Resumen
The variability in passengers? waiting times in urban mass transit is significant at the trip level since it ranges from some dozen seconds to half headway. Despite the attention paid so far to individual wait times in urban transit systems, a related issue seemed to remain unexplored: the re-use of wait time for passenger repositioning along the boarding platform. The paper is focused on passenger wait time on urban railway platforms and its re-use for longitudinal repositioning on the boarding platform in order to save on walking time at the egress station. Building upon our stochastic model of passenger?s individual journey time between access and egress stations, we refine the representation of the on-platform phases and their potential coupling, since a passenger?s relocation along the access platform influences the egress situation. In the new model, the stochastic features pertain to (i) the distribution of walking speed among passengers, (ii) the distribution of repositioning distance in relation to that of the residual time between passenger arrival and train departure at the station of passenger boarding, (iii) the distribution of in-station distances between the station access/egress points and the platform. Analytical properties are obtained, including the Probability Density Function of Tap-In, Tap-Out time pairs. It is shown that the analytical formulas for normal-distributed speed and shifted exponential-distributed distances in stations are tractable. This enables for maximum likelihood estimation of distribution parameters. A real case study of urban rail transit line RER A in Parisian region is addressed, yielding reasonable parameter values for heterogeneous and homogeneous scenarios. Furthermore, this study gives the possibility to capture pedestrian congestion in the stochastic model, and to differentiate ?intra-? vs. ?inter-? individual variabilities.