This paper presents an analytical investigation of strategic departure time choice under stochastic capacities using Vickrey's bottleneck model. The deterministic bottleneck model of Vickrey has been extended with random capacities by assuming that travelers are fully aware of the stochastic properties of the travel time and schedule delay distributions at all departure times that emerge from day-to-day due to random capacity. We study whether a long term equilibrium may exist given day-to-day travel time variations. Based on the analytical analyses, consideration of random capacities and travel time reliability in the utility function results into significant shifts in the temporal demand pattern relative to the deterministic case. Travelers depart earlier and the number of early arrivals increases. This theoretical finding is supported by empirical findings of delays at bottlenecks. Travel time variability appears to increase with the departure time, that is, the later a traveler departs, the larger travel time unreability he/she will encounter. The findings of this paper are valid not only for homogeneous travelers with identical preferred arrival time (PAT), but also for a population of travelers with a general distribution of PAT.
Samenvatting