On the fragility of a train timetable

In dense railway traffic, even the small delay of a single train may propagate through the network, causing a sequence of knock-on delays and significant deviations from the timetable. To mitigate the propagation of delays, railway infrastructure managers can generally employ two strategies: (i) in real time, train dispatchers can limit delay propagation by rescheduling trains, i.e., by adjusting the timetable in response to disturbances; (ii) in the timetable design phase, train planners can try to build delay-resilient timetables, which requires a complicated and lengthy iterative process. The ability of a timetable to “absorb” delays whenever they occur is known as robustness. While there is no unanimous consensus on a measure to quantify such robustness, it is normally a global measure, and therefore it is unable to highlight whether specific train paths or regions of the railway network are less robust than others. Moreover, only a few academic works incorporate the possibility of mitigating delays in real time through dispatching when evaluating robustness measures. These shortcomings motivate the present work. In this paper, we introduce the concept of fragility as a new practical tool to analyze a given timetable in order to identify the specific sections where a primary delay is most likely to generate knock-on delays, factoring in optimal future dispatching decisions. We also discuss the relationship between the fragility concept and the so-called recovery cost. We present computational results on real-life scenarios from a busy railway line in Norway and discuss several potential uses of fragility to improve decisions at different levels of the railway planning process, including dispatching, timetable design, and network design.