On passenger traffic along a transit line: a stochastic model of station waiting and in-vehicle crowding under distributed headways

Abstract

Abstract Traffic along a transit line involves two kinds of mobile entities: passengers versus vehicles. The paper develops a stochastic model to deal with: headways between successive runs serving stations, wait times at boarding stations, passenger flows per vehicle and by leg (i.e. pair of entry-exit stations), in-vehicle comfort differentiating between seated and standing places. While previous static models of transit assignment consider vehicle passenger flows that are averaged over the vehicle runs, we model distributed headways, thus taking into account the issues of regularity and reliability. The “Rank conservation” postulate of Leurent et al. (2012a,b) is used to establish analytical formulae for the expectation and variance of every traffic variable of interest: leg flows, link flows, wait times, leg physical times, generalized times at waiting and in-vehicle. The linkage between waiting prior to boarding and in-vehicle crowding is modeled: each user is concerned individually, conditionally to the headway during which he waits for the vehicle. A computation scheme is provided to deliver the statistical summaries of the array of traffic variables.