On Path Marginal Cost Analysis and its Relation to Dynamic System-Optimal Traffic Assignment

Abstract

This paper studies the problem of evaluating path marginal cost in system-optimal dynamic traffic assignment (SO-DTA) models. Through a series of examples, the paper demonstrates that path marginal costs are not simple additions of the corresponding link marginal costs unless the flow perturbation travels with the vehicle unit that initiated the perturbation. The paper further shows that one can compute efficiently path marginal costs for networks with a special structure (i.e. mono-centric), and proposed an evaluation method that decomposes path marginal costs to link marginal costs for such networks. Preliminary numerical experiments indicate that this solution scheme can generate numerical solutions close to analytical solutions where they are knows. At present, the method applies to networks without diverges and the embedded traffic flow models are restricted to those not considering queue spillback. The relaxation of either aspect brings in additional challenges in predicting path flow perturbation propagation, hence additional difficulties in the evaluation of path marginal costs, and is worthy of further research.

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