Side-Constrained Dynamic Traffic Equilibria

Lukas Graf () and Tobias Harks ()
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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

Operations Research, 2024, vol. 72, issue 6, 2279-2301

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.

Keywords: Transportation; dynamic traffic assignment; dynamic flow; variational inequality; equilibrium existence (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:72:y:2024:i:6:p:2279-2301

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