Quantifying railway timetable robustness in critical points

Abstract

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.

Tuning delay-propagation models to meet practical planning procedure requirements

“… Improved procedure to "cut" cycles in the activity graph  Application of the model in real-time for the dispatching of connections  Ex-ante deduction of robustness indicators from the activity graph, for example following the procedure given by Andersson et al in [18]  Analysis of samples of scheduled and effective buffer times in the timetable structure To enable the latter evaluations, notable preparatory works have already been conducted by implementing an UIC Leaflet 406 compliant compression-approach, which allows the detection of "critical paths" through the timetable structure in the initial and the concatenated situation. Linking the compression of a timetable with the knowledge gathered from delay propagation may provide new insights into timetable dynamics in the future.…”

Ex-ante robustness measures for single track train timetables

“…Andersson et al [1,2,3] Robustness in critical points (RCP) Consider the margin availability at train interaction points.…”

“…2, for example, at station C runtime margin of train 3 overlaps with the headway margin of train 2. Robustness in critical points [1,2,3] Analyzing the weakness of the timetable by identifying the delay-sensitive train slots or line sections is a common approach in the available ex-ante robustness measures [9, 11, 12, and 17]. Available measures can be used to point out the trains having inefficient margin allocation or possessing inappropriate amount of margins, however, it cannot provide any advice about the amount of margins and suitable insertion places for the margin to increase the robustness.…”

“…Andersson et al [1] used the MRD by dividing the whole track into partial stretches, which were naturally bounded by the traffic structures. It is used for both directional trains by dividing the network into partial stretches based on the traffic conditions.…”

“…Andersson et al [1,2,3] identified the limitations of RCP that it considered all the headways and runtime margins in the robustness while in reality not all of these margins were effective and focused on the double line train traffic only. Considering the limitations of RCP, CRM is concentrated on those margins which are useful for the robustness of single track train traffic.…”