Fuzzy States to Enhance Train Delay Prediction of Markov Chains

Abstract

Markov chains provide distinctive advantages and practical applicability in modeling of train delays. This modeling approach treats nearby delays in separate states as being quite different and equates distant delays within the same state, leading to higher prediction errors. To address this limitation and obtain more precise delay predictions, this study proposes MCFS (Markov chains with fuzzy states) for the first time to model train delays. The data used in the study are from the Dutch railway network. The predictions are obtained using Markov chains with crisp states and Markov chains with fuzzy states. MAE (mean absolute error) and RMSE (root mean square error) are used to compare the prediction errors of the two models with one another and with an artificial neural networks model developed. It is shown that using fuzzy delay states in Markov chains reduced the aggregated MAE by 1.31% and the aggregated RMSE by 1.76%. We performed hypothesis tests to support the significance of this improvement statistically. It was found that MCFS yields prediction errors that are significantly smaller than those of classical Markov chains and artificial neural networks. Incorporating fuzzy states into Markov models enhances prediction reliability and supports operational planning, train scheduling, and real-time decision-making in delay management.