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

TL;DR

This paper introduces a Bayesian spatiotemporal model for predicting post-disruption train travel times in metro networks, capturing complex dependencies and distributional features to improve forecast accuracy and uncertainty quantification.

Contribution

It develops a novel Bayesian framework that explicitly models train interactions, error dependence, and non-Gaussian travel time distributions during recovery periods.

Findings

Models outperform baseline methods in prediction accuracy.

Skew-$t$ distribution provides robust performance for longer journeys.

Post-disruption travel times show asymmetric distributions and error dependence.

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 Montr\'eal 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.