AbstractThe paper addresses the issue of passenger waiting and being stored at a station platform, from which point 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. The model yields individual waiting time by egress station and the assignment of vehicle capacity to the flows by egress station. Two cases are distinguished, unsaturated versus saturated. The unsaturated case is addressed by standard line combination, where service frequency is added up among the routes that service 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 is derived the individual probability to board a vehicle of limited capacity that service 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 service a given egress station, their vehicle capacities and the boarding probabilities induce a line capacity for that destination: to this is faced the passenger flow demanded during the assignment period, in a bottleneck model that yields an average waiting time per passenger. The vector of passenger stocks by egress station is shown to satisfy a fixed point problem. The existence and uniqueness of the solution are demonstrated on the basis of an equivalent, convex minimization program. A Newton-Raphson algorithm is recommended for computation and demonstrated in an instance of application.