A New Class of Instantaneous Dynamic User-Optimal Traffic Assignment Models

Bin Ran, David E. Boyce and Larry J. LeBlanc
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Bin Ran: University of Illinois at Chicago, Chicago, Illinois
David E. Boyce: University of Illinois at Chicago, Chicago, Illinois
Larry J. LeBlanc: Vanderbilt University, Nashville, Tennessee

Operations Research, 1993, vol. 41, issue 1, 192-202

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, 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 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.

Keywords: dynamic programming/optimal control: deterministic application model; networks/graphs: multicommodity; transportation; models: network traffic assignment (search for similar items in EconPapers)
Date: 1993
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Citations: View citations in EconPapers (45)

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