Dynamic Travel Choice Models

This book is the result of several years of research into the modeling and algorithm of problems in dynamic travel choice and related areas. Three types of discrete time dynamic travel choice models, along with numerical examples, are presented, i.e., deterministic, stochastic and fuzzy models. The notable features pertaining to these models are as follows: 1. The asymmetric property of the dynamic link travel time function is clearly verified, which leads to a variational inequality formulation. 2. The flow propagation constraint is implicitly defined in our model through the incidence relationship between the link inflow and route flow. 3. The inflow, exit flow, and number of vehicles on a link are identified as the three different states over time for the same vehicles under the flow propagation process. Therefore, only one link variable needs to be used in our dynamic travel choice models. This treatment can largely simplify the models' complexity, and possibly reduce the computation time. 4. The developed time-space network is consistent with scaling units both in temporal and spatial dimensions. 5. The proposed nested diagonalization method takes care of two types of link interactions, i.e., actual link travel times, and inflows other than that on the subject time-space link. 6. The equivalence analysis between a dynamic travel choice model and its corresponding equilibrium condition is performed by proving both the necessary and sufficient conditions under the presumption of equilibrated actual travel times.

Better understanding of the transportation planning process In-depth skills of mathematical programming

Inhalt
1 Analysis of Dynamic Transportation Systems.- 1.1 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.