Estimating Distributions of Walking Speed, Walking Distance, and Waiting Time with Automated Fare Collection Data for Rail Transit

Journey time is one of the key factors of public transport quality of service that is of concern to passengers. The variability in passenger journey time stems from the variability of in-vehicle travel time, walking time, and waiting time. A better understanding of passenger walking and waiting behavior along an urban rail transit line, especially in mass transit hubs and stations, is thus of much relevance. However, the estimation of passengers' walking speed, walking distance, and waiting time is still a complicated and difficult task: individual walking speed and waiting time keep changing throughout the interindividual journey. A novel stochastic model that uses automated fare collection data and automatic vehicle location data is proposed to estimate the distributions of walking speed, walking distance, and waiting time indirectly. The stochastic model relates tap-out time to tap-in time on an individual basis and with respect to train circulation on the basis of statistical distributions for the individual's cruise walking speed, in-station walking distance, and waiting time. Analytical formulas are provided, first conditional to an individual walking speed and waiting time and then without conditions. The model is applied to the maximum likelihood estimate (MLE) of the parameters with constrained numerical optimization. A case study of the urban rail transit line Reseau Express Regional [Regional Express Network (RER)] A in the Paris region yielded reasonable parameter values and factor mean values. This study paves the way for estimating passenger elementary travel time along a journey.