Table of Contents

List of Figures…………………………………………………………………………………………………………xiii
List of Tables…………………………………………………………………………………………………………. xvii
Notations ……………………………………………………………………………………………………………….. xix
Part I: Introduction…………………………………………………………………………………………………… 1
1 Introduction ………………………………………………………………………………………………………….. 3
1.1 Introduction to the Research Topic …………………………………………………………………….. 3
1.2 Research Questions and Objectives ……………………………………………………………………. 5
1.3 Research Approach ………………………………………………………………………………………….. 9
1.3.1 Research approach for questions/objectives in part 1: modeling travelers’ choice
behavior under uncertainty …………………………………………………………………………………….9
1.3.2 Research approach for questions/objectives in part 2: dynamic user equilibrium under
uncertainty …………………………………………………………………………………………………………10
1.3.3 Research approach for questions/objectives in part 3: dynamic network assignment
procedures for stochastic networks………………………………………………………………………..10
1.3.4 Research approach for questions/objectives in part 4: a reliability-based dynamic
network design methodology………………………………………………………………………………..10
1.4 Research Scope ……………………………………………………………………………………………… 11
1.5 Main Research Contributions…………………………………………………………………………… 11
1.5.1 Scientific contributions………………………………………………………………………………………..11
1.5.2 Practical relevance………………………………………………………………………………………………13
1.6 Thesis Outline ……………………………………………………………………………………………….. 14
Part II: Traveler’s Choice Behavior Modeling under Travel Time Uncertainty…………. 17
2 Modeling Traveler’s Departure Time/Route Choice Behavior under Uncertainty….. 19
2.1 Introduction …………………………………………………………………………………………………… 19
2.2 Behavioral Investigation of Uncertainty Considerations ……………………………………… 20
2.3 A Generalized Model for Traveler’s Departure Time/Route Choice Behavior Under
Uncertainty……………………………………………………………………………………………………. 22
x Reliability-based Dynamic Network Design with Stochastic Networks
2.3.1 Equivalence of the mean-variance approach and the scheduling approach………………….23
2.3.2 A new generalized utility function ………………………………………………………………………..26
2.3.3 Conclusions ……………………………………………………………………………………………………….26
2.4 Two-dimensional Parameters in the Utility Functions…………………………………………. 28
2.5 Non-linearity in Schedule Delay Costs ……………………………………………………………… 29
2.6 Conclusions …………………………………………………………………………………………………… 31
Part III: Theoretical and Simulation-based Comprehensive Network Modeling under
Uncertainty …………………………………………………………………………………………………………….. 33
3 Theoretical Investigation of Dynamic User Equilibrium in a Stochastic Bottleneck
Model ………………………………………………………………………………………………………………….. 35
3.1 Introduction …………………………………………………………………………………………………… 35
3.2 Dynamic User Equilibrium with a Deterministic Bottleneck Model……………………… 36
3.3 Dynamic User Equilibrium with a Stochastic Bottleneck Model ………………………….. 40
3.3.1 Behavioral assumptions……………………………………………………………………………………….40
3.3.2 Existence of a long term equilibrium……………………………………………………………………..41
3.3.3 Random capacities………………………………………………………………………………………………42
3.3.4 Formulation and analytical solutions to the dynamic user equilibrium……………………….43
3.3.5 Graphical results on the departure pattern at long term equilibrium …………………………..51
3.4 Conclusions and Discussions …………………………………………………………………………… 60
4 Dynamic User Equilibrium and a Simulation-based Solution Approach………………… 61
4.1 Introduction …………………………………………………………………………………………………… 61
4.2 Stochastic Network and Departure time and Dynamic Deterministic User Equilibrium
with Vertical Queues………………………………………………………………………………………. 63
4.2.1 Formulation of SN-DDDUEV………………………………………………………………………………63
4.2.2 Existence of SN-DDDUEV ………………………………………………………………………………….64
4.2.3 Simultaneous departure time/route choices …………………………………………………………….64
4.2.4 DNL with vertical queues…………………………………………………………………………………….65
4.2.5 Modeling stochastic capacities ……………………………………………………………………………..65
4.3 Stochastic Network and Departure Time and Dynamic Probabilistic User Equilibrium
with Horizontal Queues…………………………………………………………………………………… 66
4.3.1 Formulation of SN-DDPUEH ………………………………………………………………………………66
4.3.2 Existence of SN-DDPUEH…………………………………………………………………………………..67
4.3.3 Simultaneous departure time/route choices …………………………………………………………….67
4.3.4 DNL with horizontal queues…………………………………………………………………………………68
4.3.5 Capacity modeling………………………………………………………………………………………………69
4.4 Deterministic Network and Departure Time and Dynamic Deterministic User
Equilibrium with Vertical Queues…………………………………………………………………….. 71
4.5 Static Probabilistic User Equilibrium with Stochastic Networks…………………………… 72
4.6 Convergence Criteria………………………………………………………………………………………. 73
4.6.1 Gap function ………………………………………………………………………………………………………73
4.6.2 Relative flow changes………………………………………………………………………………………….73
4.6.3 Duality gap ………………………………………………………………………………………………………..74
4.7 Development of a Simulation-based Approach ………………………………………………….. 75
4.8 Application to a Single Bottleneck Model with Deterministic Capacities and Vertical
Queues………………………………………………………………………………………………………….. 77
4.9 Application to a Single Bottleneck Model with Stochastic Capacities and Vertical
Queues………………………………………………………………………………………………………….. 78
4.10 Conclusions …………………………………………………………………………………………………… 80
CONTENTS xi
Part IV: Network Design Methodology including Reliability…………………………………….. 81
5 Reliability-based Dynamic Network Design with Stochastic Networks…………………… 83
5.1 Introduction …………………………………………………………………………………………………… 83
5.2 Definition of Reliability-based Dynamic Network Design Problem ……………………… 85
5.3 Design Objectives ………………………………………………………………………………………….. 86
5.3.1 Optimize network efficiency and network reliability……………………………………………….87
5.3.2 Minimizing total network cost for travelers ……………………………………………………………89
5.4 Design Variables ……………………………………………………………………………………………. 89
5.5 Formulation of the Reliable Dynamic Network Design Problem………………………….. 90
5.6 Formulation of the Static Reliable Network Design Problem……………………………….. 92
5.7 Summary ………………………………………………………………………………………………………. 93
6 Solution Approaches of the Dynamic Network Design Problem …………………………….. 95
6.1 Introduction …………………………………………………………………………………………………… 95
6.2 Properties of the Design Problem……………………………………………………………………… 95
6.3 Generation of the Master Set of Lane Designs …………………………………………………… 97
6.4 A Road Network-oriented Genetic Algorithm………………………………………………….. 100
6.5 A Combined Genetic Algorithm and Set Evaluation Algorithm …………………………. 105
6.6 Summary …………………………………………………………………………………………………….. 105
7 Design of Complete Networks …………………………………………………………………………….. 107
7.1 Introduction …………………………………………………………………………………………………. 107
7.2 Impacts of Link Independences………………………………………………………………………. 107
7.3 Network Description …………………………………………………………………………………….. 109
7.4 Impacts of Covariance Matrix on The Evaluations……………………………………………. 110
7.5 Design Solution in Case of SN-SPUE……………………………………………………………… 112
7.6 Design Solution in Case of SN-DDPUEH with Low Capacity Variations……………. 117
7.7 Design Solution in Case of SN-DDSUEH with High Capacity Variations …………… 121
7.8 Conclusions …………………………………………………………………………………………………. 125
Part V: Conclusions ………………………………………………………………………………………………. 127
8 Conclusions and Future Research ………………………………………………………………………. 129
8.1 Introduction …………………………………………………………………………………………………. 129
8.2 Summary …………………………………………………………………………………………………….. 129
8.3 Findings and Conclusions ……………………………………………………………………………… 131
8.3.1 Modeling traveler’s departure time/route choice behavior under uncertainty…………….131
8.3.2 Dynamic user equilibrium under uncertainty ………………………………………………………..132
8.3.3 Dynamic network assignment procedures for stochastic networks …………………………..133
8.3.4 A reliability-based dynamic network design methodology ……………………………………..133
8.4 Recommendations and values to practical applications……………………………………… 134
8.5 Discussion …………………………………………………………………………………………………… 135
8.6 Future Research……………………………………………………………………………………………. 136
Bibliography …………………………………………………………………………………………………………. 137
Appendix A: Detailed Derivations of the Analytical Analyses in Stochastic Bottleneck
Model ………………………………………………………………………………………………………………… 147
Appendix B: Analytical Results on Stochastic Bottleneck Model with Scales……………. 151
xii Reliability-based Dynamic Network Design with Stochastic Networks
Summary………………………………………………………………………………………………………………. 153
Samenvatting ………………………………………………………………………………………………………… 157
概述(Summary in Chinese) ……………………………………………………………………………………. 161
About the Author ………………………………………………………………………………………………….. 165
Author’s Publications ……………………………………………………………………………………………. 167
TRAIL Thesis Series ……………………………………………………………………………………………… 171

Abstract

Transportation systems are stochastic and dynamic systems. The road capacities and the travel demand are fluctuating from time to time within a day and at the same time from day to day. For road users, the travel time and travel costs experienced over time and space are stochastic, thus desire reliable travel times and low travel costs by altering routes or departure times. Road authorities and designers aim to design road networks such that they provide efficient and reliable services to the road users. Travelers’ choice behavior under stochastic travel times/costs and the design of the road networks are mutually affecting each other. Travelers’ choice behavior under stochastic travel times, especially route/departure time choice behaviors has attracted increasing attentions in the last decade. However, in most studies on network design problems with stochastic capacity or travel demand, travelers’ choice behavior, especially their departure time choice behavior under stochastic travel times are not considered. Instead, static traffic assignment is followed in most network design studies with stochastic travel times, which from our point of view is not realistic in terms of network performance assessments. This motivated our research direction. We aim to establish a network design approach with which dynamic traffic assignment is followed to capture the dynamics in flow propagations and spillback effects. Travelers’ departure time/route choice behavior under stochastic travel times is explicitly modeled. Travel time reliability is taken into account on both the individual choice behavior and network performance evaluation with stochastic networks. Discrete network design problem is dealt with, where numbers of lanes on a set of potential links are the design variables. This dissertation firstly works on the modeling of travelers’ departure time/route choice behavior under stochastic capacities. A generalized travel cost function is proposed to model travelers’ departure time/route choice behavior under uncertainty. The derived generalized travel cost function, which is more behaviorally sound and flexible, is adopted to model the reliability-based long term user equilibrium with departure time choices. A reliability-based dynamic network design approach is proposed and formulated of which numbers of lanes on all the potential links are the design variables. A combined road network-oriented Genetic Algorithm and set evaluation algorithm is proposed to solve the dynamic network design problem. A new systematic approach is proposed to eliminate the infeasible, unconnected and illogical lane designs in order to reduce the solution space and to save computation time. The proposed reliability-based dynamic network design approach is applied to a hypothetical network, and its solutions are compared to a corresponding static network design approach. It is concluded that the static network design approach may lead to poor designs. In general static traffic assignment underestimates the overall total network travel time and total network travel costs. Dynamic network design approach appears to derive a fairly good allocation of road capacity over space and makes the best utilization of the network capacity over time. A version of Braess paradox appears in case of reliability-based cost functions in both static and dynamic networks.

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