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: | Boyce David E., Ran Bin, Leblanc Larry J |
Keywords: | networks: flow, transportation: road, Transportation: Road |
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.