Quantifying railway timetable robustness in critical points

Several European railway traffic networks experience high capacity consumption during large parts of the day resulting in delay-sensitive traffic system with insufficient robustness. One fundamental challenge is therefore to assess the robustness and find strategies to decrease the sensitivity to disruptions. Accurate robustness measures are needed to determine if a timetable is sufficiently robust and suggest where improvements should be made. Existing robustness measures are useful when comparing different timetables with respect to robustness. They are, however, not as useful for suggesting precisely where and how robustness should be increased. In this paper, we propose a new robustness measure that incorporates the concept of critical points. This concept can be used in the practical timetabling process to find weaknesses in a timetable and to provide suggestions for improvements. In order to quantitatively assess how crucial a critical point may be, we have defined the measure Robustness in Critical Points (RCP). In this paper, we present results from an experimental study where a benchmark of several measures as well as RCP has been done. The results demonstrate the relevance of the concept of critical points and RCP, and how it contributes to the set of already defined robustness measures. This paper is based on " Introducing a new quantitative measure of railway timetable robustness based on critical points, "