Dynamic system optimal traffic assignment – a state-dependent control theoretic approach

This study investigates analytical dynamic system optimal assignment with departure time choice in a rigorous and original way. Dynamic system optimal assignment is formulated here as a state-dependent optimal control problem. A fixed volume of traffic is assigned to departure times and routes such that the total system travel cost is minimised. Solution algorithms are presented and the effect of time discretisation on the quality of calculated assignments is discussed. Calculating dynamic system optimal assignment and the associated optimal toll is shown to be difficult for practical implementation. We therefore consider some practical tolling strategies for dynamic management of network traffic. The tolling strategies considered include uniform and congestion-based tolling strategies. This study contributes to the literature on dynamic traffic modelling and management, and to support further analysis and model development in this area.