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This paper propose a new approach for modelling congested transit networks with fixed timetables where it may happen that there is not enough room onboard to allow all users waiting for a given line on the arriving carrier, so that passengers need to queue at the stop until the service becomes available to them.

The traditional approach to reproduce this phenomenon within the established framework of diachronic graphs, where the supply is represented through a space-time network, is to introduce volume-delay functions for waiting arcs, which are meant to discourage passengers from boarding overcrowded carriers. However, this produces a distortion of the cost pattern, since passengers who ménage to board do not suffer any additional cost, and may also cause numerical instability.