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In public railway systems, minor disruptions can trigger cascading eventsthat lead to delays in the entire system. Typically, delays originate andpropagate because the equipment is blocking ways, operational units areunavailable, or at the wrong place at the needed time. The specificunderstanding of the origins and processes involved in delay-spreading is stilla challenge, even though large-scale simulations of national railway systemsare becoming available on a highly detailed scale. Without this understanding,efficient management of delay propagation, a growing concern in some Westerncountries, will remain impossible. Here, we present a systemic risk-basedapproach to manage daily delay cascading on national scales. We compute the{\em systemic impact} of every train as the maximum of all delays it couldpossibly cause due to its interactions with other trains, infrastructure, andoperational units. To compute it, we design an effective impact network wherenodes are train services and links represent interactions that could causedelays. Our results are not only consistent with highly detailed andcomputationally intensive agent-based railway simulations but also allow us topinpoint and identify the causes of delay cascades in detail. The systemicapproach reveals structural weaknesses in railway systems whenever sharedresources are involved. We use the systemic impact to optimally allocateadditional shared resources to the system to reduce delays with minimal costsand effort. The method offers a practical and intuitive solution for delaymanagement by optimizing the effective impact network through the introductionof new cheap local train services.

Systemic risk approach to mitigate delay cascading in railway networks