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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Bin Ran & David E. Boyce & Larry J. LeBlanc, 1993. "A New Class of Instantaneous Dynamic User-Optimal Traffic Assignment Models," Operations Research, INFORMS, vol. 41(1), pages 192-202, February.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:1:p:192-202
    DOI: 10.1287/opre.41.1.192
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