A discrete time dynamic flow model and a formulation and solution method for dynamic route choice

This paper considers the ideal dynamic user optimal (DUO) route choice problem using a route-based variational inequality approach. A discrete time dynamic flow model is developed, which uses link travel time functions to determine time-dependent network states. The proposed flow model is built on discrete time flow variables, to eliminate the discretization process of continuous time based models. Continuity of route travel time functions is proven to establish the existence of a solution, on the condition that the link travel time functions are continuous. Furthermore, flow dispersion and concentration can be simulated, which is expected to enhance the ability of capturing dynamics of traffic movements. A variational inequality formulation based on an alternative cost mapping is proposed, which is derived from a route swapping heuristic approach. As a solution method, the projection-based approach is used since the route travel time functions in our model are not smooth. To increase the performance of the projection-based methods, an efficient implementation of the projection operation is developed. Computational experiences with two example networks are provided to illustrate the model.