Exploring Patterns of Train Delay Evolution and Timetable Robustness

Uncertainty affects the overall performance of railway systems. It can be captured tracking the successive departure and arrival events of trains at stations in the scheduled railways. Markov chains has shown to be an effective means to model variabilities in the departure and arrival delays of trains. The empirical data of actual operations are used to develop the Markov matrices. Transitions between delay states comprise the internal dynamics of running and dwelling processes in probabilistic terms, presenting particular patterns of deterioration, recovery and state keeping in the prevailing timetable setting. All these features conform to the practice of railway operations as well as train dispatchers and drivers. Hence, delay-based Markov chains becomes a simple and effective tool to predict delays in the following events of trains and distribution of delays over a longer period of time using simple performance measures. We have developed the homogeneous and non-homogeneous Markov models and tested their performances using the actual data collected in the Netherlands railway network. The analysis and evaluation show that the railway corridor considered in this study performs well and the corresponding Markov chain models can be used effectively to predict train delays and to evaluate timetable robustness. The outcomes of the homogeneous and non-homogeneous model are evaluated with respect to the observed data resulting that the non-homogeneous model performs better than the homogeneous model.