Cascading dominates large-scale disruptions in transport over complex networks.

The core functionality of many socio-technical systems, such as supply chains, (inter)national trade and human mobility, concern transport over large geographically-spread complex networks. The dynamical intertwining of many heterogeneous operational elements, agents and locations are oft-cited generic factors to make these systems prone to large-scale disruptions: initially localised perturbations amplify and spread over the network, leading to a complete standstill of transport. Our level of understanding of such phenomena, let alone the ability to anticipate or predict their evolution in time, remains rudimentary. We approach the problem with a prime example: railways. Analysing spreading of train delays on the network by building a physical model, supported by data, reveals that the emergence of large-scale disruptions rests on the dynamic interdependencies among multiple 'layers' of operational elements (resources and services). The interdependencies provide pathways for the so-called delay cascading mechanism, which gets activated when, constrained by local unavailability of on-time resources, already-delayed ones are used to operate new services. Cascading locally amplifies delays, which in turn get transported over the network to give rise to new constraints elsewhere. This mechanism is a rich addition to some well-understood ones in, e.g., epidemiological spreading, or the spreading of rumours and opinions over (contact) networks, and stimulates rethinking spreading dynamics on complex networks. Having these concepts built into the model provides it with the ability to predict the evolution of large-scale disruptions in the railways up to 30-60 minutes up front. For transport systems, our work suggests that possible alleviation of constraints as well as a modular operational approach would arrest cascading, and therefore be effective measures against large-scale disruptions.