More realistic computer models to solve train disruptions

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When a train service is disrupted, dispatchers still rely on their human judgment to restore service for as many passengers as possible in the shortest possible time. In his PhD research Joris Wagenaar of Rotterdam School of Management, Erasmus University (RSM) describes mathematical solutions to practical problems that occur after train disruptions. His findings can improve existing computer models that assist train dispatchers with their decisions in the hectic few minutes after a disruption of service.

For train dispatchers, finding the best quick response to a disruption is like solving a complicated chess problem, says researcher Wagenaar. They have to tackle three matters at the same time; timetable, trains and crews. These three are connected to each other: dispatchers can adapt the timetable, trains can be moved around and train crew can be rescheduled.

Solving this puzzle in real time not only takes a lot of computational power, but also current computer models give only a very crude representation of the planning problem, and often don’t give much practical help. That’s why, just like experienced chess players, train dispatchers still rely on their experience in similar situations to make decisions on the fly. In his research, Wagenaar set out to make existing computer models correspond better to the real challenges train dispatchers face after disruptions.

Maintenance schedules

In one of his studies Wagenaar developed a computer model that ensures that trains make it to the workshop for scheduled maintenance on time, despite disruptions. It’s important, because following disruptions, some of them miss appointments for scheduled maintenance when they are sent out on non-routine routes. As a result, they are more prone to technical failures, and that causes new disruptions.

Dead-heading trips

Sometimes the best way to solve a disruption is to send an empty train to a location where it’s most needed. These so-called ‘dead-heading trips’ move much quicker through the network than a train in normal service. There are no passengers to board or alight so it doesn’t have to stop, and they only need a skeleton crew. Wagenaar found that dispatching empty trains –or train carriages- from a station with a surplus of trains to stations with a shortage of trains after a disruption may temporarily reduce the capacity at that station, but in the end leads to a greater total number of people getting a train to their destination.

Finding space in the railyard 

Finally, the researcher tested several models that can be used to solve the problem of storing trains in railyards – a complicated problem because in most yards, the last train to go in has to be the first out, and there is limited track length in such a space. These calculations can become substantial tasks for computers to tackle. For instance, one model is so realistic, it uses 24 gigahertz of computer memory (24 billion operations per second). The researcher determined which of the models is quickest and most accurate.

Wagenaar expects that human judgment will always be important for managing disruptions. At the same time, he predicts that the need for computer assistance to keep everything running smoothly will only increase, because railway networks are becoming more complicated, and more congested. Studies likes his can help to bring improved computerised assistance one step closer, he concludes.

In memory of professor Leo Kroon

Download Joris Wagenaar's thesis 'Practice Oriented Algorithmic Disruption Management in Passenger Railways' here

Rotterdam School of Management, Erasmus University (RSM) is one of Europe’s leading research-based business schools. RSM provides ground-breaking research and education furthering excellence in all aspects of management and is based in the international port city of Rotterdam – a vital nexus of business, logistics and trade. RSM’s primary focus is on developing business leaders with international careers who carry their innovative mindset into a sustainable future thanks to a first-class range of bachelor, master, MBA, PhD and executive programmes. Study information and activities for future students, executives and alumni are also organised from the RSM office in Chengdu, China.

For more information about RSM or this release, please contact Ramses Singeling, Media Officer for RSM, on +31 10 408 2028, or by email at

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