Dynamic Travel Choice Models : A Variational Inequality Approach

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1 Analysis of Dynamic Transportation Systems1.1 Introduction -- 1.2 Significance of Dynamic Transportation Network Models -- 1.3 Traffic Information and Transportation Network Models -- 1.4 Equilibrium over Transportation Networks -- 1.5 Dynamic Equilibrium Conditions -- 1.6 Scope and Organization of the Book -- 1.7 Notes -- 2 Mathematical Background -- 2.1 Variational Inequality Problem and Some Related Mathematical Problems -- 2.2 Existence and Uniqueness -- 2.3 Solution Algorithms -- 2.4 Notes -- 3 Network Flow Constraints and Link Travel Time Function Analysis -- 3.1 Flow Conservation Constraint -- 3.2 Flow Propagation Constraints -- 3.3 Nonnegativity Constraints -- 3.4 Definitional Constraints -- 3.5 First-In-First-Out Constraints -- 3.6 Link Capacity and Oversaturation -- 3.7 Link Travel Time Function Analysis -- 3.8 Notes -- 4 Dynamic User-Optimal Route Choice Model -- 4.1 Equilibrium Conditions and Model Formulation -- 4.2 Numerical Example -- 4.3 Static Counterpart Approximation -- 4.4 Multiple Optima -- 4.5 Notes -- 5 Algorithms for the Dynamic Route Choice Model -- 5.1 Link Interactions -- 5.2 Nested Diagonalization Method -- 5.3 Nested Projection Method -- 5.4 Modified Nested Projection Method -- 5.5 Numerical Example -- 5.6 Notes -- 6 Dynamic User-Optimal Departure Time/Route Choice Model -- 6.1 Equilibrium Conditions and Model Formulation -- 6.2 Nested Diagonalization Method -- 6.3 Numerical Examples -- 6.4 Analysis Period and Total Number of Time Intervals -- 6.5 Notes -- 7 Dynamic User-Optimal Models with Variable Demand -- 7.1 Dynamic User-Optimal Variable Demand/Route Choice Mode -- 7.2 Dynamic User-Optimal Variable Demand/Departure Time/Route Choice Model -- 7.3 Notes -- 8 Dynamic User-Optimal Mode Choice Models -- 8.1 Dynamic User-Optimal Mode Choice/Route Choice Model -- 8.2 Dynamic User-Optimal Mode Choice/Departure Time/Route Choice Model -- 8.3 Notes -- 9 Dynamic User-Optimal Singly Constrained O-D Choice Models -- 9.1 Dynamic User-Optimal Singly Constrained O-D Choice/Route Choice Model -- 9.2 Dynamic User-Optimal Singly Constrained O-D Choice/Departure Time/Route Choice Model -- 9.3 Notes -- 10 Dynamic System-Optimal Route Choice Model -- 10.1 Marginal Link Travel Time Function Analysis -- 10.2 Equilibrium Conditions and Model Formulation -- 10.3Nested Diagonalization Method -- 10.4 Numerical Example -- 10.5 Comparison of Network Travel Times for the DSO and DUO Route Choice Problems -- 10.6 Static Counterpart Approximation -- 10.7 Braess’s Paradox -- 10.8 Toll Policies -- 10.9 Notes -- 11 Dynamic Signal Control Systems -- 11.1 Dynamic Network Signal Control System -- 11.2 Dynamic Traffic-Responsive Signal Control System -- 11.3 Notes -- 12 Stochastic/Dynamic User-Optimal Route Choice Model -- 12.1 Stochastic/Dynamic Route Travel Time Function Analysis -- 12.2 Equilibrium Conditions and Model Formulation -- 12.3 Nested Diagonalization Method -- 12.4 Numerical Example -- 12.5 Deterministic Counterpart Approximation -- 12.6 Braess’s Paradox -- 12.7 Notes -- 13 Fuzzy/Dynamic User-Optimal Route Choice Model -- 13.1 Fuzzy/Dynamic Link Travel Time Function Analysis -- 13.2 Equilibrium Conditions and Model Formulation -- 13.3 Nested Diagonalization Method -- 13.4 Numerical Example -- 13.5 Fuzzy/Static Counterpart Approximation -- 13.6 Notes -- 14 Future Research and Applications -- 14.1 Research Directions -- 14.2 Applications -- 14.3 Notes -- References -- List of Figures -- List of Tables -- Author Index -- Summary of Notation.

10.1007/978-3-642-59980-4 [DOI]

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