A Markov Process Model for Capacity-constrained Transit Assignment

Representing the finite capacity constraints of vehicles in a transit assignment model, for networks where the vehicle capacities are small and the buses do not operate timetables, requires an accurate representation of the impacts on passenger costs and flows as well as their day-to-day variability. This paper presents a composite frequency-based and schedule-based Markov process model for transit assignment that considers the day-to-day dynamics of the transit network, whereby line frequencies are used to parameterize distributions of vehicle arrivals and the passenger flows are constrained to the individual vehicle capacities. A proof of the model’s Markov property and regularity, its sensitivity to some parameters are presented using a test network.