How can algorithms help improve train services during disruptions?

An opinion article in the section Research in a Nutshell

Every railway passenger will recognise the experience that trains do not always run on time. Moreover, sometimes trains can be overcrowded.  This is mainly caused by disruptions like malfunctioning infrastructure, broken trains or extreme weather. Every day, there are many small disruptions causing delays of single trains and sometimes larger disruptions occur. Now and then, there are huge disruptions, e.g. due to heavy snowfall as we for instance experienced in the Netherlands recently. 

In several recent research projects, we have developed mathematical models and algorithms to improve the railway operations during such disruptions. We show that delays can be reduced, while at the same time the probability of having a seat can be increased. Moreover, a total standstill of the whole rail system can be prevented in case of very severe disruptions.

In the PhD projects of Rowan Hoogervorst and Rolf van Lieshout at Erasmus School of Economics, we look at railway disruption management. Disruption management at railway operators usually follows a sequential approach: first the timetable is adjusted, then the rolling stock (the physical train units) is rescheduled and finally, the crew (drivers and guards) is rescheduled. Models and algorithms in the literature often assume that all information, such as the duration of the disruption and whereabouts of rolling stock and crew, is instantly available and correct. Unfortunately, this is often not the case in practice. Moreover, there is interaction between the different steps in disruption management, which is often ignored in the scientific literature. As a result, there is only a limited use of these algorithms in practice, making it is still a primarily manual process. 

‘We show that delays can be reduced’

Rolling stock rescheduling

In Rowan’s project, we extend mathematical models and algorithms for rolling stock rescheduling. In particular, we incorporate much more relevant, practical details in these models. For example, we also consider train delays caused by the rolling stock schedule. When a train arrives too late at a terminal station and the same rolling stock turns around again, the next train will already start with a delay. Since the railway network in, e.g., the Netherlands is very dense, it is likely that this delay will increase even further. Therefore, we have developed new models that try to reduce these delays, while at the same time incorporating other aspects of the rolling stock schedule. In particular, we also want to offer enough capacity such that (almost) all passengers can have a seat in the train.

Models for this problem can be formulated either as a network flow problem or as a path-based formulation. The network flow formulation performed the best of the two formulations. In reasonable computation times, we could find optimal solutions.  In these optimal solutions, delays could be reduced, while at the same time offering still enough seats to the passengers. For the case that even shorter computation times are required (which is of course very important when you need to decide right now), we have also developed some fast heuristics based on local search techniques. With these heuristics, we can find close to optimal solutions within one minute of computation time.

‘A total standstill can be prevented in case of huge disruptions’

Very severe disruptions

In Rolf’s project, we look at huge disruptions, such as heavy snowfall. In current practice, on those days sometimes (almost) all railway traffic is terminated. This is of course very undesirable and should be prevented. However, infrastructure availability will be limited due to for instance technical problems with switches. Therefore, we have developed a new concept where trains run up and down on certain lines without a timetable. Rolling stock and crew are dynamically assigned to certain trips based on limited local information. In this way, the whole disruption management process is decentralised and much less dependent on reliable, detailed information (which is usually not available in these situations). We show that with limited information and simple decision rules, trains can still be operated in a stable way. That means that the time between certain services on the route does not deviate too much. In this way, a total standstill of the whole system can be prevented, and most passengers can still reach their destination, albeit with some additional travel time and some additional transfers compared to the regular timetable. 


Dennis Huisman is Professor of Public Transport Optimisation at Erasmus School of Economics. He also works part-time as Expertise Manager Logistic Processes at Netherlands Railways (NS). In his research, he develops Operations Research models and algorithms to improve public transport operations.

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