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Modeling network-wide impacts of traffic bottleneck mitigation strategies under stochastic capacity conditions

ProQuest Dissertations and Theses, 2011
Dissertation
Author: Mingxin Li
Abstract:
Traffic congestion occurs because the available capacity cannot serve the desired demand on a portion of the roadway at a particular time. Major sources of congestion include recurring bottlenecks, incidents, work zones, inclement weather, poor signal timing, and day-to-day fluctuations in normal traffic demand. This dissertation addresses a series of critical and challenging issues in evaluating the benefits of Advanced Traveler Information Strategies under different uncertainty sources. In particular, three major modeling approaches are integrated in this dissertation, namely: mathematical programming, dynamic simulation and analytical approximation. The proposed models aim to (1) represent static-state network user equilibrium conditions, knowledge quality and accessibility of traveler information systems under both stochastic capacity and stochastic demand distributions; (2) characterize day-to-day learning behavior with different information groups under stochastic capacity and (3) quantify travel time variability from stochastic capacity distribution functions on critical bottlenecks. First, a nonlinear optimization-based conceptual framework is proposed for incorporating stochastic capacity, stochastic demand, travel time performance functions and varying degrees of traveler knowledge in an advanced traveler information provision environment. This method categorizes commuters into two classes: (1) those with access to perfect traffic information every day, and (2) those with knowledge of the expected traffic conditions across different days. Using a gap function framework, two mathematical programming models are further formulated to describe the route choice behavior of the perfect information and expected travel time user classes under stochastic day-dependent travel time. This dissertation also presents adaptive day-to-day traveler learning and route choice behavioral models under the travel time variability. To account for different levels of information availability and cognitive limitations of individual travelers, a set of "bounded rationality" rules are adapted to describe route choice rules for a traffic system with inherent process noise and different information provision strategies. In addition, this dissertation investigates a fundamental problem of quantifying travel time variability from its root sources: stochastic capacity and demand variations that follow commonly used log-normal distributions. The proposed models provide theoretically rigorous and practically usefully tools to understand the causes of travel time unreliability and evaluate the system-wide benefit of reducing demand and capacity variability.

TABLE OF CONTENTS

ABSTRACT ....................................................................................................................... iii LIST OF FIGURES ........................................................................................................... ix LIST OF TABLES ............................................................................................................. xi ACKNOWLEDGEMENTS .............................................................................................. xii CHAPTER 1. INTRODUCTION .......................................................................................................... 1 1.1 Background ............................................................................................................... 1 1.2 Sources of Travel Time Uncertainty Distributions ................................................... 3 1.3 Challenges and Motivations ...................................................................................... 5 1.3.1 Modeling challenges in static-state programming approach ........................... 5 1.3.2 Modeling challenges in dynamic traffic assignment approach ....................... 7 1.3.3 Modeling challenges in analytical approximation approach ........................... 8 1.4 Research Objectives .................................................................................................. 9 1.5 Overview of Approach and Organization of the Dissertation ................................. 12 2. LITERATURE REVIEW ............................................................................................. 14 2.1 Overview ................................................................................................................. 14 2.2 Role of Traveler Information Systems and Travel Time Uncertainty Sources ....... 14 2.3 Modeling Stochastic Capacity ................................................................................. 17 2.3.1 Headway-based stochastic capacity models .................................................. 17 2.3.2 Stochastic queue discharge rate model .......................................................... 19 2.3.3 Probability-based stochastic capacity models ............................................... 20 2.4 Optimization Model for Static Network Equilibrium Analysis .............................. 21 2.5 Analytical Approach for Single Bottleneck Analysis ............................................. 22 2.6 Simulation-based Approach for Network-wide Analysis ....................................... 24 3. PLANNING-LEVEL METHODOLOGY FOR EVALUATING ATIS STRATEGIES UNDER STOCHASTIC CAPACITY CONDITIONS ..................................................... 28 3.1 Introduction ............................................................................................................. 28 3.2 Conceptual Framework ........................................................................................... 29 3.2.1. Perfect information (PI) based user equilibrium .......................................... 31 3.2.2 Expected travel time (ETT) knowledge-based user equilibrium ................... 34 3.2.3. Quantification of the value of information ................................................... 38 3.3 General Mathematical Problem Formulation .......................................................... 40

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3.3.1 Formulation ................................................................................................... 41 3.3.2 Spreadsheet tool for calculating multiday user equilibrium .......................... 44 3.4 Solution Algorithm .................................................................................................. 46 3.5 Experimental Results ............................................................................................... 50 3.5.1 Measure of effectiveness (MOE) .................................................................. 53 3.5.2 Sensitivity analysis ........................................................................................ 54 3.5.3 Experiments on medium-scale networks ....................................................... 64 3.6 Summary ................................................................................................................. 70 4. MULTIDAY STATIC TRAFFIC EQUILIBRIUM ANALYSIS UNDER STOCHASTIC DEMAND AND CAPACITY CONDITIONS ....................................... 72 4.1 Introduction ............................................................................................................. 72 4.2 Problem Statement and Illustrative Example .......................................................... 74 4.2.1 Traveler information (TI) users ..................................................................... 78 4.2.2 Expected travel time (ETT) knowledge users ............................................... 79 4.3 General Mathematical Problem Formulation .......................................................... 80 4.4 Solution Algorithm .................................................................................................. 86 4.5 Numerical Experiments ........................................................................................... 89 4.6 Summary ................................................................................................................. 92 5. DAY-TO-DAY TRAVELER LEARNING FRAMEWORK ....................................... 95 5.1 Introduction ............................................................................................................. 95 5.2 Overall Modeling Framework ................................................................................. 96 5.3 Day-To-Day Traveler Learning and Route Choice Model ..................................... 98 5.3.1 Conceptual framework .................................................................................. 99 5.3.2 Route choice utility function and simplified route switching rule .............. 102 5.4 Conceptual Simulation Framework and System Implementation ......................... 106 5.5 Case Study ............................................................................................................. 110 5.6 Summary ............................................................................................................... 113 6. ANALYTICAL MODELS ON DERIVING TRAVEL TIME VARIABILITY DISTRIBUTIONS FROM STOCHASTIC CAPACITY DISTRIBUTIONS ................ 115 6.1 Introduction ........................................................................................................... 115 6.2 Review of Statistical Properties of Log-Normal Distribution ............................... 118 6.3 Deriving Travel Time Variability Distribution Based on BPR Function .............. 120 6.4 Deriving Travel Time Variability Distribution Based on Point Queue Model ..... 122 6.5 Deriving Time-Dependent Delay Variability Distribution ................................... 130 6.6 Calibrating Probability Distributions .................................................................... 133 6.7 Summary ............................................................................................................... 139 7. CONCLUSIONS AND FUTURE RESEARCH NEEDS........................................... 141 7.1 Overall Conclusions .............................................................................................. 141 7.2 Research Contributions ......................................................................................... 144 7.2.1 Theoretical Contributions ............................................................................ 144 7.2.2 Practical Contributions ................................................................................ 145 7.3 Future Research Needs .......................................................................................... 146

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APPENDIX: LIST OF TERMS ...................................................................................... 148 REFERENCES ............................................................................................................... 150  

LIST OF FIGURES   Figure Page 1.1- Illustrates the percentage of each congestion source in the nation. ............................. 2 1.2- Prebreakdown Headway Distribution for I-880. ......................................................... 5 1.3- Four main areas of interest. ....................................................................................... 13 2.1- Distribution of lane capacity converted from headway. ............................................ 20 3.1- Simple network used as an illustrative example of the framework. .......................... 30 3.2- Equilibrium solutions with 100% PI users. ............................................................... 33 3.3- Solutions with 100% ETT information users. ........................................................... 37 3.4- Solutions on a reduced-capacity day. ........................................................................ 39 3.5- Day-dependent travel times on different routes. ....................................................... 40 3.6- Spreadsheet-based calculation model. ....................................................................... 45 3.7- Solution algorithm for static traffic assignment with both PI and ETT users. .......... 47 3.8- Histogram of 100 stochastic capacity samples. ......................................................... 52 3.9- Effectiveness of information provision at varying demand levels. ........................... 55 3.10- Effectiveness of information provision with different market penetration rate. ..... 56 3.11- Effectiveness of information provision with varying toll. ....................................... 58 3.12- Effectiveness of information provision for different routes with varying toll. ....... 61 3.13- Value of information as a function of FFTT difference and demand level. ............ 63 3.14- Chicago sketch network (left) and Anaheim, California network (right). ............... 67

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3.15- Convergence patterns on Chicago sketch network. ................................................. 68 4.1- Simple network used as an illustrative example. ....................................................... 77 4.2- Time-dependent capacity, demand and travel time patterns under different vehicle information market penetration rates. ........................................................................ 77   4.3- Travel flow split solution on four different types of days. ........................................ 85 4.4- Histogram of 100 stochastic demand flow rate samples. .......................................... 91 4.5- Effectiveness of information provision under stochastic capacity with different market penetration rate. ............................................................................................. 93   5.1- Capacity-Enhancing Strategy Evaluation Framework. ............................................. 97 5.2- Comprehensive conceptual simulation framework. ................................................ 107 5.3- Portland network study area. ................................................................................... 111 5.4- Network-wide simulation results. ............................................................................ 112 6.1- Local link marginal delay evaluation method for vehicle entering at time t. .......... 124 6.2- Local marginal delay evaluation method for one unit of departure flow change at time t. ....................................................................................................................... 125   6.3- Total delay change for one unit of discharge rate change for the entire congestion duration. ................................................................................................................... 126   6.4- Waiting time variability in different queue duration cases. ..................................... 129 6.5- Time-dependent queuing evolution diagram. .......................................................... 131 6.6- Log-normal probability density function for queue discharge rate. ........................ 135 6.7- Shifted Log-normal probability density function for queue discharge rate. ............ 135 6.8- Log-normal probability density function for demand flow rate distributions. ........ 136 6.9- Log-normal probability density function for travel time index distribution. .......... 137 6.10- Complete PDF for predicted travel time variations. .............................................. 138

LIST OF TABLES   Table Page 3.1- Day-dependent path demand, capacity and travel time values. ................................. 31 3.2- Test network characteristics and computational performance. ................................. 67 3.3- Value of traveler information under different peak-hour capacity approximation schemes...................................................................................................................... 70   4.1- Sample solution for 5% TI users and 95% ETT users. .............................................. 84 4.2- Representative traveler information provision and traffic management strategies. .. 90 6.1- Summary of calibration results. ............................................................................... 136

ACKNOWLEDGEMENTS   I gratefully acknowledge the support of a great number of people who offered support, advice, inspiration and friendship throughout my time at the University of Utah. First of all, I would like to express my sincerest gratitude to my advisor, Dr. Xuesong Zhou for his support and guidance throughout my Ph.D. study. I could not have completed my graduate work without his kind guidance. My thanks also goes to Dr. Harvey J. Miller for his willingness to serve as a member of my committee and his invaluable help and insightful comments on many parts of my dissertation. I am also grateful to Dr. Richard J. Porter and Dr. Pedro Romero for their constructive comments. I must include a special word of thanks to Dr. Martin for his advice and care. He has encouraged me to clarify the scope of this dissertation, which proved to be a great piece of advice. Thanks are also extended to Dr. Nagui M. Rouphail at the North Carolina State University. His professional insights and constructive comments on the research methodology have significantly improved the quality of this dissertation. This research was conducted under the sponsorship of the Strategic Highway Research Program (SHRP2) as part of C05: Understanding the Contribution of Operations, Technology, and Design to Meeting Highway Capacity Needs. I would like to thank Dr. Billy M. Williams, Anxi Jia, Wayne Kittelson and Brandon Nevers and other team members for their valuable contributions and insight throughout the development of this research project.

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In closing, I am deeply grateful for love and support by my wife, Li Su, who sacrificed a lot in my pursuit of this Ph.D. Ultimately, I must acknowledge and thank my mom, dad for their love and endless support. There are just not enough words to express my gratitude to my family.

CHAPTER 1

INTRODUCTION

1.1 Background Traffic congestion problems lead to a wide range of adverse consequences such as traffic delays, travel time unpredictability, and increased noise pollution as well as deterioration of air quality. Broadly speaking, traffic congestion occurs because the available capacity cannot serve the desired demand on a portion of roadway at a particular time. As shown in Figure 1.1, Major sources of congestion include physical bottlenecks, incidents, work zones, bad weather, poor signal timing, special events and day-to-day fluctuations in normal traffic (Cambridge Systematics, 2005). Considerable research efforts have been devoted to understanding and quantifying the effectiveness of different traffic mitigation strategies in addressing various sources of delay. For instance, recurring congestion due to physical bottlenecks can be mitigated through road capacity enhancement. Real-time traffic information dissemination can reduce negative impacts of disruptions of nonrecurring congestion due to traffic incidents and special events. The success of advanced traveler information systems depends on careful planning and an integrated system-level perspective, which calls for advanced transportation analysis tools to estimate how effective information provision and tolling

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strategies can encourage route/departure time/mode switching to more effectively utilize network-wide capacity. This requires adopting and integrating various models that have evolved over the past decade, such as stochastic capacity analysis and dynamic traveler behavior modeling, within the classical user equilibrium analysis framework. Traffic congestion mitigation strategies may include, but are not limited to, road capacity enhancement, and technological solutions, such as traffic signal optimization, incident management on freeways and arterials, Advanced Traveler Information Systems (ATIS), and pricing, etc. As one of the critical parts of implementing Intelligent Transportation Systems (ITS) infrastructures, ATIS is intended to inform travelers of unusual traffic congestion to allow users to make better route/departure time and mode decisions under uncertain conditions. Quantifying the effectiveness of those ATIS strategies is a theoretically challenging and practically important question, because the actual assessment of the system benefits can facilitate public transportation agencies to effectively design, deploy and use the traveler information systems within funding constraints. Given the emerging availability of private-sector traffic data and services, transportation system planners and managers are extremely interested in how different sources of traffic information with different degrees of data quality, coverage, and accessibility influence travelers’ decisions and in terms of decreased congestion or improved travel time reliability provides benefits to transportation system users.

1.2 Sources of Travel Time Uncertainty Distributions To systematically evaluate the benefits of traveler information provision strategies in a realistic stochastic environment, a reliable modeling tool needs to consider various

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sources of travel time uncertainties. Generally, inherent travel time uncertainty stems from the following sources: (1) The first source of uncertainty has a bearing on system demand input, primarily caused by day-to-day variations, seasonal variations and special events. (2) The second uncertainty is due to system throughput variation, which results from stochastic capacity or incidents, work zones, and weather conditions. Under stochastic capacity and new ATIS strategies, a more dynamic learning model is needed to balance the two different sources - available information and personal experience. For example, an empirically-observed distribution of stochastic capacity (Jie, et al. 2010) is illustrated in Figure 1.2. It shows that the 50th percentile capacity on I-880 is 1,976 passenger cars per hour per lane, while the 85th percentile capacity is 1,778 passenger cars per hour per lane. Thus, 15 percent of the time, the I-880 bottleneck breaks down after only 1,778 passenger cars per hour per. (3)The third uncertainty is further compounded by the absence of precise traffic information due to inadequate sensor coverage or limited traveler knowledge and experience, which can further compound the issue of travel time uncertainty. (4) The fourth uncertainty is traveler perception errors, which is typically modeled in a stochastic traffic assignment framework to capture unbiased random noises (with a mean of zero) associated with drivers’ socio-economic characteristics, personal observations, as well as the quality of traveler information.

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Capturing stochastic capacity at the critical points of networks (such as bottlenecks) which suffer from queue and congestion more frequently, e.g., freeway bottlenecks and signalized intersections, enables reasonable and realistic modeling of travel time variability and the concept of sustainable flow rates. Without taking into account this feature, it is impossible to fully consider the variability in the transportation system due to one of its critical sources, stochastic capacity. Moreover, travel times would be stochastic on different days, which further motivate the development of day-to- day learning and route updating models to be discussed in this dissertation. In order to incorporate stochastic capacity in a user equilibrium framework and study the impact of information on drivers who tend to maximize their expected utility, de Palma, et al. (2005) used a graphical method to compare two extreme information user classes which govern day to day traffic conditions. This early investigation provides great theoretical insights in analyzing the travelers' behavior under stochastic capacity. However a more rigorous mathematical programming model and efficient solution algorithms are critically needed to describe the steady-state user equilibrium conditions on a general traffic network. Although a variety of network analysis tools are currently available to assess different traffic operations and control strategies, two challenging theoretical research questions remain for characterizing steady-state conditions under stochastic capacity: 1. How to develop mathematical models that describe realistic user behavior under stochastic capacity? 2. How to develop efficient and operational algorithms to find multiday user equilibrium solutions under stochastic capacity on a large-scale network?

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1.3.2 Modeling challenges in dynamic traffic assignment approach To describe the dynamic traveler behavior over multiple days, a day-to-day learning model is required to describe the nonequilibrium state of traffic patterns. Dynamic Traffic Assignment (DTA) methodologies uniquely address these modeling needs, and a variety of models have been developed to represent the time-dependent route choice behavior (Mahmassani, 2001; Ben-Akiva, 2001). Most day-to-day learning models focus on long-term planning applications with stable road capacity. For instance, in the day-to-day learning frameworks proposed by Hu and Mahmassani (1997), Jha et al. (1998), and Chen and Mahmassani (2004), day-to-day traffic evolution and stochasticity are mainly due to route and departure time choices. Additionally, these models mainly study the learning behavior based on historical personal traveling experiences and real- time snapshot information. In reality, travelers are more likely to utilize various information sources, before their trips and en-route, to find the most reliable routes. Three major limitations exist in past studies in terms of traveler’s learning behavior. First, most of these models only consider the day-to-day travel choice dynamic represented under deterministic capacity, rather than considering stochastic and sustainable service rate (SSR). As a result, most research on DTA models has been based only on within-day dynamics, where all parameters associated with the system (such as supply and demand) are time-dependent but still under a deterministic framework. Additionally, under stochastic capacity, travel time experience on a single day can be dramatically affected by the underlying capacity, which in turn influences drivers' travel choices. Second, drivers only utilize the experienced travel times on the latest days to reach convergence, e.g., myopic adjustment model (Hatcher and Mahmassani, 1992).

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Third, users are assumed to have complete network knowledge and perfect information regarding the time dependent system conditions and are able to make optimal route choices to minimize their travel times. However, these models ignore the multiple user classes (MUC) with different information availability. In this context, the primary challenging research questions considered are: 3. How to update variability of travel time estimates due to stochastic capacity for different information groups? 4. How to model predictive information and day-to-day evolution which result from user decision and network dynamics?

1.3.3 Modeling challenges in analytical approximation approach Substantial development attention has been given to both the traffic network modeling and traffic flow theory fields in an effort to quickly estimate and predict travel time variability from its underlying uncertainty sources, because traffic systems can be viewed as stochastic processes with nondeterministic demand and capacity inputs. Focusing on analytical travel time performance functions, e.g., widely used U.S. Bureau of Public Roads (BPR) functions, a number of studies have developed various numerical approximation methods to characterize travel time variability distributions as a result of stochastic capacity and stochastic demand. A well recognized limitation of the BPR function and other static travel time functions is that it cannot effectively describe the dynamic buildup and dissipation of traffic system congestion. Consequently, the travel time variability estimation methods from the above studies are more suitable for analyzing long-term steady-state traffic equilibrium results; dynamic traffic-oriented

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models are still critically needed for quickly estimating path travel time variability distributions, especially under heavy congestion conditions. Given a set of observed or simulated traffic conditions, e.g., traffic flow and queue profiles on a link or a corridor, this dissertation provides efficient analytical approximation methods to specify the Probability Density Function (PDF) of travel time distributions as a result of stochastic capacity and demand distributions. This study aims to address the following two research questions: 5. For planning-level applications, how can a quick characterization of travel time reliability statistics be used without resorting to the comprehensive but computationally challenging day-to-day simulation or numerical approximation approaches? 6. For real-time traffic prediction applications, how can an analytical relationship be derived and constructed between the capacity change and the waiting time change on a bottleneck?

1.4 Research Objectives To meet the six research questions described previously, this research introduces and extends the following research methodologies. To address research questions (1-2), this research will first focus on modeling and solving the steady-state user equilibrium problem with stochastic capacity, to find a single path flow pattern that satisfies the generalization of Wardrop’s first principle: travelers with the same OD and departure time experience the same and minimum expected travel time along any used paths on different days, with no unused path offering a lower expected travel time. A new model will be developed to explicitly address the

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stochastic nature of network capacity and represents travelers’ imperfect route choice in response to capacity fluctuation in a day-to-day learning framework. The resulting problem is an expected utility-based dynamic user equilibrium problem that is formulated using a gap function approach, based on the gap function-based terminology given by Smith (1993) and a recent paper by Lu et al. (2009). To address research question (3), the traveler decision will be simulated in a day- to-day learning behavioral framework. This task will adapt the empirically calibrated choice model by Noland et al. (1998) to explicitly account for travel times, early and late schedule delays, and travel time reliability. The utility function will therefore take into account the essential traffic attributes, such as alternative travel time and travel time reliability. The underlying travel behavior model in the enhanced traffic simulator should be able to (1) combine multiple data sources to make travelers’ own “predictions”; (2) dynamically adjust travelers’ confidence levels on different information sources, based on experienced travel times. To address research question (4), this research will formalize a new theoretical traffic estimation-prediction framework that considers a variety of information sources and can quantify the impact of information accuracy. Essentially, the travel behavior model will consider three major information sources: historical/experienced, pretrip, and en-route information. This research aims to seamlessly incorporate stochastic capacity models at freeway bottlenecks and signalized intersections, and develop adaptive day-to- day traveler learning and route choice behavioral models under the travel time variability introduced by random capacity variations. The model will adaptively recognize and

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capture the systematic day-to-day traffic evolution, and also maintain robustness under disruptions as a result of unexpected incidents and random weather conditions. To address research questions (5-6), this study will utilize several key statistical properties of the log-normal distribution, which is a state-of-practice distribution used in many empirical studies for describing travel time variability. By assuming log-normal distributions for stochastic demand and capacity, and in the context of the BPR function as travel time performance functions, this study proves that the resulting travel time follows a log-normal distribution, so the travel time variability can be analytically derived from the variation parameters in demand and capacity. Furthermore, this research considers a more realistic point queue model. Under an assumption of log- normal distributions for stochastic capacity variations, the corresponding total waiting time will be characterized through log-normal distributions. This dissertation then plans to use simplified peak-hour demand profiles to derive time-of-day travel time variability functions at a traffic bottleneck. Additionally, this dissertation provides theoretical investigation results for the following emerging practical questions from ATIS planning and deployment applications. (1) Given low-resolution traffic information freely available from radio stations and freeway Variable Message Signs (VMS), can additional high-quality traffic information provision services, such as Internet-connected GPS navigation devices, improve the system-wide average travel time or travel time reliability? (2) Typically, travelers do not have full knowledge of historical traffic patterns for each link in a transportation network, and they acquire and update their own network knowledge based on their past experienced travel time. Recently, many websites, such as

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Google Maps, have begun to provide free color-coded maps for displaying historical regional travel time patterns. This source provides additional opportunities for commuters to learn the traffic conditions and enhance their network knowledge beyond their own experienced routes. Can the improved network knowledge quality improve the overall system performance? (3) In addition to many real-time ATIS strategies that focus on informed route switching, many traffic management strategies, such as telecommuting and flexible working hours, aim to reduce and smooth the overall day-to-day travel demand variations. Transportation agencies need to quantify the benefit and then prioritize various potential congestion mitigation solutions: With limited funding constraints, should the transportation agencies increase ATIS market penetration rates, improve real-time data quality, or reduce day-to-day traffic demand variations?

1.5 Overview of Approach and Organization of the Dissertation This dissertation has seven chapters. The comprehensive evaluation framework in Figure 1.3 indicates the structure of this dissertation. Aiming to provide a comprehensive review on various traffic bottlenecks and congestion modeling elements, Chapter 2 discusses several topics pertaining to ATIS, stochastic capacity modeling, optimization approach for equilibrium analysis, analytical approach for a single bottleneck analysis and simulation-based approach for dynamic traffic travel time analysis. Focusing on steady-state static user equilibrium analysis, Chapter 3 considers stochastic capacity and travel time performance functions in an advanced traveler information provision environment. Chapter 4 further considers the steady-state evaluation of traveler

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Figure 1.3- Four main areas of interest.   information provision strategies with stochastic traffic demand, stochastic road capacity, and different degrees of traffic information provision quality. Chapter 5 presents a simulation-based method to seamlessly incorporate stochastic capacity models at freeway bottlenecks and signalized intersections, and develops adaptive day-to-day traveler learning and route choice behavioral models under the travel time variability introduced by random capacity variations. With a focus on a single bottleneck with stochastic demand/supply distributions, a volume-to-capacity ratio-based travel time function and a point queue model are used in Chapter 6 to demonstrate how day-to-day travel time variability can be explained from the underlying stochastic demand and capacity distributions. Concluding remarks and future research extensions are given in Chapter 7.

CHAPTER 2

LITERATURE REVIEW

2.1 Overview This chapter reviews topics relevant to modeling stochastic capacity and three categories of analysis approaches associated with travel time uncertainty, network equilibrium and single bottleneck issue. After a short introduction to the role of ATIS and the sources of network evolution uncertainty, section 2.3 highlights three approaches for modeling stochastic capacity, namely headway-based stochastic capacity models, stochastic queue discharge rate model and probability-based stochastic capacity models. Section 2.4 reviews the literature pertaining to optimization model for static network equilibrium analysis. Section 2.5 overviews major analytical approaches for single bottleneck analysis. Finally, the literature on simulation-based approach for network- wide dynamic traffic evolution analysis is reviewed in section 2.6.

2.2 Role of Traveler Information Systems and Travel Time Uncertainty Sources Advanced Traveler Information Systems (ATIS) is intended to inform travelers of unusual traffic congestion, and further allow users to make better route/departure time

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and mode decisions under uncertain conditions. How to quantify the effectiveness of those ATIS strategies is a theoretically challenging and practically important question, as the actual assessment of the system benefits can facilitate public transportation agencies to effectively design, deploy and use the traveler information systems within funding constraints. Given the emerging availability of private-sector traffic data and services, transportation system planners and managers are extremely interested in how different sources of traffic information with different degrees of data quality, coverage, and accessibility influence travelers’ decisions and provide benefits to transportation system users, e.g., in terms of decreased congestion or improved travel time reliability. Generally, inherent travel time uncertainty stems from the following sources: (1) The first source of uncertainty has a bearing on system demand input and is primarily caused by day-to-day variations, seasonal variations and special events. Another level of traveler decision uncertainty is related to random departure times and route choice, which can lead to uncertain demand input for a certain set of links (Noland and Polak, 2002). (2) The second uncertainty is due to system throughput variation, which results from stochastic capacity (Brilon et al., 2005, Chen et al., 2002), incidents, work zones, or weather conditions (Srinivasan and Guo, 2004). Under stochastic capacity and new ATIS strategies, a more dynamic learning model is needed to balance the two different sources- available information and personal experience. Past studies focusing on sources of day- to-day variation and capacity reliability for a road network do not fully consider uncertainty related to alternative route, which should have different features compared with the current selected route.

Full document contains 170 pages
Abstract: Traffic congestion occurs because the available capacity cannot serve the desired demand on a portion of the roadway at a particular time. Major sources of congestion include recurring bottlenecks, incidents, work zones, inclement weather, poor signal timing, and day-to-day fluctuations in normal traffic demand. This dissertation addresses a series of critical and challenging issues in evaluating the benefits of Advanced Traveler Information Strategies under different uncertainty sources. In particular, three major modeling approaches are integrated in this dissertation, namely: mathematical programming, dynamic simulation and analytical approximation. The proposed models aim to (1) represent static-state network user equilibrium conditions, knowledge quality and accessibility of traveler information systems under both stochastic capacity and stochastic demand distributions; (2) characterize day-to-day learning behavior with different information groups under stochastic capacity and (3) quantify travel time variability from stochastic capacity distribution functions on critical bottlenecks. First, a nonlinear optimization-based conceptual framework is proposed for incorporating stochastic capacity, stochastic demand, travel time performance functions and varying degrees of traveler knowledge in an advanced traveler information provision environment. This method categorizes commuters into two classes: (1) those with access to perfect traffic information every day, and (2) those with knowledge of the expected traffic conditions across different days. Using a gap function framework, two mathematical programming models are further formulated to describe the route choice behavior of the perfect information and expected travel time user classes under stochastic day-dependent travel time. This dissertation also presents adaptive day-to-day traveler learning and route choice behavioral models under the travel time variability. To account for different levels of information availability and cognitive limitations of individual travelers, a set of "bounded rationality" rules are adapted to describe route choice rules for a traffic system with inherent process noise and different information provision strategies. In addition, this dissertation investigates a fundamental problem of quantifying travel time variability from its root sources: stochastic capacity and demand variations that follow commonly used log-normal distributions. The proposed models provide theoretically rigorous and practically usefully tools to understand the causes of travel time unreliability and evaluate the system-wide benefit of reducing demand and capacity variability.