A new class of instantaneous dynamic user-optimal traffic assignment models

A new class of instantaneous dynamic user-optimal traffic assignment models

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Article ID: iaor1994294
Country: United States
Volume: 41
Issue: 1
Start Page Number: 192
End Page Number: 202
Publication Date: Jan 1993
Journal: Operations Research
Authors: , ,
Keywords: networks: flow, transportation: road, Transportation: Road
Abstract:

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. In this paper, the authors introduce a different definition of an instantaneous DUO state. Using the optimal control theory approach, they 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 solutions 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.

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