A traffic assignment model for passenger transit on a capacitated network: Bi-layer framework, line sub-models and large-scale application

Document Type

Journal Article

Publication Date


Subject Area

place - europe, place - urban, mode - mass transit, mode - bus, mode - rail, operations - capacity, operations - crowding, operations - frequency, planning - network design


Traffic equilibrium, Bi-layered assignment, Seat capacity, Vehicle capacity, Transit bottleneck, Platform stock, Wait time, Vehicle load, Frequency adaptation, Track occupancy, Line model


In the urban setting, the roadway and railway modes of mass transit are basically purported to carry large flows of passengers. Thus the issue of flowing capacity is crucial in the design and planning of a transit network. As a transit system involves two types of traffic units, respectively passengers and vehicles, there is a broad range of capacity phenomena: (i) as a vehicle has given seat capacity, additional riders have to stand which is less comfortable and more exposed to in-vehicle crowding, (ii) the total capacity in a vehicle, including sitting and standing places, influences the wait time on platform if it is exceeded by the number of candidate riders, (iii) the exchange capacity at vehicle doors influences the vehicle dwell time at a station, (iv) from the station dwell times stems the run time of vehicles – hence of passengers – and in turn the service frequency, (v) vehicle traffic is constrained by dwell time and operating margins, which may reduce the frequency delivered, etc. The paper provides a static, macroscopic model of traffic assignment to a transit network, in which these capacity phenomena are captured. A key feature is the line sub-model that deals with a line of operations, comprised of one or several service routes, by using the topological order of stations. From a matrix of flows by pair of access-egress stations, the sub-model derives the matrix of average passenger costs by access-egress pair, as well as local passenger wait time and the apparent frequency of each leg. At the network level, passenger route choice is modeled by optimal hyperpaths that are route-based (as in De Cea and Fernandez, 1989). It is shown that there exists a state of traffic equilibrium. A Method of Successive Averages is put forward to compute equilibrium. A large scale application to the whole transit network of greater Paris is presented, with focus on capacity issues.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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