This paper studies a bottleneck model in which the capacity of the bottleneck is constant within a day but changes stochastically from day-to-day between a designed value (good condition) and a degraded one (bad condition). The study relates the travel cost variability due to stochastic capacity with commuters' departure time choice behaviors. We postulate that commuters acquire the variability of travel cost based on past experiences and factor such variability into their departure time choice consideration by minimizing their travel cost budget (TCB), defined as a weighted average of mean travel cost and standard deviation of travel cost. We show that the consideration of TCB yields seven possible equilibrium patterns. Closed form solutions to all possible equilibrium patterns and their corresponding parameter ranges are derived. The rationality of the patterns has been investigated. Dependence of travel cost and the duration of peak hours on the commuters' risk attitude has also been derived in each equilibrium pattern. Finally, numerical studies have been conducted to illustrate the properties.

本文研究了一个瓶颈模型，其中瓶颈的容量在一天内是恒定的，但在设计值（良好状态）和降级的（不良状态）之间每天随机变化。该研究将由于随机容量导致的旅行成本变异性与通勤者的出发时间选择行为联系起来。我们假设通勤者根据过去的经验获取旅行成本的可变性，并通过最小化旅行成本预算（TCB）（将其定义为平均旅行成本和旅行成本标准差的加权平均值），将这种可变性纳入出发时间选择考虑中。我们表明，TCB的考虑会产生七个可能的平衡模式。得出所有可能的平衡模式及其对应参数范围的封闭形式解。已经研究了模式的合理性。在每种均衡模式中，都还得出了出行成本和高峰时段的持续时间对通勤者风险态度的依赖关系。最后，进行了数值研究以说明其性质。