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Dynamic network traffic assignment considered as a continuous time optimal control problem. (English) Zbl 0691.49029
Summary: Two continuous time formulations of the dynamic traffic assignment problem are considered, one that corresponds to system optimization and the other to a version of user optimization on a single mode network using optimal control theory. Pontryagin’s necessary conditions are analyzed and given economic interpretations that correspond to intuitive notions regarding the dynamic system optimized and dynamic user optimized traffic flow patterns. Notably, we offer the first dynamic generalization of Beckmann’s equivalent optimization problem for static user optimized traffic assignment in the form of an optimal control problem. The analysis further establishes that a constraint qualification and convexity requirements for the Hamiltonian, which together ensure that the necessary conditions are also sufficient, are satisfied under commonly encountered regularity conditions.

49L20 Dynamic programming in optimal control and differential games
49K15 Optimality conditions for problems involving ordinary differential equations
90B10 Deterministic network models in operations research
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