On Individual Repositioning Distance along Platform during Train Waiting

Out of waiting times spent in rail stations on boarding platforms, some part can be reinvested by the trip-makers to optimize their positions of boarding and save on travel time for the rest of their trips. This paper provides a stochastic model, in which user’s journey is decomposed into phases of, successively, walking in the access station, platform positioning, waiting for boarding, train riding, and walking in the egress station. Walking speed and target position are modeled as individual factors, and in-station distances as random variables. Service timetable is exogenous. This makes egress times and exit instants random variables that are characterized by distribution and mass probability functions under closed-forms, for both single and distributed walking speeds. Specific statistical distributions are shown to ease computation. The resulting PDF formulae make likelihood functions of the model parameters. Maximum likelihood estimation is proposed and applied to a case study of commuter rail line in Paris: journeys between stations Vincennes and La Défense along line A of the Regional Express Railways. Based on data from Automated Fare Collection and Automatic Vehicle Location systems and pertaining to an individual user, satisfactory results were obtained