To help improve punctuality by understanding how delays propagate and identifying critical trains, researchers from the Complexity Science Hub (CSH), in collaboration with Austrian Federal Railways (ÖBB), have developed a new network-based method.
[Vienna, 10.12.2024] —Train delays are not only a common frustration for passengers but can also lead to significant economic losses, especially when they cascade through the railway network. When a train is delayed, it often triggers a chain reaction, turning minor issues into widespread delays across the system. This can be costly. A report from the Association of American Railroads (AAR) indicates that a nationwide rail disruption in the US could cost the economy over $2 billion per day. Therefore, the pressing question for railway operators is: How to manage the cascading effect of delays efficiently and with minimal effort?
Using a novel network-based approach, CSH researchers quantified the systemic risk posed by individual trains to the entire rail network in Austria. “This allows us to identify weak points in the system—those trains that significantly transfer delays to subsequent services,” explains Vito Servedio from CSH. The study was published in npj Sustainable Mobility and Transport.
Identifying "Influencer Trains"
The researchers constructed a network model by analyzing data from the busy Vienna Central Station to Wiener Neustadt route (with up to 1,000 passenger trains running daily) between 2018 and 2020, along with additional data from all train routes across Austria over a period of 14 days. In this model, nodes represent train services, and links represent interactions that could potentially cause delays. Using this model, the researchers were able to rank trains based on their potential to propagate delays and identify “influencer trains.” To validate their findings and assess delay mitigation strategies, they built an agent-based simulation of the Austrian railway, replicating daily train dynamics and interactions.
The results show that trains operating slightly before and during the first rush hour are the most critical — “which is perhaps little surprising. However, we can distinguish which ones are the most impactful in the intricate network of connections during the rush hours,” says Simone Daniotti who is a PhD candidate at CSH and first author of the study.
Moreover, the team observed that the risk associated with these trains is rooted in their scheduled dependencies. Only when a disruption occurs, the critical nature of these dependencies is revealed.
Rolling Stock as Primary Cause of Delay Cascades
The researchers found that delay cascades in the model were primarily caused by sharing rolling stock (locomotives and wagons), despite there being fewer contact points between rolling stocks than between infrastructure. Daniotti explains: “What we see is that materials like rolling stock and personnel, play an even more significant role in spreading delays through the rail network than the trains’ movements themselves.” For example, if a train scheduled to depart at 2 PM relies on a rolling stock used by a train that departed at 8 AM, any delay in the earlier train can significantly disrupt the later one. This creates a hard constraint that can be highly disruptive.
Although the current model does not account for personnel shifts due to a lack of data, it is designed to incorporate additional factors, such as staffing, at any time. This flexibility will allow for a more precise analysis of delay impacts when those data points are accessible.
Three different layers contribute to the spread of a delay: infrastructure contact, rolling stock contact, and personnel contact. (a) When infrastructure (e.g., tracks or platforms) is occupied, for example, by another train in transit, the upper train will spread its delay onto the bottom train. (b) A train service has to wait for the arrival of the corresponding traction units being used by another service. The arriving train can spread the delay to the waiting train. (c) This example shows how delays can be passed on through infrastructure and rolling stock. Data for personnel were not available for the study. (d) A train service can transmit its delay through proximity contact (light blue) and rolling stock contact (orange). In this example, trains A and B compete for infrastructure resources (a free track section) at time t1. Trains B and C have a similar interaction at time t3, propagating the delay generated from A. Train D shares its rolling stock with train E at time t2, meaning train E needs to wait for train D’s arrival.
Additional Train Services
To explore potential solutions, the researchers simulated a one-hour delay for the top 2% of trains on the highly frequented Austrian Southern Railway Line from Vienna Central Station to Wiener Neustadt. Those trains were identified as having the most impact on the network. “We found that adding just three additional train services in the model could reduce overall delays during critical days by approximately 20%,” explains Servedio.
Applying this approach across the entire Austrian railway system could reduce delays in the model by 40% with the addition of 37 new trains or connections, the researchers say. They also observed that the more traffic a railway line has, the more challenging it is to optimize.
Since the most cost-effective train services for railway companies to add are local trains with electric traction units, while long-distance trains are more difficult and expensive to substitute, the researchers examined whether different effects depend on which train services are added. “Interestingly, we found that we can achieve a similar reduction of about 20% in overall delays by adding three of the most cost-effective train services to the Southern Railway Line,” states Servedio.
Pioneering Approach
“Punctuality is one of the main goals of ÖBB. The model which CSH developed provides us with an additional tool to reach this goal in our complex rail system”, says ÖBB program manager Aad Robben-Baldauf.
“Simulating a national railway system is complex, involving vast numbers of trains and operational points that generate billions of scenarios. Traditional methods often fall short at this scale, but network analysis and complexity science offer robust modeling tools to identify systemic vulnerabilities,” says CSH president Stefan Thurner. This study exemplifies the significant benefits of bridging scientific research with industry expertise, demonstrating how collaborative innovation can yield impactful solutions to complex operational issues.
About the Study
The study “Systemic risk approach to mitigate delay cascading in railway networks” by S. Daniotti, V. D. P. Servedio, J. Kager, A. Robben-Baldauf, and S. Thurner was published in npj Sustainable Mobility and Transport.
This study was conducted as part of the "Train Operating Forecasting" project, a joint initiative between the Complexity Science Hub and ÖBB, aimed at developing optimization strategies for ÖBB’s passenger transport to reduce overall annual delays in the system.
About CSH
The Complexity Science Hub (CSH) is Europe’s research center for the study of complex systems. We derive meaning from data from a range of disciplines — economics, medicine, ecology, and the social sciences — as a basis for actionable solutions for a better world. Established in 2015, we have grown to over 70 researchers, driven by the increasing demand to gain a genuine understanding of the networks that underlie society, from healthcare to supply chains. Through our complexity science approaches linking physics, mathematics, and computational modeling with data and network science, we develop the capacity to address today’s and tomorrow’s challenges.
