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We consider a dynamic traffic assignment model formulated as a nonlinear and noneonvex mathematical program. Necessary optimality conditions require equalization of certain marginal costs for all the paths that are being used, and these optimality conditions are shown to be a generalization of the optimality conditions of a conventional static traffic assignment problem. We also examine the behavior of the dynamic model under static demand conditions and show that in this case our model is a generalized version of a standard static model. Our model suggests a promising refinement of the objective function for the static case.
Merchant et al. (Tue,) studied this question.