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.
View on arXiv