Snowball effect for disruptions in complex networks

Model proves local train delays can lead to nation-wide gridlock

Scientists at Utrecht University have developed a model for predicting the potentially severe consequences of minor disruptions in a complex transport network. One such network is a railway timetable, where an initially localised problem can result in nation-wide gridlock. “The interaction between staff and trains makes the system vulnerable.” Their article has been published in the prestigious academic journal PLOS ONE.

Recording statistics

Those who regularly travelled long distances by train (before the pandemic) know that if your first train is delayed, then there’s a good chance that you’ll miss your connection. The dispatching units of NS and ProRail try to mitigate disruptions and be on schedule as soon as possible. However, sometimes various local disruptions have a national impact, as railway personnel, and even the trains themselves, can be affected by delays.

“That sounds logically intuitive”, says Mark Dekker, PhD candidate at Utrecht University’s Centre for Complex Systems Studies. “But it’s never been quantified, for a variety of reasons. That’s due in part to the availability of useful data and traditional train models’ focus on the regional level.”

Dekker models the consequences of minor adjustments to complex systems. He has analysed several major railway disruptions in the Netherlands and the rest of Europe over the past few years. Dekker collaborates closely with the Nederlandse Spoorwegen (NS) and ProRail for his research.

In many European countries, railways are complex networks, where local delays can have national consequences. Image: Mark Dekker and Debabrata Panja

Real-life assessment for dispatchers

Dekker “For NS and ProRail, timetable adjustments are a daily occurrence. Trains and crews are assigned to different routes, as dispatching units make changes to work schedules. This almost never fails: the model proves that their work mitigates lots of delay. But the interaction between staff, trains and lines makes the system vulnerable to a snowball effect.” As a result, it is not always possible to get trains and crews to the right place at the right time, which in turn can cause delays for other lines. Generally, such major delays happen just a few times per year and lead to what we call ‘black days’. A total collapse of the railway network is even more rare, and happens in general once in a few years.

Dekker: “As it is today, the model can, for incidents in the past, identify where the problem originated and whether people reacted as they should. Furthermore, it can serve as a real-life assessment and discover which potential problems can cause current delays if you don’t dispatch. Those insights can help dispatchers in their work.”

A delay for train line 3028 from Nijmegen to Alkmaar (a) can result in disruptions of the rolling stock for the return journey (b) and the crew for the train to The Hague (c). Image: Mark Dekker and Debabrata Panja

Predictive value

The model also has a predictive value. Dekker: “You can use the model to predict the potential impact of a delay of one train on other trains, based on the current situation” That was also the goal for the collaboration with NS and ProRail. “In 2012, a series of storms and major disruptions brought the national railway network to a standstill. To find a solution to the problem, an NWO-project was started, which served as the basis for my research questions. Our model can help us better understand and predict snowball effects, and prevent such severe incidents from occurring.”

This article has been revised on 1 February.


Mark M. Dekker, Debabrata Panja

Cascading dominates large-scale disruptions in transport over complex networks

PLOS ONE, 25 januari 2021,

Both researchers are affiliated with the Department of Information and Computing Sciences and the Centre for Complex Studies at Utrecht University.