A Bayesian Framework for Post-disruption Travel Time Prediction in Metro Networks

2026-02-23

AI Summary

This study addresses the high uncertainty in travel times following subway disruptions, caused by irregular train operations during service recovery. The authors propose a Bayesian spatiotemporal modeling framework that decomposes travel time into a baseline component and a delay component. Innovatively, the model jointly captures inter-train dependencies through a moving average error structure, accounts for headway imbalance, and characterizes the asymmetric heavy-tailed nature of travel times during recovery periods using skew-normal and skew-t distributions. Evaluated on high-resolution track occupancy data from the Montreal metro system, the approach outperforms existing baselines in both point prediction accuracy and uncertainty quantification, with the skew-t variant demonstrating particularly robust performance for long-distance trips.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Disruptions are an inherent feature of transportation systems, occurring unpredictably and with varying durations. Even after an incident is reported as resolved, disruptions can induce irregular train operations that generate substantial uncertainty in passenger waiting and travel times. Accurately forecasting post-disruption travel times therefore remains a critical challenge for transit operators and passenger information systems. This paper develops a Bayesian spatiotemporal modeling framework for post-disruption train travel times that explicitly captures train interactions, headway imbalance, and non-Gaussian distributional characteristics observed during recovery periods. The proposed model decomposes travel times into delay and journey components and incorporates a moving-average error structure to represent dependence between consecutive trains. Skew-normal and skew-$t$ distributions are employed to flexibly accommodate heteroskedasticity, skewness, and heavy-tailed behavior in post-disruption travel times. The framework is evaluated using high-resolution track-occupancy and disruption log data from the Montréal metro system, covering two lines in both travel directions. Empirical results indicate that post-disruption travel times exhibit pronounced distributional asymmetries that vary with traveled distance, as well as significant error dependence across trains. The proposed models consistently outperform baseline specifications in both point prediction accuracy and uncertainty quantification, with the skew-$t$ model demonstrating the most robust performance for longer journeys. These findings underscore the importance of incorporating both distributional flexibility and error dependence when forecasting post-disruption travel times in urban rail systems.

Problem

• post-disruption travel time prediction
• metro networks
• travel time uncertainty
• train operation irregularity
• urban rail systems

Innovation

• Bayesian spatiotemporal modeling
• post-disruption travel time prediction
• skew-t distribution
• error dependence
• train interaction