Dynamic traffic assignment: formulations, properties, and extensions

Abstract

Dynamic Traffic Assignment (DTA), which is to determine the network traffic pattern over time as a result of dynamic supply and demand interactions, is an important research area because DTA models have a wide range of applications in 1) real-time traffic control and management, and 2) off-line network planning and policy evaluations. Essentially, DTA consists of two components: a travel choice principle and a traffic-flow component. The travel choice principle models how travelers decide on whether to travel or not, and if so, how they select their routes, departure times, modes, or destinations. The traffic-flow component, on the other hand, depicts how traffic propagates inside a transport network. This thesis develops three general frameworks for DTA problems through the nonlinear complementarity problem approach, the variational inequality problem approach, and the fixed-point problem approach. Rather than considering traffic dynamics or the traffic-flow component as constraints, as is typically accomplished in the literature, the proposed frameworks model traffic through a unique mapping of route flows directly. This approach opens up a new way to analyze DTA problems. These frameworks allow the encapsulation of a range of dynamic traffic flow models and can be solved by many existing solution methods. For the traffic-flow component, this thesis reviews and compares two modeling paradigms for DTA purposes: point-queue and physical-queue paradigms, and depicts existing dynamic traffic-flow modeling approaches under each modeling paradigm, including their advantages and disadvantages. A numerical study is performed to demonstrate their different travel time predictions, time-dependent queuing locations, and time-dependent link occupancies. This thesis also investigates and discusses the implications of the properties of point-queue and physical-queue DTA problems, in the areas of causality, the continuity, differentiability, and monotone properties of route travel times, the existence and uniqueness of solutions, the first-in-first-out properties, and the continuity property of origin-destination travel times. In particular, this thesis proves that the existence of solutions to the DTA problems with physical queues is not guaranteed. This could be problematic because most existing planning and management procedures are developed under the equilibrium notion. Nevertheless, this finding may prove to be important in the search of new travel choice principles that are behaviorally sound and consistent with actual network behavior. Finally, based on the notion of bounded-rationality, this thesis proposes the tolerance-based Dynamic User Optimal (DUO) principle that includes the DUO principle as a special case. This new principle is behaviorally sound and consistent with actual traffic behavior. Based on the theoretical gap, the condition for the existence of solutions to the problem is provided. Two new design methods are proposed and discussed. Numerical examples are provided to illustrate the effects of parameters and initial solutions to the existence of solutions and network performance over time. Future research directions are addressed.