Dynamic traffic assignment in a corridor network: Optimum versus equilibrium

This study investigates dynamic system-optimal (DSO) and dynamic user equilibrium (DUE) traffic assignment of departure/arrival-time choices in a corridor network. A morning commute problem with a many-to-one pattern of origin–destination (OD) demand and an evening commute problem with a one-to-many OD pattern are considered. Specifically, we first derive a closed-form solution to the DSO problem based on the regularities of the cost and flow variables. By utilizing this solution, we prove that the bottleneck queuing delay of the DUE solution is equal to the optimal toll that eliminates the queue in the DSO solution under certain conditions on a schedule delay function. This enables us to derive a closed-form DUE solution from the DSO solution. We also show theoretical relationships between the DSO and DUE assignment. Numerical examples are provided to illustrate and verify the analytical results.