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arXiv · 2604.13831

Departure Time Choice with Parametric Heterogeneity: Equilibrium and Instability

Hillel Bar-Gera·Stephen D. Boyles·Liron Ravner
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Abstract

Vickrey's classic single-bottleneck departure time choice equilibrium model exhibits instability under many plausible day-to-day learning dynamics. Such instability is not observed in reality -- does this difference stem from the day-to-day dynamics or from one of the simplifying assumptions of the basic model? This paper explores a variant of the basic model with a continuous distribution of schedule delay parameters which we intuitively expect to have more favorable stability properties. To attain tractability we assume a monotonic relationship between earliness and lateness parameters. We first verify the existence and uniqueness of the equilibrium solution for this model. We then study a broad class of day-to-day dynamics satisfying local pressure and order preservation conditions. Our main contribution is a formal proof that, surprisingly, all such day-to-day dynamics in this context are unstable.

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Hillel Bar-Gera, Stephen D. Boyles, Liron Ravner. 2026-04-15. Departure Time Choice with Parametric Heterogeneity: Equilibrium and Instability. https://arxiv.org/abs/2604.13831

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