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Perturbed Utility Stochastic Traffic Assignment

Author

Listed:
  • Rui Yao

    (School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland)

  • Mogens Fosgerau

    (Department of Economics, University of Copenhagen, 1353 Copenhagen, Denmark; Department of Technology, Management and Economics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark)

  • Mads Paulsen

    (Department of Technology, Management and Economics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark)

  • Thomas Kjær Rasmussen

    (Department of Technology, Management and Economics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark)

Abstract

This paper develops a fast algorithm for computing the equilibrium assignment with the perturbed utility route choice (PURC) model. Without compromise, this allows the significant advantages of the PURC model to be used in large-scale applications. We formulate the PURC equilibrium assignment problem as a convex minimization problem and find a closed-form stochastic network loading expression that allows us to formulate the Lagrangian dual of the assignment problem as an unconstrained optimization problem. To solve this dual problem, we formulate a quasi-Newton accelerated gradient descent algorithm (qN-AGD*). Our numerical evidence shows that qN-AGD* clearly outperforms a conventional primal algorithm and a plain accelerated gradient descent algorithm. qN-AGD* is fast with a runtime that scales about linearly with the problem size, indicating that solving the perturbed utility assignment problem is feasible also with very large networks.

Suggested Citation

  • Rui Yao & Mogens Fosgerau & Mads Paulsen & Thomas Kjær Rasmussen, 2024. "Perturbed Utility Stochastic Traffic Assignment," Transportation Science, INFORMS, vol. 58(4), pages 876-895, July.
    • Handle: RePEc:inm:ortrsc:v:58:y:2024:i:4:p:876-895
    DOI: 10.1287/trsc.2023.0449
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