In an urban transit system where the service is perceived in terms of frequency of the different lines, the mathematical description of the route choice strategy is not trivial, because the wait at the stop, as pointed out in many studies in the last 30 years, is a complex phenomenon which requires a specific analysis (e.g. Chriqui and Robillard [1975], Marguier [1981], Gendreau [1984], Spiess [1984]). In order to develop an effective model for planning the service, it is very important to define a representation of the wait at transit stops which is at once consistent with users’ behaviour, mathematically sound and practically usable within the more general assignment models. This is the reason that has induced us to rethink globally to the wait problem, by analyzing the stochastic process of vehicle and passenger arrivals at transit stops and the relations among them, without assuming as given facts some hypotheses that are usually adopted. Indeed, some works written during the 80’s [Marguier, 1981; Gendreau, 1984; Marguier and Ceder, 1984] already pointed out that some modelling choices are not easily justifiable, although often utilized in the following years.
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