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Punctuality-based departure time scheduling under stochastic bottleneck capacity: formulation and equilibrium

This paper proposes a departure time scheduling model for a single bottleneck that is subjected to degradable capacity. Instead of considering travel cost due to uncertainty (either in form of schedule delay or travel time variance) as an additional cost term to be traded with congestion delay and other out-of-pocket costs, it is supposed that travellers deal with uncertainty by adjusting their departure times in order to achieve a certain desirable level of punctuality in accordance to their behavioural preference and trip characteristic. This paper develops the formulation in solving for the scheduling equilibrium, with a detailed exposition on how the expected travel time and schedule delays can be computed. Moreover, this paper discusses the existence of equilibrium of the proposed scheduling equilibrium. In the deterministic bottleneck model and subsequent works that extend to the case of stochastic bottleneck, it is often assumed that the start time of congestion (first appearance of queue) is fixed; in this paper, it is demonstrated that the congestion start time is in fact dependent on the random bottleneck capacity. Lastly, some interesting properties regarding the equilibrium departure profile are discussed and compared with the deterministic bottleneck results.