An activity-based bottleneck model with stochastic capacity

Abstract

This study investigated commuters’ departure time choice with stochastic capacity. It has typically been solved by using Vickrey’s bottleneck model which doesn’t take the impact of commuters’ activity on decision-making into account. We added activity utility parameters to Vickrey’s bottleneck model. Travel costs became negative utility. The model considered home-activity utility before work and work-activity utility in the morning rush. Simultaneously, the capacity of the bottleneck changed randomly between a designed value (good condition) and a degraded one(bad condition). We derived six reasonable equilibrium patterns by maximizing the commuters’ activity utility and closed form solutions to all possible equilibrium patterns. The departure rate curve for each equilibrium pattern was made within a reasonable parameter range.