The planning of urban public passenger transport often requires considering the capacity constraints and congestion effects. Modelling the person capacity of a transit route has been the purpose of several recent research works to develop network traffic assignment models along the following tracks:

• effective frequencies, by De Cea and Fernandez, and Cepeda et al;
• the capacity by route segment, by Lam et al;
• failure-to-board probability, by Kurauchi et al;
• strategy based on a user preference set, by Hamdouch et al;
• availability frequency, by Leurent and Askoura.

Our objective is to describe and compare the models. We characterise and discuss their assumptions and also apply them to a test case which is treated parametrically. We consider specifically:

• making explicit a capacity constraint;
• priority for passengers already on board over those boarding;
• the route’s waiting time for a boarding passenger;
• the distribution of boarding volumes between the attractive routes from a station to a given destination.

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