Capacity restraint assignment model for congested public transport systems

In this paper, a time-dependent capacity restraint assignment model is proposed for transit networks with passenger queues and congestion at stations. In this model the passenger waiting cost is a function of both combined frequency of the transit lines and congestion at stations because of insufficient capacities of transit lines in a particular time period. The conservation of the time-dependent passenger flows and queues at any station is derived and incorporated in the proposed model. The objective is to minimize the sum of the expected total passenger travel time (including waiting time) and the total number of passenger queues at stations in the study period. An equivalent mathematical programming problem is formulated for the time-dependent transit system optimization assignment and the solution algorithm is proposed. Numerical example is used to illustrate the applications of the new transit assignment model.