Modeling the Morning Commute Problem With Stochastic Travel Time in a Bottleneck Model

This paper studies the traffic behavior of travelers who drive from living areas to workplaces through bottleneck roads during the early rush hours when the travel time on the road is uncertain. Based on the travel time which is assumed stochastic and follows a uniform distribution, the equilibrium properties of the proposed model are derived and individual travel cost is obtained. According to the assumptions, three possible departure-time intervals have been considered when users always arrive early, arrive early or late, always arrive late. Travelers' travel choice behaviors are analyzed in detail and equilibrium is achieved with these three situations. The results show that even if they start at the same time, they may arrive early or late, but not necessarily early or late. Numerical examples verify the theoretical analysis, and it is found that the time interval of arriving at the workplace also changes when the stochastic degree of travel time increases.