This paper presents an analytical investigation of departure time choice under stochastic capacity using Vickreyfs bottleneck model. The deterministic bottleneck model of Vickrey has been extended with random capacities. It is assumed that travelers are fully aware of the stochastic properties of the travel time and schedule delays at all departure times that emerge from day to day due to random capacity. Based on the analytical analyses, consideration of random capacities and travel time reliability in the utility function appears to result in significant shifts in the temporal demand pattern. Travelers will depart earlier and departure flows become more spread over a longer time period. Long term equilibrium is achieved under stochastic capacities. These theoretical findings are supported by empirical findings of delays at bottlenecks. Correctly modeling departure time distributions under stochastic supplies over days plays a crucial role in the assessment of the network performance and in the evaluation of dynamic traffic management measures.
Abstract