Modeling and solving dynamic traffic assignment problems in continuous time

Dynamic Traffic Assignment (DTA) is one of the most challenging problems in transportation science, aiming to provide detailed prediction of the time-varying traffic flows, measurement of time and cost and travel choices, so that time-varying operation strategies become possible. Different from its static counterpart, the DTA is challenging due to not only its conceptual complexity but also numerical difficulties. Being a specific problem in the DTA research, Dynamic user equilibrium (DUE) aims to predict future dynamic traffic states in a short-term fashion assuming travelers follow certain rational behavioral choices. However, comprehensive studies on continuous-time DUE are sparse in the literature. Another specific problem of the DTA is categorized as dynamic system optimum (DSO) or system optimal dynamic traffic assignment (SO-DTA). DSO predicts the optimal traffic states of a network under time-dependent traffic conditions from the perspective of the entire system. The DSO provides a benchmark for controlling and managing dynamic traffic networks. This dissertation aims to build a series of DTA models in continuous time and develop their solution methods and applications. Multiple approaches are proposed to model DTA problems in continuous time. The proposed continuous-time DUE formulations are based on differential complementarity systems, and can capture the time-varying variational condition and the time-delayed ordinary differential equations at the same time in a unifying and coherent framework. The proposed continuous-time DSO formulation is based on a continuous-time optimal control framework. By reformulating the DSO objective functions, specific solutions can be achieved. Comprehensive analysis is introduced for these continuous-time DTA models. Rigorous analysis is investigated on convergence issues. Methods on dealing with the time-varying state-dependent time-delay are developed. Departure-time choice and other realistic phenomena such as spillback are incorporated, which makes the models more realistic and practical. Numerical analysis and solution methods are developed for these continuous-time DTA models. Various applications of the continuous-time DTA models are discussed in this dissertation. The instantaneous DUE model and its solution techniques are applied to real-world networks, and the model performances for predicting drivers' behaviors and traffic dynamics are evaluated with the field data. The DSO model is applied to emergency evacuation planning and macroscopic emission modeling. Further, a control scheme with the dynamic tolling mechanism is proposed to alter drivers' route choice behaviors from a DUE to a DSO pattern in order to minimize the system cost in terms of travel costs and environmental costs.