Incidents and other random factors may create variations to the transportation system and thus result in stochastic road capacity during the travel period. The realized capacity on a given day (i.e., an average value over the travel period) changes from day to day. For instance, existing empirical studies indicate that incident capacity reduction can be approximated as a continuous random variable. This study examines the morning commute problem with a road bottleneck whose capacity is constant within a day but changes stochastically from day to day. This study extends existing stochastic bottleneck model studies by considering a more general distribution of the bottleneck capacity. In particular, the capacity of bottleneck is at the designed value under good external conditions and degrades into a smaller value within an interval (i.e., the capacity degradation range) under adverse external conditions (a “mixed” distribution). Commuters’ departure time choices follow the Wardrop’s first principle in terms of their mean individual travel cost. Given the considered distribution of capacity, additional equilibrium departure/arrival patterns not identified by the literature have been identified and examined. How the mean travel cost and the mean of total travel time may vary with the capacity degradation probability and the level of capacity degradation have been analyzed. The impacts of the width of degraded capacity range have also been investigated to quantify how the results are affected if the degraded capacity is assumed as the mean value (rather than a degraded capacity range). Our results indicate that with less severe capacity degradation, the mean travel cost always decreases and improving the capacity under the “worst condition” can be more effective than improving the capacity under the “best adverse condition”. However, it is not always the case for reducing the total travel time, and the mentioned measures may exacerbate the system’s congestion, especially when the capacity degradation rarely occurs. Under a given mean capacity, the mean travel cost would be underestimated if the capacity degradation range is ignored. We also compare system performance considering different capacity distributions. It is found that the “mixed” capacity distribution defined in this study outperforms the binary capacity distribution in terms of evaluating the departure/arrival pattern and the mean travel cost. This study enhances our understanding on the morning commute problem under capacity uncertainty.

事件和其他随机因素可能会对交通系统造成变化，从而导致出行期间道路通行能力的随机变化。给定日期的实际容量（即，旅行期间的平均值）每天都在变化。例如，现有的实证研究表明，事件容量减少可以近似为一个连续的随机变量。本研究检查了具有道路瓶颈的早上通勤问题，道路瓶颈的通行能力在一天内是恒定的，但每天随机变化。本研究通过考虑瓶颈容量的更一般分布来扩展现有的随机瓶颈模型研究。特别是，瓶颈容量在良好的外部条件下处于设计值，并在一个区间内退化为较小的值（即，容量退化范围）在不利的外部条件下（“混合”分布）。通勤者的出发时间选择遵循 Wardrop 的第一原则，即他们的平均个人旅行成本。鉴于考虑到的容量分布，已经确定和检查了文献未确定的其他均衡出发/到达模式。分析了平均旅行成本和总旅行时间的平均值如何随容量退化概率和容量退化水平而变化。还研究了降级容量范围宽度的影响，以量化如果将降级容量假定为平均值（而不是降级容量范围），结果将如何受到影响。我们的结果表明，在容量下降不太严重的情况下，平均旅行成本总是下降的，提高“最坏条件”下的能力比提高“最佳不利条件”下的能力更有效。然而，减少总行程时间并不总是如此，上述措施可能会加剧系统的拥堵，尤其是在容量下降很少发生的情况下。在给定的平均容量下，如果忽略容量退化范围，则平均旅行成本将被低估。我们还比较了考虑不同容量分布的系统性能。结果发现，在评估出发/到达模式和平均旅行成本方面，本研究中定义的“混合”容量分布优于二元容量分布。