Estimation of denied boarding in urban rail systems: alternative formulations and comparative analysis

Monitoring rail transit system performance is important for effective operations planning. The number of times passengers are denied boarding is becoming a key measure of the impact of near-capacity operations on customers and is fundamental for calculating other performance metrics, such as expected waiting time for service. This paper reviews existing methods and proposes a denied boarding probability distribution inference method for closed Automated Fare Collection (AFC) urban rail systems. Using AFC (tap-in and tap-out) and Automated Vehicle Location (AVL) data, the method relaxes some of the limitations of existing approaches. The problem is modeled using a mixture distribution framework that incorporates a priori structural information. It is data-driven and requires neither observations of denied boardings, nor assumptions about access/egress time distributions. Also, for comparison purposes, the paper presents an event-based deterministic transit assignment model with explicit capacity constraints. While the network assignment works at the network level and requires train capacity, the mixture model works at the station level, requires no external parameters, and can be easily applied to any station and for any time period. A case study illustrates the application of the proposed methods using actual data and compares the results against existing methods, and also survey data. The results demonstrate the mixture model’s robustness and applicability for monitoring denied boarding.