An Unsupervised Learning Approach for Robust Denied Boarding Probability Estimation Using Smart Card and Operation Data in Urban Railways

Abstract

Urban railway systems in many cities are facing increasing levels of crowding and operating near capacity. Crowding at stations and on trains is a concern due to its impact on safety, service quality, and operating efficiency. Denied boarding is becoming a key measure of the impact of near-capacity operations on customers, and it is fundamental for calculating other performance metrics, such as the expected waiting time. Several approaches have been proposed to infer denied boarding using smart card and train movement data. They formulate the inference as a maximum-likelihood estimation problem on observed trip journey times, with an a priori model assumption on independent journey time components, and they require extensive ground truth data collection and model calibration for practical deployment. This article proposes a data-driven unsupervised clustering-based approach to robustly infer denied boarding probabilities for access-plus-waiting times by decomposing trip journey times (instead of directly on journey times). The approach is applicable to closed fare collection systems and consists of two main steps: grouping passengers to trains via trip exit information by using a probabilistic model and inferring denied boarding probabilities by using a structured mixture distribution model with physical constraints and systematic parameter initialization. The method is data driven and requires neither observations of denied boarding nor assumptions about model components’ independence and parameter calibrations. Case studies validate the proposed method by using actual data and comparing it with state-of-the-art models and survey data. The results demonstrate the proposed model’s robustness and applicability for estimating denied boarding under both normal and abnormal operation conditions.