Statistical learning for train delays and influence of winter climate and atmospheric icing

This study investigated the climate effect under consecutive winters on the arrival delay of high-speed passenger trains. Inhomogeneous Markov chain model and stratified Cox model were adopted to account for the time-varying risks of train delays. The inhomogeneous Markov chain modelling used covariates weather variables, train operational direction, and findings from the primary delay analysis through stratified Cox model. The results showed that temperature, snow depth, ice/snow precipitation, and train operational direction, significantly impacted the arrival delay. Further, by partitioning the train line into three segments as per transition intensity, the model identified that the middle segment had the highest chance of a transfer from punctuality to delay, and the last segment had the lowest probability of recovering from delayed state. The performance of the fitted inhomogeneous Markov chain model was evaluated by the walk-forward validation method, which indicated that approximately 9% of trains may be misclassified as having arrival delays by the fitted model at a measuring point on the train line. With the model performance, the fitted model could be beneficial for both travellers to plan their trips reasonably and railway operators to design more efficient and wiser train schedules as per weather condition.