Measuring Robustness of Timetables in Stations using a Probability Distribution

Stations are often leading to network effects, especially at at-grade junction stations where conflicts between train routes results in interdependencies between the railway lines converging at the station. A train delayed on one line at a junction station may therefore propagate to other lines because of headway constrains and conflicting train routes. Depending of the size of the initial delay, the length and characteristics of the line(s), the initial delay can propagate to the whole railway network.

The interdependencies between lines at a junction station can be reduced by removing conflicts between train routes by changing the track layout, the plan of operation or the timetable. Existing methods can be used to calculate the complexity of a station, which can be used to quantify these changes. Reducing the complexity of a station will reduce the interdependencies or the consecutive delays caused by interdependencies, and result in a more robust operation. Currently three methods to calculate the complexity of station exists:
1. Complexity of a station based on the track layout
2. Complexity of a station based on the probability of a conflict using a plan of operation
3. Complexity of a station based on the plan of operation and the minimum headway times

However, none of the above methods take a given timetable into account when the complexity of the station is calculated. E.g. two timetable candidates are given following the same plan of operation in a station; one will be more vulnerable to delays (less robust) while the other will be less vulnerable (more robust), but this cannot be measured by the above methods.

In the light of this, the article will describe a new method where the complexity of a given station with a given timetable can be calculated based on a probability distribution fitted to empirical data. The method will make it possible to evaluate different timetables and/or timetable variants choosing the most robust one with the least amount of consecutive delays and network effects.