A Novel Markov Model for Near-Term Railway Delay Prediction

TL;DR

This paper introduces a non-homogeneous Markov chain model with a novel matrix recovery technique for accurate near-term train delay prediction, outperforming traditional models in interpretability and prediction accuracy.

Contribution

It presents a new Markov chain-based delay prediction model with a Gaussian kernel density estimation recovery method, improving accuracy and simplicity over existing approaches.

Findings

The Markov model outperforms other time series models in accuracy.

The matrix recovery approach enhances transition matrix estimation.

The model is computationally efficient and suitable for large-scale forecasting.

Abstract

Predicting the near-future delay with accuracy for trains is momentous for railway operations and passengers' traveling experience. This work aims to design prediction models for train delays based on Netherlands Railway data. We first develop a chi-square test to show that the delay evolution over stations follows a first-order Markov chain. We then propose a delay prediction model based on non-homogeneous Markov chains. To deal with the sparsity of the transition matrices of the Markov chains, we propose a novel matrix recovery approach that relies on Gaussian kernel density estimation. Our numerical tests show that this recovery approach outperforms other heuristic approaches in prediction accuracy. The Markov chain model we propose also shows to be better than other widely-used time series models with respect to both interpretability and prediction accuracy. Moreover, our proposed model does not require a complicated training process, which is capable of handling large-scale forecasting problems.