We investigate the impact of random deviations in planned travel times using an extension of Vickrey’s celebrated bottleneck model. The model is motivated by the fact that in real life, users can neither exactly plan the time at which they depart from home, nor the delay they experience before they join a particular congestion bottleneck under investigation. We show that the strategy advocated by the Nash equilibrium in Vickrey’s model is not a user equilibrium in the model with travel time uncertainty. We then investigate the existence of a user equilibrium for the latter and show that in general such an equilibrium can neither be a pure Nash equilibrium, nor a mixed equilibrium with a continuous density. Our results imply that when random distortions influence user decisions, the dynamics of deterministic bottleneck models are inadequate to describe this more complex situation. We illustrate with numerical analysis how the mechanics of a bottleneck with delayed arrivals are unstable for any continuous strategy, thus shedding more light on the non-existence result. Alternatively, we formulate a logit model for the day-to-day dynamic adjustment in response to previous travel experiences. We further investigate the conditions for convergence of the dynamic choice model and numerically illustrate the resulting equilibrium strategy.

我们使用Vickrey著名的瓶颈模型的扩展来研究随机偏差对计划的出行时间的影响。该模型的动机是，在现实生活中，用户既无法准确规划出门的时间，也无法准确规划出他们正在调查的特定拥堵瓶颈之前所经历的延迟。我们证明了维克瑞模型中纳什均衡所提倡的策略不是具有旅行时间不确定性的模型中的用户均衡。然后，我们研究了后者的用户平衡的存在，并表明一般而言，这种平衡既不能是纯Nash平衡，也不能是具有连续密度的混合平衡。我们的结果表明，当随机失真影响用户决策时，确定性瓶颈模型的动力学不足以描述这种更为复杂的情况。我们通过数值分析说明了对于任何连续策略而言，延迟到达瓶颈的机制是如何不稳定的，从而更多地揭示了不存在的结果。或者，我们根据以前的旅行经历为日常动态调整制定logit模型。我们进一步研究了动态选择模型收敛的条件，并在数值上说明了由此产生的均衡策略。我们根据以前的旅行经历为日常动态调整制定了logit模型。我们进一步研究了动态选择模型收敛的条件，并在数值上说明了由此产生的均衡策略。我们根据以前的旅行经历为日常动态调整制定了logit模型。我们进一步研究了动态选择模型收敛的条件，并在数值上说明了由此产生的均衡策略。