Probabilistic Predictions of Train Delay Evolution

The prediction of train delays in railway networks is essential to manage railway traffic in real-time and is also an important service for passengers. This paper presents a stochastic event-driven approach to predict the evolution of train delays in real-time based on stochastic processes. We model train arrival and departure delays with continuous distributions assuming the Markov property for the delay evolution along a train’s journey. We analyze the effectiveness of different probability distribution assumptions for running and dwelling processes location specifically. Therefore, we apply big-data learning methods to understand the development of delays in a railway network using historic train movement observations data. In this way, we propose a probabilistic approach to model the uncertainty of the evolution of actual train delays. The results can be used for risk-based real-time traffic control management and reliable information communication to railway passengers. We present a case study of our model on a busy corridor of the Swiss railway network and discuss the quality of our predictions for different prediction horizons. We show that the quality of the predictions is robust to different distribution assumptions for the railway operation processes in our model.