Departure Time Choice with Parametric Heterogeneity: Equilibrium and Instability
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.
Keywords
Cite
@article{arxiv.2604.13831,
title = {Departure Time Choice with Parametric Heterogeneity: Equilibrium and Instability},
author = {Hillel Bar-Gera and Stephen D. Boyles and Liron Ravner},
journal= {arXiv preprint arXiv:2604.13831},
year = {2026}
}