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A new class of instantaneous dynamic user-optimal traffic assignment models. (English) Zbl 0771.90039
Summary: The instantaneous dynamic user-optimal (DUO) traffic assignment problem is to determine vehicle flows on each link at each instant of time resulting from drivers using instantaneous minimal-time routes. Instantaneous route time is the travel time incurred if traffic conditions remain unchanged while driving along the route. We introduce a different definition of an instantaneous DUO state. Using the optimal control theory approach, we formulate two new DUO traffic assignment models for a congested transportation network. These models include new formulations of the objective function and flow propagation constraints, and are dynamic generalizations of the static user-optimal model. The equivalence of the solution of the two optimal control programs with DUO traffic flows is demonstrated by proving the equivalence of the first- order necessary conditions of the two programs with the instantaneous DUO conditions. Since these optimal control problems are convex programs with linear constraints, they have unique solutions. A numerical example is presented indicating that this class of models yields realistic results.

90B06 Transportation, logistics and supply chain management
93C95 Application models in control theory
90C25 Convex programming
90B10 Deterministic network models in operations research
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