Train Delay Predictions Using Markov Chains Based on Process Time Deviations and Elastic State Boundaries

Train delays are inconvenient for passengers and major problems in railway operations. When delays occur, it is vital to provide timely information to passengers regarding delays at their departing, interchanging, and final stations. Furthermore, real-time traffic control requires information on how delays propagate throughout the network. Among a multitude of applied models to predict train delays, Markov chains have proven to be stochastic benchmark approaches due to their simplicity, interpretability, and solid performances. In this study, we introduce an advanced Markov chain setting to predict train delays using historical train operation data. Therefore, we applied Markov chains based on process time deviations instead of absolute delays and we relaxed commonly used stationarity assumptions for transition probabilities in terms of direction, train line, and location. Additionally, we defined the state space elastically and analyzed the benefit of an increasing state space dimension. We show (via a test case in the Swiss railway network) that our proposed advanced Markov chain model achieves a prediction accuracy gain of 56% in terms of mean absolute error (MAE) compared to state-of-the-art Markov chain models based on absolute delays. We also illustrate the prediction performance advantages of our proposed model in the case of training data sparsity.