How Do Individual Walk Lengths and Speeds, Together with Alighting Flow, Determine the Platform Egress Times of Train Users?

Abstract

Egress times of railway passengers from train alighting up to station exit typically amount to some tens of seconds, but with much variability even at the train level. Here, we first model the egress time as the ratio of the walk length to the preferred walk speed, under free-flow conditions. Then, we model the possible occurrence of congestion among the users alighting from a train as a traffic bottleneck affecting those passing at a “queue focal point” during a “queued time interval.” Analytical formulas are provided for the CDF and PDF of egress times, covering the free-flow case and the congested case. Their computation is straightforward for bivariate Gaussian length-speed walk pair. A maximum-likelihood method is developed, together with a quick estimation procedure. A case study of four contrasted trains serving an urban mass transit station in Paris is reported. One train experienced free-flow alighting conditions, whereas each of the other three had its own bottleneck. The MLE method enabled us to recover all parameters but one, due to an issue of identifiability: the solution was to take the mean walk speed as exogenous.