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Side-Constrained Dynamic Traffic Equilibria

Author

Listed:
  • Lukas Graf

    (Faculty of Computer Science and Mathematics, University of Passau, 94032 Passau, Germany)

  • Tobias Harks

    (Faculty of Computer Science and Mathematics, University of Passau, 94032 Passau, Germany)

Abstract

We study dynamic traffic assignment with side constraints. We first give a counter-example to a previous result from the literature regarding the existence of dynamic equilibria for volume-constrained traffic models in the classical linear edge-delay model. Our counter-example shows that the feasible flow space need not be convex, and it further reveals that classical infinite dimensional variational inequalities are not suited for the definition of general side-constrained dynamic equilibria. We then propose a new framework for side-constrained dynamic equilibria based on the concept of admissible γ -deviations of flow particles in space and time. We show under which assumptions the resulting equilibria can still be characterized by means of quasi-variational and variational inequalities, respectively. Finally, we establish first existence results for side-constrained dynamic equilibria for the nonconvex setting of volume-constraints.

Suggested Citation

  • Lukas Graf & Tobias Harks, 2024. "Side-Constrained Dynamic Traffic Equilibria," Operations Research, INFORMS, vol. 72(6), pages 2279-2301, November.
    • Handle: RePEc:inm:oropre:v:72:y:2024:i:6:p:2279-2301
    DOI: 10.1287/opre.2023.0577
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