Recently, Daganzo introduced the cell transmission model—a simple approach for modeling highway traffic flow consistent with the hydrodynamic model. In this paper, we use the cell transmission model to formulate the single destination System Optimum Dynamic Traffic Assignment (SO DTA) problem as a Linear Program (LP). We demonstrate that the model can obtain insights into the DTA problem, and we address various related issues, such as the concept of marginal travel time in a dynamic network and system optimum necessary and sufficient conditions. The model is limited to one destination and, although it can account for traffic realities as they are captured by the cell transmission model, it is not presented as an operational model for actual applications. The main objective of the paper is to demonstrate that the DTA problem can be modeled as an LP, which allows the vast existing literature on LP to be used to better understand and compute DTA. A numerical example illustrates the simplicity and applicability of the proposed approach.

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This paper is concerned with the stochastic shortest path problem with recourse when limited forms of spatial and temporal arc cost dependencies are accounted for. Recourse is defined as the opportunity for a decision maker to reevaluate his or her remaining path when en-route information is available. Formulations with recourse typically provide opportunities for corrective actions when information becomes available; information here is modeled as arc cost dependencies, defined as spatial and temporal. System properties are stated and proved and solution algorithms are developed for limited cases of spatial and temporal arc cost dependencies. The numerical results verify some of the theoretical insights and demonstrate the applicability of the introduced algorithms.

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