Study on Optimal Frequency Design Problem for Multimodal Network Using Probit-Based User Equilibrium Assignment

Document Type

Journal Article

Publication Date


Subject Area

operations - frequency, planning - route design, ridership - commuting, policy - fares, mode - bus, mode - rail, mode - pedestrian


Walking distance, Waiting time, User equilibrium, Travel time, Route selection, Route choice, Rail transit, Probits, Probit models, Multimodal transportation, Multimodal systems, Multimodal networks, Journey time, Intracity bus transportation, Human comfort, Frequency design problem, Fares, Comfort, Bus transit, Automobile use, Automobile usage, Automobile travel


In this paper, a probit-based multimodal transport assignment model is developed. Three transport modes (railway system, bus system, and automobiles) and their interactions are considered. The walking time to a bus stop or a station also plays an important role in multimodal networks. Thus, walking to a bus stop or to a railway station is included in the model. The factors affecting travelers’ route choices considered in this model include actual travel times, discomfort effects on transit systems, expected waiting times, fares, and constants specific to transport modes. A route in the model may be composed of different modes. The paper also deals with the optimal transit frequency design problem. The frequency design problem is formulated as an implicit program in which the objective function of total disutility in the multimodal network is minimized with respect to frequencies of transit lines. The flows on a multimodal network follow a probit-based stochastic user equilibrium assignment. A numerical example is presented.