A transit bottleneck model for waiting passengers and its implications for traffic assignment

The paper addresses the issue of passenger waiting at a station platform, from which they plan to board transit services towards egress stations. Each transit service has a specific set of downstream egress stations and is operated at given frequency using homogeneous vehicles of limited available capacity. We propose a static model that yields “passenger stocks” on the platform and individual waiting times by egress station, as well as the assignment of vehicle capacity to the flows by egress station. Two cases are considered; unsaturated versus saturated. The unsaturated case is addressed by standard line combination, where service frequency is added up among the routes that serve a given egress station. The saturated case is addressed by making explicit the average number of passengers waiting on platform for a given egress station. From these passenger stocks, we deduce the individual probability to board a vehicle of limited capacity that serves a given route (hence a given subset of egress stations). Waiting passengers are assumed to be mingling on the origin platform. The subset of routes that serve a given egress station, their vehicle capacities along with the associated boarding probabilities give a line capacity by destination. The bottleneck model confronts this capacity to demand during the assignment period and provides both the stock of waiting passengers and an average waiting time per passenger. The vector of passenger stocks by egress station is shown to satisfy a fixed point problem. The existence of a solution is demonstrated.