A Stochastic Framework to Extract Individual Pedestrian Speeds from Congested Transit Data: Application to Paris RER A

This study develops a stochastic model to extract individual passenger walking speeds from standard transit data, correcting for the bias introduced by station congestion. The method leverages the synergy between Automated Fare Collection (AFC) and Automated Vehicle Location (AVL) data. We formulate the problem using a physical model of egress, where walk time is a ratio of distance and speed. From this, we derive two Bayesian stochastic models (Gaussian and Log-Normal) to describe the joint distribution of these variables at the train level. The framework first identifies queuing episodes at platform exits. By assuming a First-In-First-Out (FIFO) discipline, it reconstructs the unobserved, congestion-free egress times for affected passengers. These corrected times then serve as input for a second-stage maximum likelihood estimation (MLE) to infer individual-specific walking speed distributions. We demonstrate the application on a case study of 41 daily commuters on the Paris RER A line. The model successfully generates a profile of personalized walking speeds, with a mean of 1.18 m/s, from data originally corrupted by queuing delays. This approach provides a novel, data-driven pathway to obtain individual behavioral parameters for microscopic pedestrian simulations, bypassing the need for costly direct observation while explicitly accounting for congestion effects.