Modelling and Analysis of Operations in Railway Networks

Reliable and punctual rail transport is essential in solving the Dutch mobility problem. When trains are frequently running late, many people will still choose to travel by car instead. TU Delft is developing mathematical models that can be used to analyze, evaluate and increase the reliability of train network timetables. 

Train reliability
Many Dutch motorways are overcrowded during rush hour, resulting in traffic jams. In order for more people to want to use the railway network, it needs to be more reliable. Train timetables often don’t have a large enough time buffer, which means that if a delay occurs somewhere along a train’s route, this delay passes over to other trains at every next station the train passes, because other trains have to wait for the delayed one to pass first. By taking possible variations in train running and dwell times into account when making the timetable, these delays can be prevented. That is why researchers at TU Delft have developed math-based software to evaluate timetables before implementation.

A reliable timetable allows enough extra time at the right places to prevent delays from building up and spreading through the network. We are developing models that can calculate the stability of timetables and the propagation of train delays on the network. For this, we use a suitable type of algebra, called max-plus algebra, which allows us to analyze large-scale networks quickly. In addition, we use the log files from the rail network’s train tracking systems (TNV) to gather insight into the actual train running and dwell times and the effects of disturbances.

Practical use
The data analysis and the mathematical models developed by TU Delft researchers can predict delays and proactively prevent them. Amongst the computer software we have developed, is PETER (Performance Evaluation of Timed Events in Railways), which is used by ProRail, infra manager of the Dutch railway network, to analyze the stability of timetables. We have also developed TNV-Prepare, software that couples track occupancy and signal data with train numbers, making is possible to backtrack a certain train’s whereabouts, second by second. Similarly, TNV-Filter can accurately estimate a train’s delay.

We are currently expanding our mathematical models to take distortions of the planned situation into account, allowing the software to predict the effects of these distortions. Furthermore, we are introducing random variables and probability into our models.  

The Modelling and Analysis of Operations in Railway Networks project is part of the larger, research project ‘Modelling and Analysis of Operations in Railway Networks: the Influence of Stochasticity’ in which the TU Delft’s faculties of Civil Engineering and Geosciences, Electrical Engineering, Mathematics and Computer Science and the Vrije Universiteit Amsterdam participate. It is supported by ProRail, NS Reizigers and consultancy firms Movares and Arcadis.

To learn more about our research into Modelling and Analysis of Operations in Railway Networks, please contact Rob Goverde, Faculty of Civil Engineering and Geosciences, Transport & Planning section.
Telephone: +31 (0)15 27 83178

Name author: webredactie
© 2016 TU Delft