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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.

MSC:
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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