 $0.75 $1.25 $1.50 44 $1.50 $1.00 $1.00 $0.75 $0.50 $0.50 $0.75 $1.00 $1.25 $1.50 45 $1.50 $1.25 $1.00 $0.75 $0.50 $0.50 $0.75 $1.00 $1.25 $1.50 Table 3 6 Performance measures for increased d emand s cenario Performance m easures Original Optimized % Improvement HOT avg speed (mph) 45.67 47.56 4.14% GP avg s peed (mph) 40.01 41.08 2.67% Reliabili ty 65.28% 76.11% 16.60%
79 Table 3 7 Optimized DST for increased d emand s cenario LOS Traffic d ensity Change in traffic d ensity (TD) 6 5 4 3 2 +2 +3 +4 +5 +6 B 12 $1.00 $0.75 $0.50 $0.25 $0.25 $0.25 $0.25 $0.50 $0.75 $1.00 13 $1.00 $0.75 $0.50 $0.25 $0.25 $0.25 $0.25 $0.50 $0.75 $1.00 14 $1.00 $0.75 $0.50 $0. 5 0 $0.25 $0.25 $0.25 $0.50 $0.75 $1.00 15 $1.00 $0.75 $0.50 $0.50 $0.25 $0.25 $0.25 $0.50 $0.75 $1.00 16 $1.00 $1.00 $0.50 $0.50 $0.25 $0.25 $0.25 $0.50 $0.75 $1 .00 17 $1.25 $1.00 $0.50 $0.50 $0.25 $0.25 $0.25 $0.50 $0.75 $1.00 18 $1.25 $1.00 $0.50 $0.50 $0.25 $0.25 $0.25 $0.75 $0.75 $1.00 C 19 $1.25 $1.00 $0.50 $0.50 $0.25 $0.25 $0.25 $0.75 $0.75 $1.00 20 $1.25 $1.00 $0.50 $ 0.50 $0.25 $0.25 $0.25 $0.75 $0.75 $1.00 21 $1.25 $1.00 $0.50 $0.50 $0.25 $0.25 $0.25 $0.75 $0.75 $1.00 22 $1.25 $1.00 $0.50 $0.50 $0.50 $0.25 $0.25 $0.75 $0.75 $1.00 23 $1.25 $1.00 $0.50 $0.50 $0.50 $0.25 $0.50 $0.75 $1.00 $1.00 24 $1.25 $1.00 $0.50 $0.50 $0.50 $0. 5 0 $0.50 $0.75 $1.00 $1.00 25 $1.25 $1.00 $0.50 $0.50 $0.50 $0.50 $0.50 $0.75 $1.00 $1.25 26 $1.25 $1.25 $0.50 $0.50 $0.50 $0.50 $0.50 $0.75 $1.00 $1.25 27 $1.25 $1.25 $0.50 $0.50 $0.50 $0.50 $0.5 0 $0. 75 $1.00 $1.25 28 $1.25 $1.25 $0.50 $0.50 $0.50 $0.50 $0.50 $0.75 $1.00 $1.25 29 $1.25 $1.25 $0.50 $0.50 $0.50 $0.50 $0.50 $0.75 $1.00 $1.25 D 30 $1.25 $1.25 $0.75 $0.50 $0.50 $0.50 $0.50 $0.75 $1.00 $1.25 31 $1.25 $1.25 $0.75 $0.50 $0.50 $0.50 $0.50 $0.75 $1.00 $1.25 32 $1.25 $1.25 $0.75 $0.50 $0.50 $0.50 $0.75 $0.75 $1.00 $1.25 33 $1.25 $1.25 $0.75 $0.50 $0.50 $0.50 $0.75 $0.75 $1.00 $1.25 34 $1.25 $1.25 $0.75 $0.50 $0.50 $0.50 $0.75 $0.75 $1.00 $1.25 35 $1.25 $1.25 $0.75 $0.50 $0.50 $0.50 $0.75 $0.75 $1.00 $1.25 E 36 $1.25 $1.25 $0.75 $0.50 $0.50 $0.50 $0.75 $0.75 $1.25 $1.25 37 $1.25 $1.25 $0.75 $0.50 $0.50 $0.50 $0.75 $0.75 $1.25 $1.25 38 $1.25 $1.25 $0.75 $0.50 $0.50 $0.50 $0.75 $0. 75 $1.25 $1.25 39 $1.25 $1.25 $0.75 $0.75 $0.50 $0.50 $0.75 $0.75 $1.25 $1.25 40 $1.25 $1.25 $0.75 $0. 75 $0.50 $0.50 $0.75 $0.75 $1.25 $1.25 41 $1.25 $1.25 $0.75 $0.75 $0.50 $0.50 $0.75 $0.75 $1.25 $1 .25 42 $1.25 $1.25 $0.75 $0.75 $0.50 $0.50 $0.75 $0.75 $1.25 $1. 25 43 $1.25 $1.25 $1.00 $0.75 $0.50 $0.50 $ 0.75 $ 0.75 $1.25 $1.50 44 $1.25 $1.25 $1.00 $0.75 $0.50 $0.50 $0.75 $ 0.75 $1.25 $1.50 45 $1. 5 0 $1.25 $1.00 $0.75 $0.50 $0 .50 $0.75 $1.00 $1.25 $1.50
80 CHAPTER 4 PRICING OF MULTI SEGMENT HOT LANE FAC ILITIES S ome of the HOT lane facilities currently implemented in the U.S. are single segment while others are multi segment. Essentially, a single segment HOT lane facility has one main ingress, one main egress and includes one tolling point Therefore, motorists who enter th e facility during the same tolling interval pay the same toll amount. On the other hand, a multi segment HOT lane facility consists of multiple entrances a nd exits that are located relatively far from each other. D ownstream of every entrance there usually is a toll gantry and motorists will pay different tol l s depending on where they enter ed and how far they travel ed on the HOT lane facility. The exact toll amount a motorist has to pay when traveling on a multi segment HOT lane depends on the toll structure implemented. T he pricing approach for a multi segment HOT lane facility should provide superior traffic flow conditions on the HOT lanes while maximizing the the pricing for a single segment HOT lane facility. Moreover, it should avoid creating inequality issues among motorists entering the facility at different ingress points T herefore, pricing a multi segment facility is more cha llenging than pricing a single segment facility. T he tolling algorithm and structure for a multi segment facility must ensure similar traffic conditions within every segment of the facility without causing excessive lane changes before each HOT lane entran ce or equity issues among motorists. This chapter outlines the possible toll structures that can be implemented to manage a multi segment HOT lane facility and the current practice of multi segment facilities It, also, presents the main advantages and di sadvantages of each toll
81 structure. After all the different toll structures are described, the future 95 Express that will be a multi segment facility is introduced and recommendations on how to price the future 95 Express a re made. 4.1 Multi Segment HOT L anes in the U.S. From the ten HOT lanes in operation in the U.S. the following six have multiple segments: I 15, Salt Lake City, Utah. I 10 (Katy Freeway), Houston, Texas. I 394, Minneapolis, Minnesota. SR 167 between Renton and Auburn, Washington. I 15 San Diego, California. I 85, Atlanta, Georgia. 4.1.1 Toll Structures Although a multi segment facility often ha s multiple tolling points, a motorist does not necessarily have to pay at each point. Where a motorist is charged depend s on the toll structur e implemented. In general, the toll structures for multi segment facilities can be classified as zone based, origin specific, O D based and distance based. All four structures have been implemented in practice. The following section describes each toll str ucture, reviews the tolling practice for the multi seg ment HOT facilities in the U.S. and compares their advantages and disadvantages In order to better explain each toll structure, the multi segment HOT lane facility illustrated in Figure 4 1 is conside red In this facility, there are two HOT lanes and three GP lanes The HOT lanes are separated from the GP lanes by double solid line. Motorists can access the HOT facility only at the access point s that are indicated by dashed line s I1, I2, and I3 repres ent the entrances from the GP lanes to the HOT lanes while O1, O2, and O3 show the exits from the HOT
82 lanes back to the GP lanes. A toll gantry is located downstream to each HOT lane entrance. Figure 4 1. Example of a m ulti se gment H OT l ane facility 188.8.131.52 Zone based tolling In this approach, a HOT lane facility is divided into multiple zones. Whenever a motorist enters a new zone, he or she pays a specific toll. Consequently the toll amount that a motorist pays depends on t he numbers of zones he or she has traversed Each zone can include multiple HOT lane entrances and exits. T he toll at all the entrances that belong to the same zone is the same however For instance, suppose that the facility in Figure 4 1 is divided into two zones, one zone from I1 to O1 and one zon e from I2 to O3. In this case, Zone 1 has one e ntrance and one exit while Zone 2 has two entrances and two exits. Zone 2 has also two tolling points, one downstream of I2 and one downstream of I3. The tolls cha r ged at these points are equal, or in other words, toll 2 is equal to toll 3. Motorists who travel thr ough Zone 1 will pay toll 1 and motorists who travel through the entire facility will pay toll 1 plus toll 2. Travelers who enter at either I2 or I3 and t hen exit at either O2 or O3 will pay the same toll which is equal to the price of Zone 2
83 The zone based toll structure has been implemented on the I 15 Express lanes in Salt Lake City, the I 10 HOT lane corridor in Houston and the MnPass I 394 HOT lanes in Minneapolis. I 15 Salt Lake City, Utah I 15 e xpress l anes in Salt Lake City opened in September 2006 and i n August 2010 the express lanes were divided into four payment zones and dynamic pricing was implemented. The toll rate at the entrance of each zone is determined by the real time traffic condition in that particular zone, aiming to maintain a speed of at least 55 mph. Signs at the entrance of each zone and several other upstream locations display the price for traveling in that zone. A traveler who enters in the middle of a zone will have to pay the full amount for the entire zone. The price range for a solo driver is $0.25 $1.00 for each zone. It was determined based on public opinions and traffic analysis, with reference to the price ranges in other HOT lanes (UDOT, 2010b). I 10 (Katy Freeway), Houston, Texas T he toll structure of the Katy m anaged lanes is zone based and the toll s vary by time of day according to a pre determined schedule. There are three tolling points along the facility and a driver who traverses the entire HOT facility needs to pay three separate tolls. Although time of day tolling is easier to implement it may not be able to adequately manage the traffic demand when there are substanti al demand fluctuations, such as during holidays or large sport s events. I 394, Minneapolis, Minnesota The I 394 corridor is divided into two tolling zones. The pric e of each zone is determined independently from the others to manage the demand in that particular zone. A sign at each entry po int lists the tolls by
84 destination, that is the ending point of each zone. If a motorist exits anywhere before or at the first destination, he or she will pay only that first price for his or her trip. If the motorist continues beyond that point, he or sh e will also pay the second price posted on the sign at the entrance. 184.108.40.206 Origin specific tolling In origin specific tolling the toll a motorist will pay depends only on where he or she enters the facility. Regardless of how far the motorist travels, h e or she pays the toll displayed at the entry point. In the example network in Figure 4 1, there are three origins, I1, I2, and I3. Motorists who enter at I1 will pay toll 1 regardless of which exit, O1, O2, or O3 they are going to take In this case, a d river who travels from I1 to O1 will pay the same toll amount as s omeone who travels through the entire HOT facility This c an be unfair to the drivers who travel short distances on the HOT lanes. On the other hand, travelers can choose just once whether o r not to use the HOT lanes and know in advance exactly how much they are going to be charged. SR 167, Washington State O rigin specific tolling was implemented on SR 167 HOT lanes so u sers of the SR 167 HOT lanes pay the toll displayed at their entrances even if they traverse the entire facility. Sometimes, when traffic volume on the HOT lanes increases significantly, may be displayed at the HOT entrances indicating that SOVs cannot enter. 220.127.116.11 OD based tolling OD based tolling implies tha t the toll rate a motorist will pay depends on where he or she enters and leaves the facility so there is a different price for motorists who travel through different OD pairs In t he example network (Figure 4 1), there are seven OD pa irs (I1 O1, I1 O2, I1 O3, I2 O2, I2 O3, I3 O2, I3 O3) and drivers have to pay
85 depending on the ir OD. The toll per mile can be different for different OD pairs thus creating some equality issues among drivers. The tolls displayed before each toll gantry show the price to major destinations but do not indicate the exact amount a driver will finally pay. This toll structure is implemented on I 15 in San Diego. I 15, San Diego, California The sign at each entrance of the I 15 HOT lanes displays the minimum toll for entering the facility, the toll rate (i.e., toll per mile ) and the toll amount for traveling to the end of the facility (i.e., the maximum toll) Transit riders, carpools, vanpools, motorcycles and permitted clean air vehicles may access the lanes for free. For solo drivers, the toll depends on the distance traveled in the HOT lanes and the rate per mile at their entry location The toll rate is calculated e very few minutes but travelers pay the toll rate that was displayed at the time they entered the HOT lane facili ty. T he system will recalculate the toll rate based on the level of traffic demand in the corridor, ensuring free flow traffic conditions in the HOT lanes. When a motorist enters the facility, he or she needs to pay at least the minimum toll, regardless of his or her eventual exit location. The sign at each entrance also advises one or more possible fares for longer trips to upcoming freeway interchanges, such as SR 56 or 163. If the destination is somewhere after the first possible interchange, the expecte d toll will fall between the minimum and the toll for traveling al l the way to the end of the facility (SANDAG, 2010) 18.104.22.168 Distance based tolling In this toll structure, the toll charge that a motorist will pay depends on the distance he or she travels on the HOT lanes. The rate, that is toll per mile, is the same for all entry locations at a specific time interval. For example, in the network in Figure 4 1, the toll per mile for all the three entrances, I1, I2, and I3 will be the same at a certain tim e
86 interval. At each entrance, the toll per mile is displayed Such a toll structure has been recently implemented on I 85 HOT lanes in Georgia I 85, Atlanta Georgia I 85 HOT lanes have multiple entrances in each direction. The sign at each entry locati on displays the toll rate to the first downstream exit, which is the minimum toll one has to pay when he or she enters the facility, and the toll rate to the last exit which is the maximum someone can be charged. A traveler who exits bet ween the first and last exit, pays depending on the miles traveled on the HOT lanes. 4.1.2 Summary Table 4 1 summarizes the characteristics and toll structures of the multi segment HOT facilities in the U.S. The detailed description of each tolling algorithm is not availabl e in the open literature. 4.1.3 Pros and Cons of Toll Structures This section further compares the pros and cons of the above four toll structures. In the zone based tolling, the toll charged for one zone is usually determined b ased on the traffic conditi on s in that particular zone. The toll rate will be displayed at the entrance to each zone. Therefore, the tolling algorithm for each zone is essentially the same as for a single segment facility. In this sense, the zone based toll structure is eas ier to im plement. M otorists can make their decisions on whether to pay to access the HOT lanes mu ltiple times and they know in advance exactly how much they will pay when they make those lane choice decisions. One of the critical issues in implementing a zone based toll structure is to de termine the number and location of zones. If a zone is too long, pricing becomes less effective in managing demand. Conversely many short zones will create additional lane changes, possibly yielding moving bottlenecks and disrupt in g the managed lane operations.
87 Table 4 1. Summary of multi segment HOT f acilities in the U.S. Facility Length Access p oints Tolling p oints GP/HOT s eparation Toll s tructure I 15 Salt Lake City, Utah 38 miles 18 access points 1 2 entrances and 1exits at each direction 4 one at the end of each zone Double white l ine Zone based: dynamic p ricing I 10 Houston, Texas 13 miles 5 entrances and 3 exits WB and 3 entrances and 5 exits EB 3 one at the end of each zone Flexible b arriers Zone based: t ime of day pricing I 394 Minneapolis, Minnesota 11 miles 5 EB and 5 WB 5 EB and 5 WB Double w hite line Zone based: d yna mic p ricing SR 167 Renton & Auburn, Washington 10 miles 6 entrances and exits NB and 4 entrances and exits SB 6 NB and 4 SB Double w hite line Origin specific: dynamic p ricing I 15 San Diego, California 8 miles 9 entrances and 8 exits NB and 9 entrances and 9 exits SB 2 8 NB and 9 SB Concrete b arriers OD based: dynamic p ricing I 85 Atlanta, Georgia 16 miles 5 entrances and 6 exits NB and 4 entrances and 4 exits SB 6 NB and 4 SB Double s hite line Distance based: dynamic p ricing 1 Access points are the points where drivers can either enter or exit the HOT lanes. 2 Information provided by the I 15 Express Lanes Customer Service Center Th e origin specific toll structure is also relatively eas y to implement Origin specific tolling is convenient for users because they only need to make their lane choices once. However, this toll structure is likely to create inequity if the facility is long because the toll per mile at an upstream entrance may be less than that at a downstream entrance.
88 Otherwise, the capacity of HOT lanes upstream would be wasted. Consequently, users who enter midway or downstream of the HOT lanes may pay more for traveling a shorter distance, which may be viewed unfair to many. Similar to some ramp metering strategies, this toll structure tends to favor the long distance travelers. If not designed properly, it may lead to public resistance, like the opposition to ramp meter ing in the Twin Cities, Minnesota area where the state legislature passed a bill in the Spring of 2000 requiring a ramp meter shut off experiment. The OD based toll structure, at least theoretically, can effectively manage demand and utilize available ca pacity on a long multi segment HOT facility. The toll rates can be carefully designed to reduce inequality among users who access the facility via different entrances. I t is however, more sophisticated and thus more difficult to implement than the previou s two structures It can require a relatively high implementation cost because the system should keep track of where the vehicles enter and exit. Another downside of this structure is that, when users make their lane choices, they may not be sure of the ex act amount of toll they will have to pay for their trips. In the current practice (i.e., I 15 in San Diego ), when a motorist enters the facility, he or she needs to pay the minimum toll, regardless of his or her destination. A sign at each entrance advises one or more possible fares for longer trips to upcoming exits. If the destination is somewhere after the first possible exit, the expected toll can fall between the minimum and the toll for traveling all the way to the last exit of the HOT lanes Compara tively, the distance based toll structure seems easier to implement than the OD based tolling. F rom a software point of view, the implementation difficulty for both schemes is approximately the same. D istance based tolling is more flexible than
89 the origin based structure i n managing the traffic demand and i t may not create m uch equity concern as all travelers pay the same rate per mile. However, it may still result in unused capacity in the network. Table 4 2 summarizes the advantages and disadvantages of the different toll structures presented above. Table 4 2. Pros and cons of toll s tructures Toll s tructure Pros Cons Zone based Easy to implement, particularly when expanded from a single segment HOT facility Additional lane changes at the beginning o f each zone may cause disruptions; difficulty of balancing utilization of capacity and the disruptions caused by lane changes Origin specific Easy to implement and convenient for users Inefficient utilization of capacity ; possible inequality concerns OD based Effectively manage demand and utilize capacity More costly to implement Distance based No equity concern More costly to implement ; inefficient utilization of capacity 4.2 The Future 95 Express The 95 Express will be deployed in two phases. Phase 1 has been completed, and includes express lanes between SR 836/I 395 and Miami Gardens Drive/NW 186th Street in Dade County. Phase 1 is the current 95 Express Phase 2 will expand the express lanes northward to Browar d Boulevard in Broward County. The f utu re 95 Express includes the express lanes constructed during both Phase 1 and Phase 2. Figure 4 2 is a map of the c urrent 95 Express and Figure 4 3 illustrates the future completed, 95 Express. It can be seen that the current 95 Express is essentially a si ngle segment facility while the future 95 Express is slated to be a multi segment facility. More specifically, the future 95 Express will have five entrances and four exits
90 southbound and four entrances and five exits northbound (Figure 6 3 ) and three toll ing points in each direction Some of these entrances and exits will be located very close to each other, while others will be at distance s of approximately 10 miles. This implies that setting one toll amount may not be effective in managing traffic demand or be fair to all users. Therefore, the future 95 Express may better be managed as a multi segment facility. Figure 4 2 Map of the 95 Exp ress after Phase 1 c ompletion ; left is southbound, right is northbound (Source: http://www.95express.com/PDF/2008 05 19_Entry Exit%20Phase%201.pdf )
91 Figure 4 3 Completed 95 Express Left is southbound, right is northbound. (Source: http://www.95express.com/PDF/2008 05 19_Entry Exit%20Phase%201.pdf ) 4.3 Recommendations for Pricing the Future 95 Express As mentioned previously, the future 95 Express will have multiple entrances and exits and three toll ing points in each direction which means that it will be better managed as a multi segment facility. T here are four different toll structures that can be applied to operate a multi segment HOT lane facility but not all may be appropriate for the 95 Express Taking into account the advantages and disadvantages of these toll structures the design of the future 95 Express, and the number and location of its access and tolling points, zone based tolling seem s more appropriate for the 95
92 Express. In zone based tolling, each zone is treated as a single segment facility so the fact that the future 95 Express is an expansion of the current 95 Express provides an additional advantage to this tolling structure as there is already a pricing algorithm developed and imp lemented for the current 95 Express. This algorithm could be applied to manage the individual zone s of the future 95 Express. If the zone based tolling is selected, t he critical issue is to determine the zoning or in other words how to divide the facili ty into zones One suggestion to determin e t he zoning is to ensure that each zone contains exactly one bottleneck. For this, once it is completed the facility could be opened with free acce ss for a certain period of time so that can be observed and studied and the recurring bottlenecks in the facility be identified If the above approach is not practical or feasible, we can rely on simulation studies to evaluate and compare multiple zoning designs. Based on the design and locati on of the HOT lane entrances and exits ( Figure 4 3 ), one possible zoning scenario is to treat Phase 1, that is, the current 95 Express, as one zone and the extended portion as another two zones, as shown in Figure 4 4. More specifically, the pote ntial Z one 3 fo r the southbound direction and Z one 1 for the northbound direction ar e the current 95 Express while Z ones 1 and 2 for southbound, and Z ones 2 and 3 for northbound are the extension. These additional two zones in each direction can be combined into one zone, depending on the O D demand pattern of the facility. The tolling algorithm to be implemented for each zone can be similar to the current one, b ut the parameters may need fine tuning. Looking in the northbound direction, Z one 1 is the current 95 E xpr ess which is about 7.3 miles long. In the first scenario, Z one 2 begins just downstream of the on
9 3 ramp from Miami Gardens Drive and ends upstream of the on ramp from Hallandale Beach Boulevard Zone 2 is about 5 miles long, consisting of one extra exit up stream of the off ramp to Ives Dairy R oa d. Zone 3 starts right after where Z one 2 ends and extends to the end of the com pleted 95 Express at Broward Boulevar d. It has two more exits upstream of Stirling B oulevard and Davie B oulevard and is about 8.5 miles long. In the second scenario, Z ones 2 and 3 are combined into one zone approximately 13.5 miles long with a total of two entrances and three exits. Figure 4 4 Potential z oning for the 95 Express Left is southbound, right is northbound For determi ning the price of each zone, the 95 Express dynamic pricing algorithm or responsive pricing was used with the same DST parameters. However, the minimum Potential Zone 1 Potenti al Zone 3 Potential Zone 3 Potential Zone 2 Potential Zone 1 Potential Zone 2
94 and maximum toll values in the LOS setting table ( Table 3 2 ) for LOS D, E and F were increased to match the increased zone length, as shown in Table 4 3 Table 4 3. Toll ranges for the zones of f uture 95 Express Scenario 1, Zone 3 Scenario 2, Zone 2 LOS Traffic Density Toll Rate LOS Traffic Density Toll r ate (vpmpl) Min Max (vpmpl) Min Max A 0 11 $0.25 $0.25 A 0 11 $0.25 $0.25 B > 11 18 $0.25 $1.50 B > 11 18 $0.25 $1.50 C > 18 26 $1.50 $3.00 C > 18 26 $1.50 $3.00 D > 26 35 $3.00 $5.75 D > 26 35 $3.00 $9.25 E > 35 45 $4.75 $7.00 E > 35 45 $8.75 $11.00 F > 45 $6.25 $8.50 F > 45 $11.25 $13.50 The performance of the t wo different zoning designs for the northbound direction proposed above (Figure 4 4) is tested using the enhanced CORSIM. CORSIM is microscopic traffic simulation software that until recently, had very limited capability in simulat ing the HOT lanes operations However, as is described in detail in the next chapter, it was enhanced to sim ulate HOT lanes operations by implementing three different modeling components including a variety of pricing algorithms, a lane choice model and toll structures for managing multi segment HOT lane facilities. The simulated performance measures of the t wo zoning designs are summarized in Table 4 4 The data used for the calibration were obtained from the STEWARD database every 15 minutes for three weekdays, May 10 12, 2011, for all the detectors along the future 95 Express corridor. As Table 4 4 indicate s, the three zone design produces similar performance as the two zone design. The primary reason is that t he freeway segment of Phase 2 (Z ones 2 and 3 ) is not very congested in the CORSIM simulation. Thus, based on the network
95 performance measures, i t is s ufficient to treat Phase 2 as a single zone and use dynamic pricing to effectively manage the segment. Table 4 4. Future 95 Express zoning performance m easures Zone d esigns Three zone d esign Tolls Zone 1 Zone 2 Zone 3 Facility Range $0.25 $2.75 $0.25 $0.25 $0.25 $0.50 $0.75 $3.25 Avg. peak p eriod $1.41 $0.25 $0.27 $1.93 HOT GP HOT GP HOT GP HOT GP Avg s peed (mph) 56 40 60 54 66 63 61 54 HOT lanes o perated a bove 45 mph 99.9% 100% 100% 99.9% Two z one d esign Tolls Z one 1 Zone 2 Facility Range $0.25 $2.25 $0.50 $0.75 $0.75 $2.75 Avg. p eak p eriod $1.05 $0.52 $1.57 HOT GP HOT GP HOT GP Avg s peed (mph) 56 41 65 61 61 54 HOT lanes operated a bove 45 mph 99.8% 100% 99.9% In the three zone design each zone has one entrance and drivers are charged three times to travel along the entire HOT lane facility. This means that each time a car passes through a toll gantry, it gets charged. However, in the two zone design, the second zone has two entrances and motorists who enter at the upstream entrance should not get charged when they are passing through the downstream entrance. This may require a different configuration of the second entrance of the second zone so only the motorists who enter the facility there get cha rged. If the same entry configuration is used at all entrances, then all the drivers entering the second zone need to be tracked and charged accor dingly. This means that the two zone design has a higher
96 imp lementation cost than the three zone design. Also, the two zone design will generally produce less revenue than the three zone design. highly depends on the implementation cost and the willing ness to produce more revenue while fewer zones so they get charged fewer times the total of which is less.
97 CHAPTER 5 ENHANCEMENT OF CORSIM Microscopic simulation is very useful in evaluat ing pricing schemes and other managed lane oper ational strategies (Zhang et al., 2009). Unfortunately, there is not any software that is able to explicitly simulate the HOT lane operations. This chapter focuses on the effort to enhanc e a traffic simulation tool called CORSIM for simulating HOT lane ope rations. CORSIM was selected because it is a trustworthy traffic simulation tool and our ability to modify it through the Mc Trans Center 5 .1 Introduction CORSIM is a widely used and comprehensive microscopic traffic simulation program. It was initially d eveloped by FHWA and is now being maintained and further developed by Mc Trans at the University of Florida. During recent years, CORSIM has been expanded to simulate signal pre emption two lane rural highways, and new vehicle technologies and ha s enabled large scale network simulation. CORSIM has limitations, h ow ever. T he current version of CORSIM is very limited in its ability to simulat e dynamic tolling strategies of tolls. In order t o incorporate HOT lane simulation in to CORSIM three modeling components were developed. The first set wa s to simulate a variety of pricing strategies. The second wa GP and HOT lanes in the presence of toll s based on a specific lane ch oice model selected. The third wa s to allow for different toll structures or charging approaches for multi segment HOT lane facilities. In the following paragraphs, these three components are described
98 5 .2 Pricing Strategies In the literature, many studies h ave been conducted to develop pricing algorithms that can be potentially used for HOT lane operations. However, m any of these studies (see, e.g., Morrison, 1986; Palma and Lindsey, 1997; Arnott et al., 199 8 ) consider hypothetical and idealized situations t o derive analytical solutions. For example, the travel demand function or travel demand is usually assumed to be known For the CORSIM enhancement, practical and easy to implement pricing algorithms, including the one implemented for the 95 Express in S out h Florida called here responsive pricing and the approach proposed by Yin and Lou (2009) that determines time varying tolls based on the concept of feedback control were selected In addition, time of day pricing was implemented since it is being impleme nted at a few HOT lane facilities. T he three pricing algorithms are presented below in detail 5 .2 .1 R esponsive Pricing Responsive pricing is an approach to determin e toll values based on the current HOT lane conditions to manage traffic demand and mainta in free flow conditions on HOT lanes. The algorithm is described in detail in section 3 2 In CORSIM implementation, the tolling interval the parameter all values in DST ( Table 3 1) and the minimum and maximum toll thresholds in Table 3 2 can be modified by a user. 5 .2 2 C losed l oop c ontrol b ased Pricing Algorithm A c losed loop control based algorithm is another method for adjustin g the toll based on real time traffic measurements. The toll for each subsequent time interval depends on the toll at the current interval, the current traffic density ( ) and the critical or desired density ( ). The procedure for determining th e toll is described as follows:
99 1) Calculate average traffic density of the HOT lanes, denoted as 2) Calculate toll for the next time interval ( ) based on the following equation: where is the cur rent toll; is a regulator parameter defined by a user. It is used to adjust the disturbance of the closed loop control, that is the effect of the difference between the measured traffic density and the critical density on the toll amount; and is the critical or desired density defined by a user. 3) Compare with the minimum and maximum toll thresholds defined by the user. If is less than the minimum threshold or greater than the maximum one, it takes the minimum or maximum thresh old value. In addition to those user defined parameters mentioned above, the tolling interval can also be specified by a CORSIM user. 5 2.3 Time of d ay P ricing Scheme Time of day pricing is the third pricing scheme implemented in CORSIM for HOT lane o perations. In this case, the toll is not determined based on real time traffic conditions. Instead, it follows a toll schedule predetermined by a user. This scheme is useful for freeway facilities that have stable traffic demand pattern during weekdays fo r example In CORSIM implementation, multiple tolling periods (having different toll and durations ) can be simulated. The number of tolling periods can be up to 24, and the duration of each tolling period varies from 3 to 60 minutes, with a toll amount ra nging from $0.00 to $12.00. These values were selected based on the current practice where tolls are set based on the time of day pricing scheme. For instance, the toll on SR 91 in California changes every hour and its highest value is $10.05.
100 5 .3 Lane Cho ice In the enhanced CORSIM, HOT and GP lanes are integrated as a single facility and lane choice behaviors are simulated endogenously. Empirical studies (e.g., Sullivan, 2000; Lam and Small, 2001; Brownstone et al.,2003; Li, 2001; Burris and Xu, 2006) show saving, toll amount, travel time reliability, trip purpose, ( including income, age, gender and education ) Implementing a sophisticated lane choice mo del developed from those empirical studies (e.g., Lam and Small, 2001; Brownstone et al.,2003; Small et al., 2005a ) in CORSIM is technically feasible. However, a model calibrated for one facility may not be transferable to another without calibration, whic h is often too costly to do for the new site. Even if the model is transferable, a CORSIM user would need to provide site specific input data for many explanatory variables in the model and such data are often not readily available For these reasons, the lane choice model selected for implementation with in CORSIM is essentially based on a simple decision rule : motorists will pay to use HOT lanes if the benefit they perceive from travel time saving (TTS) is greater than t he toll amount they are charged Th e perceived benefit is the VOT multiplied by the perceived TTS, which is assumed to follow a truncated normal distribution whose mean is the real ( actual ) TTS (RTTS) and a standard deviation that can be customized by a CORSIM user. RTTS is the d ifference between travel times on GP and HOT lanes, averaged across a user specified time interval and calculated internally by the software The lane choice procedure for a particular vehicle, say j that is approaching a warning sign upstream to a HOT la ne entrance is illustrated in Figure 5 1.
101 Figure 5 1 e c hoice in CORSIM Previous studies ( Miller, 1996; Small, 1982; Waters, 1982) suggested that the average VOT of an individual i s about 50% of his or her wage rate while others (e.g., Small et al., 2005b; USDOT, 2003) point ed out tha t the VOT can be as high as 120% of the wage rate, depending on the length and type of travel. Moreover, Outwater and Kitchen (2008) suggested that the VOT of a vehicle representativ e increases as the vehicle occupancy increases. The increase of VOT between HOV 2 and HOV 3+ can range from 3.8% to 39.7%.
102 each toll paying vehicle type (including cars, HOV2, HOV3+ and trucks) can be specified by a user. 5 4 T oll Structures Capturing different toll structures is very important in simulating multi segment HOT lane facilities. Currently, all four toll structures implemented in practice ; that is zone based, orig in specific, OD based and distance based, are fully implemented in CORSIM. In a zone based structure, the HOT lane facility is divided into zones. Each zone can have multiple entrances or exits. The toll is computed at the first entrance to a zone and wil l be assigned to all the entrances that belong to the same zone. When dynamic pricing (responsive or closed loop control based) is implemented, the density used for toll calculation for a zone is the average of densities along the HOT lane segments in that zone. The total toll amount that a motorist pays will be the sum of toll amounts of the zones he or she traversed. Moreover, a driver will have to make a lane choice decision every time he or she enters a new zone. In an origin specific structure, toll s are calculated for each entrance and travelers simply pay the toll displayed upon first enter ing the HOT lanes. More precisely, a traveler pays the toll amount displayed on a sign at his or her entry point regardless of how far the traveler intends to tr avel on the HOT lanes. Consequently, the traveler will only have to face the lane choice once. The toll at a specific HOT lane entrance is calculated based on the average of all densities on HOT lane segments between that entrance and the nearest HOT lane termination link (specified by the CORSIM user).
103 In an OD based structure, the toll amount that motorists pay depends on where they enter and leave the HOT lanes ; that is it is based on their ingress and egress points In this case, the prices to major e xits are displayed at each entry point so that motorists can estimate approximately the price they have to pay. They can then decide whether they want to use the HOT lanes or not. In a distance based tolling, the toll a motorist is charged depends on the d istance that he or she travels on the HOT lanes. The toll rate, that is toll per mile, is the same for all HOT lane entry locations at a specific time interval. The entrance sign displays the minimum toll for entering the facility (the toll to the immedia tely downstream exit), the toll per mile, and the maximum toll for traveling to the end of the facility. In CORSIM, the toll calculation in distance based tolling is similar to that with in zone based tolling. More specifically, a CORSIM user also needs to specify zones T oll calculation also takes place at the first HOT entry link to each zone. To find the toll per mile the toll is then divided by the length of the zone. The toll per mile is the same at all the entrances to the same zone, but can be differ ent from zone to zone. 5. 5 Summary CORSIM enhancement inclu des The first includes three different pricing algorithms for the toll calculation. The second after the toll is set T he third applies a toll structure to multi segment HOT lanes facilities. The enhanced CORSIM evaluation is presented in the next c hapter. Appendix A provides a user guide on how to simulate HOT lanes in CORSIM.
104 CHAPTER 6 EVALUATIO N OF THE ENHANCED CORSIM This chapter consists of two parts. In the first part, the northbound direction of the current (Phase 1) 95 Express is simulated to evaluate the accuracy of the enhanced CORSIM and the optimized 95 pricing algorithm presented in C hapter 3 is evaluated using the calibrated current 95 Express. In the second part, the future (Phase s 1 and 2) 95 Express is simulated to test the ability of the enhanced CORSIM to simulate multi segment HOT lanes and evaluate the performance of the differ ent toll structures on the facility. 6 .1 S imulating the C urrent 95 E xpress In order t o demonstrate the ability of the enhanced CORSIM to simulate single segment facilities, the northbound direction of the current 95 Express (Figure 4 2 ) was simulated The data used in the simulation were obtained from the STEWARD database every fifteen minutes between May 10 and 12, 2011 (Tuesday, Wednesday and Thursday). On those days, the data from most detectors w ere available and there were no special event s Based on the 95 Express Monthly Operations Report of May 2011 (FDOT, 2011), the peak period was 4:00 7:00pm for the northbound direction We thus calibrated our model against this time period and an additional thirty minutes w ere used for initialization. Table 6 1 compares the reported performance statistics of the northbound direction of the 95 Express (95 Express Monthly Operations Report of May 2011) with the simulated performance statistics obtained from the CORSIM simulation It can be observed that t he simula tion model replicates th e major performance measures closely. In the simulation, the actual TTS w ere calculated by CORSIM every
105 minute and w ere then used for lane choice decision s in the next minute. Also, the standard deviation of the perceived TTS distri bution was assumed to be half of the actual TTS. In order to achieve the lane distribution between the HOT and GP lanes on 95 Express network is shown in Table 6 2. The percent of vehicles columns represent the percentage of vehicles that have VOT equal to the value shown in the adjacent cell. For example, 10% of the cars have a VOT equal to $ 8 per hour and 10% of the HOV2s have VOT equal to $ 10 per hour. Table 6 1 Com parison of performance s tatistics for n orthbound PM p eak p eriod Simulation m odel Reported (May 2011) Tolls Range $0.25 $5.75 $0.00 $5.50 Avg. peak r eriod $2.17 $2.12 HOT GP HOT GP Avg s peed (mph) 57 49 58 46 HOT Lanes operated a bove 45 mph 99.6% 99.7% The calibrated VOT values shown in Table 6 2 appear to be consistent with findings in the literature. The avera ge VOT is about 75% of the average wage rate in the Miami/Fort Lauderdale area (Bureau of Labor Statistics, 2011), and is thus considered to be reasonable. An increase of 20% from HOV2 to that of HOV3+ also appears to be reasonable. It should be emphasized that another set of VOT values may also yield a good match. As Phase 1 of the 95 Express has been fully operational for almost two years, drivers of the corridor have become familiar with the system. A behavioral study can be conducted to better understan s whether or not to use the HOT lanes and estimate their travel time values for the I 95 corridor or
106 in South Florida. The study will provide much valuable information for the planning and operations of the future HOT network in the region. The lan e choice model in CORSIM was applied only to toll payin g vehicles; although there are some toll exempt vehicles on the 95 Express, including public transit, hybrid vehicles and vehicles registered as HOV 3+. The types an d percentages of the toll exempt vehicles can be specified in CORSIM. According to the 95 Express Monthly Operations Report of May 2011 approximately 11% of the HOT traffic is toll exempted. 6 .2 Evaluation of Optimized DST for 95 Express Tolling Algorith m U sing CORSIM A GA based optimization procedure to optimize pricing algorithms for HOT lanes was presented in Chapter 3. The 95 Express tolling algorithm was used as a case to demonstrate the GA procedur e and the optimized algorithm parameters were obtain ed by macroscopic simulation. In order t o further examine and evaluate the performance of the optimized DSTs described in section 3.2.5 as well as compare it to th at of the original DST, the calibrated CORSIM simulation model of the current 95 Express wa s used. The simulation res ults for both the base a nd 5% increased demand scenario are summarized in Table 6 2 The following observations can be made from the CORSIM simulation studies. The original and optimized DSTs give comparable performances in both d emand scenarios. They both effectively achieve the operating objectives of the 95 Express. In the increased demand scenario, the optimized DTS slightly increases the speed reliability, but charges a higher average toll. However, the highest toll value does not go beyond $5.00, while the original DST charges up to $7.00.
107 Table 6 2 Comparison of optimized and o riginal DSTs Original Optimized Base d emand Tolls Range $0.25 $5.75 $0.25 $5.50 Avg. peak p eriod $2.17 $2.12 HOT GP HOT GP Avg s peed (mph) 57.20 49.10 58.61 46.23 HOT l anes o perated a bove 45 mph 99.6% 99.7% 5% d emand i ncrease Tolls Range $0.25 $7.00 $0.25 $5.00 Avg. p eak p eriod $2.07 $2.87 H OT GP HOT GP Avg s peed (mph) 56.55 47.62 56.83 46.00 HOT l anes o perated a bove 45 mph 95.3% 97.7% T he optimized DSTs do not appear to produ ce much noticeable improvement in the CORSIM simulation. This is due to the discrepancy between the Matlab macros copic simulation tool used for the optimization and CORSIM. If the latter is incorporated into the GA procedure, more substant ial improvement can be expected, although a C ORSIM based GA optimization would be very time consuming, yet it remains feasible to utilize a parallel computing framework to expedite the optimization process. 6.3 Simulating the Future 95 Express The evaluation of e multi segment toll structures is presented in this section. For the demonstration, the northbou nd direction of the future 95 Express is simulated The data used for the simulation and calibration were obtained
108 from the STEWARD database every fifteen minutes for three weekdays, May 10 12, 2011, for all the detectors along the future 95 Express corrid or. Figure 6 1 shows the major entrances from the GP lanes to the HOT lanes and exits from the HOT lanes back to the GP lanes Along the HOT lane network, there are nine input output (I O) pairs T he simulation results, including the toll range, average t oll, GP and HOT lanes average speed s and reliability of the HOT lanes for each toll structure are presented for each I O pair in Tables 6 4 to 6 7 I1 O4 represents the entire facility extending from SR 836/I 395 to Broward Boulevard In all toll struct ures that were tested, toll s were calculated from the tolling algorithm currently implemented on the 95 Express. 6.3 .1 Zone based Toll Structure Z one based tolling as described in Chapter 4 is one of the easiest toll structures to implement. The facility is divided into zones so that each zone includes only one main entrance to HOT lanes, and one toll gantry This leads to three zones in the northbound direction. I1 O1 represents Z one 1 which is from SR 836/I 395 to the Golden Glades Interchange I2 O2 re presents Z one 2 which starts north of the Golden Glades Interchange and ends at Griffin Road and I3 O4 is Z one 3 which extends from Ives Dairy Road to the end of the facility at Broward Boulevard In Table 6 3 the facility performance measures under zone based tolling are presented R esults indicate that the facility can be effectively managed using a zone based toll structure. The average toll is $1.41, $0.25, and $0.27 for the first, second, and third zone, respectively. The toll values for both Z one 2 a nd 3 are equal to the minimum toll for most time intervals because these zones did not appear to be congested in CORSIM.
109 Figure 6 1 Entrances and exits of the F uture 95 Express northbound d irection (Source: http://www.95express.com/images/2011_11_Phase%202_Alternative%201_E ntryExit_Handout.jpg ) I1 O1 I2 O2 I3 O3 O4
110 On the other hand, there is so me congestion in Z one 1, with the average speed on the GP lanes be i ng approximately 40 mph. A toll for Zone 1 can reach u p to $2.75. A motorist who travels through the entire HOT lane facility will have to pay on average a total of $1.93. 6.3.2 Origin specific Toll Structure Table 6 4 presents the performance measures of the origin specific tolling on the future 95 Express. The HOT lanes can be effectively managed with this type of charging, but there are equality issues among the motorists. A motorist who is traveling from I1 to O1, a 7.3 mile stretch, will pay the same a mount of toll as someone who is traveling through the entire facility, I1 O4, which is about 21.0 miles long. This implies that the driver who travels from I1 to O1 will pay a toll rate of $0.42/mile while the driver who travels from I1 to O4 will pay a ra te of $0.15/mile. However, t his structure is easy to implement and convenient for users because they pay just once to use the facility. In this structure the average toll a motorist pays to travel the entire facility is $3.13 which is about $1.00 highe r than under the three zone toll structure. In the latter, each zone is managed as a single HOT lane facility, and thus each toll is not very high. In contrast, with origin based tolling, tolls at the first entrance need to be much higher, to ensure superi or flow conditions on HOT lanes along the entire facility.
111 Table 6 3 Value of t ime ($/hr) Table 6 4 Performance measures of Future 95 Express under zone based tolling I1 O 1 I1 O 2 I1 O 3 I1 O 4/ facility I 2 O 2 I 2 O 3 I 2 O 4 I 3 O 3 I 3 O 4 Toll r ange ($) 0.25 2.75 0.50 3.00 0.75 3.25 0.75 3.25 0.25 0.25 0.50 0.75 0.50 0.75 0.25 0.50 0.25 0.50 Avg. p eak Period t oll $1.41 $1.66 $1.93 $1.93 $0.25 $0.52 $0.52 $0.27 $0.27 HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP Avg s peed (mph) 56.1 40.1 56.9 43.0 60.6 52.3 61.1 54.1 60.0 53.8 64.4 60.8 64.6 61.3 66.0 62.9 65.8 62.8 HOT lanes o perated a bove 45 mph 99.9 % 99.9 % 100 % 100 % 100 % 100 % 100 % 100 % 100 % Table 6 5 Performance measures of Future 95 Express under origin based tolling I1 O 1 I1 O 2 I1 O3 I1 O4/ facility I2 O 2 I2 O 3 I2 O 4 I3 O 3 I3 O 4 Toll r ange ($) 1.00 6.25 1.00 6.25 1.00 6.25 1.00 6.25 0.50 0.50 0.50 0.50 0.50 0.50 0.25 0.25 0.25 0.25 Avg. p eak Period t ol l $ 3.13 $ 3.13 $ 3.13 $ 3.13 $ 0.50 $ 0.50 $ 0.50 $ 0.25 $ 0.25 HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP Avg s peed (mph) 56.1 42.7 56.9 45.0 60.6 53.5 61.2 55.2 59.9 53.9 64.5 61.1 64.6 61.6 65.7 63.0 65.6 62.9 HOT lan es o perated a bove 45 mph 99.9 % 99.9 % 99.9 % 99.9 % 100 % 100 % 100 % 100 % 100 % percent vehicles VOT percent vehicles VOT percent vehicles VOT percent vehicles VOT percent vehicles VOT Weighted Average Cars 10 8 15 10 50 16 15 18 10 22 15.2 HOV 2 10 10 15 12 50 19 15 22 10 26 18.2 HOV 3+ not registered 10 12 15 14 50 23 15 26 10 31 21.8
112 Table 6 6 Performance measures of Future 95 Express under OD based tolling I1 O 1 I1 O 2 I1 O3 I1 O4/ facility I2 O 2 I2 O 3 I2 O 4 I3 O 3 I3 O 4 Toll r ange ($) 0.5 0 4 .00 1.5 0 5 .0 0 1.5 0 5 .00 1.75 5.25 0.75 0.75 1 .00 1 .00 1 .00 1 .00 0.25 0.25 0.25 0.25 Avg. p eak Period t oll $ 2.08 $ 3.08 $ 3.25 $ 3.39 $ 0.75 $ 1 .00 $ 1 .00 $ 0.25 $ 0.25 HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP Avg s pe ed (mph) 56 .1 38.6 56.8 41.8 60.7 51.7 61.2 53.7 60.1 53.8 64.7 60.8 64.8 61.3 66.0 63.0 65 .8 6 2.8 HOT lanes o perated a bove 45 mph 99.8% 99.8% 99.9% 99.9% 100 % 100% 100 % 100 % 100 % Table 6 7 Performance measures of Future 95 Express under distance bas ed tolling I1 O 1 I1 O 2 I1 O3 I1 O4/ facility I2 O 2 I2 O 3 I2 O 4 I3 O 3 I3 O 4 Toll r ange ($) 0. 75 2.25 1.00 3.00 1.5 0 5 .00 2.25 6.50 0. 25 0. 5 0 0.75 2.50 1 .25 4.00 0. 5 0 1 .25 0 .75 2. 5 0 Avg. p eak Period t oll $1.09 $1.41 $2.45 $ 3 .13 $ 0. 27 $ 1 23 $ 1 .00 $0.63 $1.18 HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP HOT GP Avg s peed (mph) 56.0 43.2 56.9 45.4 60.2 53.7 61.1 55.3 59.7 53.9 64.4 61.1 64.6 61.7 65.7 63.0 65 .6 63 .0 HOT lanes o perated a bove 45 mph 99.8% 99.8 % 99.9% 99.9% 100% 100% 100% 100% 100 %
113 6. 3 .3 OD based Toll Structure In an OD based structure the tolls are calculated for each different OD pair. The results for this structure are given in Table 6 5. As stated earlier, the responsive tolling algorit hm was applied when testing all toll structures. However, i deally, a more sophisticated tolling algorithm should be developed to charge users based on their origins and destinations This would help to maintain desired traffic condition s on the express lan es and would help to fully utilize express lanes available capacity without creating excessive inequa lity among different O D pairs In this case, the toll per mile is different for every OD pair. More precisely the average toll per mile is $0.28, $0.38 $0.20, $0.16, $ 0.49, $0.12, $0.08, $0.07, and $0.03 for I1 O1, I1 O2, I1 O3, I1 O4 I2 O2 I2 O3 I2 O4 I3 O3 and I3 O4 respectively, which may also cause some equ ity concerns among the drivers. 6. 3 4 Distance based Toll Structure In the distance ba sed structure, a toll rate for the entire HOT lane facility is set. Drivers are charged that rate multiplied by the number of miles they have traveled on the facility. This should result in less equity concern, but the structure might fail to maintain desi red traffic conditions on the HOT lanes. Table 6 6 shows the results when distance based tolling is implemented to the future 95 Express. The average toll rate for the simulated period is $0.15 per mile and the tol l for traveling between each OD pair is d ifferent as each OD has a different length. Because the facility is not very congested, the distance based structure was able to maintain superior LOS on the HOT lanes. 6.3.5 Toll Variation The toll variation for the entire facility for each toll structure is illustrated in Figure 6 2. In the zone based model the toll a motorist has to pay to travel through the entire
114 HOT lane facility is calculated as the summation of the tolls for each individual zone. In the origin specific structure the toll to travel the entire facility is equal to the toll at the first entrance. In the OD based structure, it is equal to the toll per mile at the first entrance multiplied by the total number of miles of the facility, while i n the distance based structure it is also ca lculated by multiplying the toll per mile at the first entrance by the entire length of the HOT lane facility. T he toll pattern is the same for all the structures except for the origin specific structure. T he origin specific toll pattern has high fluctuati ons at some time intervals. For example, at time interval 7, the toll increases from $1.25 to $6.25 while in the next time interval the toll drops from $6.25 to $2.25. This could be caused by the increased number of travelers who choose to enter the HOT l anes at the first entrance and travel through the entire facility as they have to pay only once. In general motorists pay less total toll amount when the zone based structure is applied Figure 6 2 Average t oll by toll structure 0.25 0.75 1.25 1.75 2.25 2.75 3.25 3.75 4.25 4.75 5.25 5.75 6.25 6.75 1 2 3 4 5 6 7 8 9 10 11 12 Toll ($/hr) Time Interval (15min) Zone-based Origin-specific OD-based Distance-based
115 6. 4 Summary In summary CORSIM was enhanced to simulate both single segment and multi segment HOT lane facilities. T he current 95 Express was simulated to demonstrate segment HOT lane facility while the future 95 Express w as simulated to show that CORSIM can adequately simulate the HOT lane operation components and different toll structures for multi segment HOT lanes All four toll structures for multi segment HOT lanes were simulated. In addition, the zone base d toll str ucture was recommended for the future 95 Express. The recommendation was made based on the advantages and disadvantages of the toll structures. However, one should not use the results presented in this chapter to compare toll structures and draw a conclusi on on which particular toll structure outperforms the other This is because the toll rates are not optimized against each structure and the results could differ with the type and design of each HOT lane facility
116 CHAPTER 7 SUMMARY AND CONCLUSIONS This dissertation focuse s on enhancing and evaluating dynamic pricing strategies for managed lane facilities Initially, a thorough literature review of the managed lanes operation components including pricing algorithms current practice of single segment and mul ti segment HOT lane facilities and lane choice models was conducted. D ifferent simulation programs that can be used to simulate HOT lanes were also reviewed The majority of the pricing algorithms currently implemented in practice are heuristic so the toll rates they produce can be further optimized against the network traffic conditions For this purpose, a GA based optimization framework for fine tuning practical pricing algorithms was developed in this dissertation In order to validate the optim ization framework, t he pricing algorithm cu rrently implemented on the 95 Express in South Florida was optimized The GA optimization procedure was implemented in Matlab The simulation experiments demonstrated that the procedure produces good results and y ield s improvement s. In order t o achieve more noticeable improvement s it will be necessary to incorporate a microscopic simulation platform that is able to simulate HOT lane operations like CORSIM into the GA procedure. Further research is needed to impr ove the computational efficiency of the microscopic simulation based GA optimization procedure. T he current practice of managing multi segment HOT lanes facilities showed that there are four different methods (i.e., zone based, origin specific, OD based, a nd distance based) to charge the low occupancy vehicles that use the HOT lanes. Each toll
117 structure has advantages and disadvant ages and the selection of one over the others highly depends on the local conditions and the goals of the HOT lanes operator. As the implementation of HOT lanes is becoming more accept ed and popular in the U.S., a traffic simulation tool that can replicate the HOT lane operation s is very useful in designing and ev aluating managed lanes operation strategies Our literature review in dicate s that there is no t any software presently on the market that can fully simulate the different components of HOT lanes. Therefore, this research also enhanced microscopic simulat or CORSIM to simulate all the function s of HOT lanes. More specifically, t hree main com ponents were developed. They comprise three pricing strategies, a lane choice module and four toll structures for multi segment HOT facilities. The CORSIM enhancements w ere demonstrated by simulating the current and future 95 Express in S ou th Florida. Using data from the current 95 Express, the simulation was calibrated to provide a good match with the actual operation performance measures. The experiments showed that the CORSIM enhancements appear to be able to captur e the primary character istics of HOT lane operations and management. Then segment HOT lane facilities was demonstrated by simulating a ll four toll structures on the future 95 Express which will be a multi segment facility by the end of 2014.
118 APPENDIX A SIMULATING HOT LANES IN CORSIM This appendix provides a guide on how to use CORSIM to simulate a HOT lane network. It describes all the steps in coding a network, selecting a pricing algorithm, choice parameters and spe cifying the toll structure for multi segment HOT lane facilities. When drafting this appendix, it was assumed that readers are already familiar with using CORSIM to simulate a regular freeway network. The steps for simulating HOT lanes in CORSIM are shown in Figure A 1 and are described in detail in the following sections. Figure A 1 HOT l ane s imulation in CORSIM
119 A.1 C oding HOT L ane N etwork The first st ep in simulating a HOT lane facility in CORSIM is to code a HOT lane network, that is specify the links of a freeway network where HOT lanes are present There are three HOT lane use codes that can be placed on a link as shown in Figure A 2 A HOT entry link is placed to represent a HOT lane entrance where vehicles first enter the HOT lanes; HOT continuation links are then placed downstream to a HOT entry link ; and a HOT termination link is used to indicate the en d of the HOT lane segment or facility. The HOT termination link also indicates the last link whose density will be used for the average density calculation for toll determination, as explained later in this appendix. For each HOT lane use code, Figure A 1 presents two types of HOT lanes : non exclusive/ concurrent and exclusive. Exclusive HOT continuation links can be placed along the links/sections where vehicles are neither allowed to enter nor to exit the HOT lanes while the non exclusive counterparts are to indicate that vehicles are allowed to exit but not enter the HOT lanes. Apparently, e ven though the two types of HOT lanes are available for all the HOT lane use codes, the only type that is reasonable for HOT entry and HOT termination links is the n on exclusive one. Finally, HOT lanes can be placed either at the left or the right side of the freeway. After specifying the lane use code for each HOT lane link, the lane characteristics should be input. The HOT lane characteristics introduced in the fol lowing paragraphs including toll paying and free usage vehicles, pricing algorithm and all the parameters associated with the selected pricing algorithm are specified only for HOT entry link s
120 Figure A 2 HOT/HOV lane use c odes First, the vehicles that are allowed to access the HOT lanes either by paying or for free should be specified CORSIM has the following options for these vehicle groups ( See Figure A 3 and Figure A 4 ): Toll paying vehicles Cars with transponders Cars and HOV 2 with transponders All vehicles with transponders All traffic Closed to all traffic Free usage vehicles Registered HOV 2, Registered HOV 3+ and Buses Registe red HOV 3+ and Buses All HOV 2, all HOV 3+ and Buses
121 All HOV 3+ and Buses Only registered HOV 3+ Only Buses All traffic except trucks All traffic Closed to all traffic Figure A 3 Toll paying v ehicles Since toll collection on the HOT lanes is conducted electronically among toll paying vehicles only those equipped with a transponder can legally enter the HOT lanes. The percentage of such vehicles for each vehicle type can be entered in CORSIM. The free usage vehicles are n ot required to have a transponder to use the HOT lanes but they may need to register. Registered vehicles are those that are register ed to the HOT lane authority to use the facility without paying a toll. The HOT
122 lane authority specifies which vehicles are eligible for registration and also the registration process and requirements. Eligible vehicles for registration can be cars with two or more occupants, buses and others. Not every HOT lane operator require s vehicles to register in order to be toll exemp t. However, if the HOT lane authority ha s such requirement, all non registered vehicles are expected to pay to enter the HOT lanes. Figure A 4 Free usage v ehicles Both the percentage of vehicles with transponders and regi stered vehicles for each vehicle type can be input under Edit > Global > Network Properties > Vehicle Types as illustrated in Figure A 5 and Figure A 6
123 Figure A 5 Specifying network p roperties in TSIS Next Figure A 6 Transponder and registered percentage i nput A.2 S etting the P ricing A lgorithm After all the parameters mentioned above are set the prici ng algorithm and the corresponding pricing interval ( in minutes ) for toll calculation should be selected The former specifies how a toll amount is computed while t he latter indica tes how often the
124 toll amount will be calculated and updated In CORSIM, th ree different pricing algorithms are implemented as shown in Figure A 7 Figure A 7 Prici ng a lgorithm s a vailable in CORSIM The first is a so called responsive pricing which is a methodology for determining toll amounts based on the current HOT lane conditions to manage the HOT traffic demand and maintain free flow conditions on HOT lanes. In responsive pricing, the performance measure used to calculate the toll is traffic density ( ). The steps for the toll determination are the following: 1) is calculated for each HOT lane link and further averaged for each HOT lane segment for every toll interval. is then rounded to an integer and multiplied by an alpha parameter whic h adjusts the calculated to reflect segment specific
125 conditions, such as weaving areas and geometric conditions. The default alpha parameter is set to one implying no impact on the calculation. The alpha value can be specified under the model pa rameters tab ( Figure A 10 ) ; 2) calculated for the previous time interval is subtracted from of the current interval to determine the change in ( ); 3) Using the Delta Settings Table ( Figure A 8 ), a toll change is determined. The toll change is either added or subtracted to the toll of the previous interval to calculate the current toll. All the parameters in the Delta Settings Table are user modifiable ; 4) The tol l is compared with the minimum and maximum toll values in the LOS setting table (table on the left in Figure A 9 ). If the toll is outside the acceptable toll range for the corresponding the maximum or minimum toll is applied correspondingly Again, the toll intervals for each LOS are user modifiable. Figure A 8 Delta settings table for responsive p ricing
126 Figure A 9 Minimum and maximum toll v alues for responsive and c losed loop control b ased pricing a lgorithms The second pricing algorithm is a so called closed loop control based approach that also determin es toll values based on real time traffic conditions In this approach, t he toll value at the current time interval depends on the toll at the previous interval the traffic density ( ) at the current time interval and the critical or desired density denoted as The steps for the toll determination are described below: 1) Calculate as in responsive pricing; 2) The toll for the next time interval is calculated as follows: 3) w here is the current toll ; and is a regulator parameter defined by the user under the model parameters tab ( Figure A 10 ) is used to adjust the dis turbance in th e closed loop control, that is the effect of the difference between the measured traffic density and the critical density on the toll amount. is the critical or desired density defined also by the user under the model parameters tab ( Figure A 10 ) is rounded to the closest quarter
127 4) Compare with the minimum and maximum toll values defined by the user (table on the right in Figure A 9 ). If is less than the minimum value or greater than the maximum value, then it takes the minimum or maximum value respectively. Figure A 10 Model p arameters for p ricing a lgorithms T he third pricing scheme that can be selected in CORSIM is time of day pricing As its name suggests, the toll value is not determined in real time in this approach. Instead, it varies according to a toll schedule pre defined by users. This scheme is useful for freeway facilities that have similar tr affic pattern for example, on weekdays. In CORSIM, t he number of tolling intervals can be up to 24, and the duration of each interval varies from 3 to 60 minutes, with a toll amount varying from $0.00 to $12.00. The inputs for time of day pricing are show n in Figure A 11 :
128 Figure A 11 Time of day p ricing A.3 Lane C hoice P arameters After the toll amount is calculated lane choice between t he HOT and the GP lanes is simulated in CORSIM The lane choice model implemented is based on a decision rule that motorists will pay to use the HOT lanes if the benefit they perceive from the travel time savings (TTS) is greater than the toll they are cha rged. The perceived benefit is the value of tim e (VOT) of the traveler multiplied by the perceived TTS, which is assumed to follow a truncated normal distrib ution whose mean is the real ( actual ) TTS (RTTS) and standard deviation customized by a software us er. The RTTS is the difference between travel times on GP and HOT lanes, averaged across a user specified time interval. The RTTS interval in minutes can be input in the HOV/HOT lane tab (see Figure A 7 ) which det ermine s how often RTTS will be evaluated. For example, if it is 1 0 min utes RTTS will be evaluated
129 every 1 0 minutes, and all decisions made in the next 1 0 minutes will be based on the average of the previous 1 0 minutes. Decisions made during the first 1 0 m inutes are based on the value of average RTTS at time 0. Decisions made during minutes 1 1 to 20 will be based on the average RTTS calculated at time 1 0. The lane choice decisions are made whenever a vehicle encounters a HOT lane entry warning sign The loc ation s of the warning sign s are specified by the user ( Figure A 7 ). D ( $/hr ) can be input under Edit > FRESIM > Calibration > Value of Time tab as shown in Figure A 12 and Figure A 13 Figure A 12 FRESIM c alibration A.4 Toll S tructures When a HOT lane facility has multiple segments, motorists can be charged in different ways based on the toll structure implemented by a user There are four basic toll structure s for multi segment facilities: zone based, origin specific distance based and origin destination (OD) based. The toll structure can be selected in the Value of Time tab under F RESIM Setup ( Figure A 13 is provided which mean s that each HOT segment functions as a stand alone single segment HOT lane facility
130 Figure A 13 Value of Time T ab under FRESIM Setup A.4.1 Zone based T olling The HOT lane facility is divided into multiple zones. Each zone can have multiple entrances (HOT entry links) or exits (HOT continuation non exclusive or HOT termination links). To specify in which zone a HOT entry link belongs, a zone number can be input for each HOT entry link, as illustrated in Figure A 10 The toll amount is the same for all entrances that belong to the same zone. The toll amount is calculated at the first HOT entry link in to a zone and is assigned to be associated with all the downstream HOT entry links in the same zone. The total toll amount a motorist pays depends on the numbers of zones he or she traverse s A vehicl e has to make a lane choice decision a t every warning sign upstream of a HOT entry link. Note that when
131 each zone consists of only one HOT entry link, the zone based tolling essenti ally HOT lanes charge individ option. A.4 .2 Origin based Tolling In origin based tolling, the toll is calculated at every HOT entry link and the toll amount that travelers pay depends only on their origins. More precisely, the traveler pays the toll that is displayed on a sign at their entry poin t regardless of how far they intend to travel on the HOT lanes Consequently, they will only have to face the lane choice between HOT and GP lanes once. The toll at a specific HOT entry link is calculated based on the average density of all HOT lane segmen ts between that HOT entry link and the nearest HOT termination link. A.4.3 Distance based Tolling In this toll structure, the toll charged to a motorist depends on the distance that he or she travel s on the HOT lanes. The toll rate, that is toll per mile is the same for all entry locations at a specific time interval. The sign at the entrance displays the minimum toll for entering the facility ( i.e., the toll amount to the immediately downstream exit), the toll per mile and maximum toll for traveling to the end of the facility. In CORSIM, the toll calculation in distance based tolling is similar to that in zone based tolling. More specifically, a user also needs to specify zones. T oll calculation also tak es place at the first HOT entry link to each zone Then, to find the toll per mile the toll is divided by the length of the zone. The toll per mile is assigned to every HOT entry link that belong s to the same zone. The toll per mile for each zone can be different and drivers are charged based on the mile s the y traveled on each zone.
132 A.4.4 OD based Tolling In OD based tolling, the toll that motorists pay depends on where they enter and leave the HOT lanes. In this case, the prices to major destinations are displayed at each entry point so that motorists can estimate approximately the price they have to pay. They can then decide whe ther they want to use the HOT lanes or not. All four tolling structures are fully implemented in CORSIM. A.5 Example Below an example for coding a multi segment facility in CORSIM i s provided Assuming that a HOT lane network consists of the following links: 5a 6a 6b 5b 6c 7a 5c 6d 6e 6f 7b w here 5a, 5b, and 5c are entry links, 6a, 6c, 6d and 6f are continuation exclusive links, 6b and 6e are continuation non exclusive links, and 7a and 7b are termination links. The different implementation for the example network are described below. A.5.1 HOT Lanes Charge I ndividually HOT lanes charge individually option is selected there will be three different toll calculations. The se calculations can be done using any of the three pricing schemes available in CORSIM including responsive, closed loop control based, or time of day. If either of the f irst two is chosen dyna mic pricing is used: 1) The toll amount at entrance 5a will be calculated based on the average density of segments 5a 7a ; 2) The toll amount at entrance 5b will be calculated based on the average density of segments 5b 7a ; 3) The toll amount at entrance 5c will be calculated based on the average density of segments 5c 7b.
133 Drivers make the lane choice decision upstream of every HOT entry link and they are charged each time they travel through a HOT entry link. A.5.2 Zone based T olling If we assume that the network has two zones : 5a 7a and 5c 7b, the toll displayed at 5a and 5b should be the same and drivers who travel from 5a to 7b need to pay two tolls : the one displayed at entrance 5a and the one displayed at entrance 5c. Drivers traveling from 5b to 7b will also have to pay two tolls. If dynamic pricing is implemented, we have the following: 1) The toll amount at entrance 5a will be calculated based on the average density of segments 5a 7a ; 2) The toll amount at entrance 5b is the same as the toll at entrance 5a as these two entrances belong to the same zone; 3) The toll amount at entrance 5c will be calculated based on the average density of segments 5c 7b. A.5.3 Origin based T olling In this case, vehicles that enter at entrance 5a will pay the toll amount displayed a t that entrance regardless of where they exit. Thus, vehicles traveling from 5a to 7b and those traveling from 5a to 6b will pay the same toll. For this specific example network, toll calculation in dynami option. A.5.4 Distance based T olling As mentioned above t he distance based tolling is similar to the zone based tolling in the sense that zones should be specified for both structures. If we assume that there are two zones, that is 5a 7a and 5c 7b, the toll rate displayed on 5a and 5b will be the same. The toll calculation is the same as in the zone based tolling. However, in
134 distance based tolling, a driver who exits before the end of a zone will be charged less than in zone based tolling. A .5.5 OD based T olling In the example network, there are the following OD pairs: 5a 6b 5a 7a 5a 6e 5a 7b 5b 7a 5b 6e 5b 7b 5c 6e 5c 7b Consequently, there will be nine toll calculations. A more complicated pricing algorithm will be developed and implemented in the future. A.6 HOT Lane S imulation O utputs When HOT lanes are simulated, CORSIM generates an additional .csv output file that includes the basic HOT lane inputs and outputs. T here are eighteen columns in this file (see, Figure A 14 (A) and (B ) ). The first nine column s summarize the basic input information and the last nine provide the outputs generated by the software. All these columns are further explained in Table A 1
135 Table A 1 HOT output e xplanation Column No Column n ame Explanation Inputs 1 TIME Simulation time when the toll is calculated and updated. 2 UPSTREAM NODE Upstream node of the HOT entry link. 3 DOWNSTREAM NODE Downs tream node of the HOT entry link. 4 PRICING ALGORITHM Pricing algorithm selected for toll calculation. 5 ORIGIN Origin (applies only to OD based tolling to be implemented). 6 DESTINATION Destination (applies only to OD based tolling to be implemented). 7 ZONE Zone number (applies only to zone and distance based tolling). 8 MIN TOLL Minimum toll set by the user (applies only to responsive and closed loop control based pricing) 9 MAX TOLL Maximum toll set by the user (applies only to responsive and cl osed loop control based pricing) Outputs 10 DENSITY Average density calculated over a zone or segment (applies only to responsive and closed loop control based pricing) 11 DELTA DENSITY Difference in density between two tolling intervals (applies only t o responsive pricing) 12 PRICE Toll 13 TOLL PER MILE Toll rate, i.e., toll per mile (applies only to distance based tolling) 14 MIN CHARGE Minimum toll for entering the facility (applies only to distance based tolling) 15 MAX CHARGE Toll amount for traveling to the end of the facility (applies only to distance based tolling) 16 RTTS Real or actual travel time saving 17 REVENUE Revenue 18 ZONE REVENUE Revenue for each zone (applies only to zone and distance based tolling)
136 HOT Entry Link I nputs UPSTREAM DOWNSTREAM PRICING TIME NODE NODE ALGORITHM ORIGIN DESTINATION ZONE MIN TOLL MAX TOLL A Distance based charging outputs DENSITY DELTA DENSITY PRICE TOLL PER MILE MIN CHARGE MAX CHARGE RTTS REVENUE ZONE REVENUE B Figure A 14 HOT lane o utput A) Summary of Inputs B) Output
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144 BIOGRAPHICAL SKETCH Dimitra Michalaka was born and grew up in Papados, a small Greek village (population 1,500) at the Lesvos i s land In 2001, after she passed the national general exams, she enrolled as a student at the National Technical University of Athens, where she received a Bachelor of Science in civil engineering in 2006. In August 2007, she moved to Gainesville to pursue graduate studies at the University of Florida (UF). In 2009 she e a rned a Master of Science in civil e ngineering and won the Pikarsky Award for Outstanding M.S. Thesis in Science and Technology from the Council of University Transpor tation Research Centers. After she g raduated with the M.S. degree, she was hired as a transportation engineer at the UF Transportation Research Center Then, in Spring 2010 she enrolled at UF in the Ph.D. program in civi l engineering with a focus on transportation engineering In addition to her studies, Dimitra has been involved with several professional organizations and groups such as the UF n Seminar (WTS) student chapter, the UF Institute of Tra nsportation Engineers (ITE) student chapter the Tau Beta Pi (the honorary engineering society), t Bureau (ISSB ) and the Civil and Coastal Engineering (CCE) Graduate Student Advisory Group in which she has often taken leadership positions Dimitra is looking forward to wh at the life after graduation has to bring.