System-optimal dynamic traffic assignment with and without queue spillback: Its path-based formulation and solution via approximate path marginal cost

The knowledge of path marginal cost (PMC) is central to system-optimal dynamic traffic assignment (SO-DTA) problems. In this paper, we propose a method to approximate PMC in general networks when traffic dynamics are modeled by either the point-queue or the kinematic wave traffic flow model. This study examines in detail the flow interactions between downstream and upstream bottleneck links, and shows that the changes in cumulative flows on all the network links caused by an arbitrary flow perturbation can be computed. This offers a way to approximate PMC, which is incorporated in the solution of the least marginal cost problem, a central component of the path-based SO-DTA problem. The approximation scheme allows us to solve path-based SO-DTA problems for general networks with and without queue spillback and/or departure time choices. Numerical examples are provided to demonstrate the effectiveness of the proposed method, and the results show that the SO state produces considerably lower total network cost, shorter congestion duration, and smaller travel delay on bottleneck links than those of produced by the user-optimal state, particularly when the departure time choice is considered.

► A method to approximate path marginal cost (PMC) in general networks is proposed for two traffic flow models.
► Path-based SO-DTA problems for general networks are solved using approximate PMC.
► Holding all the queues at the periphery of the network minimizes travel time cost for many-to-one networks.
► For networks with many origins and destinations, optimal solution may contain residual queues.