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.

翻译：维克里的经典单瓶颈出发时间选择均衡模型在多种合理的逐日学习动态下表现出不稳定性。然而，这种不稳定性在实际中并未被观察到——这一差异是源于逐日动态本身，还是源于基础模型的某个简化假设？本文探讨了基础模型的一个变体，其引入了计划延误参数的连续分布，我们直观预期该变体具有更有利的稳定性特性。为便于处理，我们假设早到参数与迟到参数之间存在单调关系。首先，我们验证了该模型均衡解的存在性与唯一性。接着，我们研究了一类满足局部压力和顺序保持条件的广泛逐日动态过程。我们的主要贡献在于一个形式化证明：令人惊讶的是，该语境下的所有此类逐日动态过程均是不稳定的。