Properties of system optimal traffic assignment with departure time choice and its solution method

This paper investigates dynamic system optimal traffic assignment with departure time choice and its solution method. Dynamic system optimal assignment is formulated 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 minimized. We derive and discuss the necessary conditions on the network inflow for operating the transportation system optimally. We further provide detailed mathematical analysis and discussion of dynamic system optimal assignment when the deterministic queuing model is adopted. Solution algorithm is developed and investigated for solving the traffic assignments. The effect of choosing the underlying traffic model and time discretization on the quality of the corresponding assignment results are also discussed. This paper contributes to the literature on dynamic traffic modelling and management, and to support further analysis and model development in this area.