Exploiting smartcard data to estimate distributions of passengers' walking speed and distances along an urban rail transit line

:Passengers' walking speed and walking distance along an urban rail transit line are two key factors in the Quality of Service of a public transit system (TCQSM, 2013). Therefore, variability in both walking speed and distance partially causes that in journey time. Estimation of those factors is still a complicated and difficult task. This is due to not only the difficulty of the data collection, but also the lack of an appropriate estimation approach: individual walking speed keeps changing throughout the inter-individual journey. To accomplish that, we propose a stochastic model to estimate indirectly the distributions of those factors from individual Automatic Fare Collection data along an urban rail transit line. Our stochastic model relates tap-out time to tap-in time on an individual basis and with respect to the trains' timetable, on the basis of statistical distributions for the individual “cruise walking speed” and the in-station walking distances at access and egress stations. Analytical formulae are provided for (i) the probability distribution of tap-out time conditional on the train's arrival time, (ii) the probability to take a vehicle run at access station, (iii) the distribution of tap-out time conditionally to tap-in time; first conditional to an individual “cruise walking speed”, then deconditioned. The model is applied to Maximum Likelihood estimation of the parameters in the assumed distributions, using constrained numerical optimization and special treatment of raw AFC data. A case study of suburban rail line “RER A” in greater Paris is addressed, yielding reasonable estimates of the parameter values.