Method of analysis for delay propagation in a single-track network

Delay propagation is a key factor in punctuality of rail services. Propagation of delays reflects the degree of robustness of timetable design and the stability of train operations. This paper studies delay propagation for trains on single-track railways as the Norwegian rail network comprises primarily single-track operations. The analysis is based on real-time punctuality data. We present an algorithm and results from application of the algorithm. The algorithm is a recursive implementation of a set of conditions that (i) detects cases of knock-on delays, revealing dependencies between two trains on single-track railway, and (ii) finds the networks of dynamic delay propagations by tracing the propagation of knock-on delays from one interaction between trains to the next. Finally, we compare our results to delay cause registrations and theoretical calculations of the expected propagation factors. The propagation factors based on our model for a five-month period are typically around two, and over 70% of dynamic delay propagations consist of two trains. This indicates that each delay minute generates an additional delay of 1 min for other trains, which is higher than the present delay registrations. The presented method and analysis can be applied in punctuality improvement work, including timetable analysis.