Cascading failures

Transportation systems, power grids and even financial systems are organized by large amount of components and their intrinsic complex coupling. When these systems are disturbed randomly or maliciously, the local perturbations can propagate through the coupling and ultimately induce global cascading failures and catastrophic consequences. The spatial propagation of cascading failures has become a fundamental question in the study of complex system reliability. The development of reliability technology on complex systems depends on the understanding of failure propagation behaviours in complex systems.

Our finding suggests the possibility and direction of rescuing systems from cascading failures by global protection and mitigation strategies, which should decouple the long rage correlations between failures to localize failures from spreading. Faced with the challenges of robust control and reliable management for networked infrastructures, we believe the spatial pattern and its evolution of cascading failures we have found will be useful for the realization and improvement of the future Intelligent Transportation Systems and Smart Grid.

Spatial Networks

Networks consist of entities (nodes) and their connections (links). Usually, networks are embedded either in two- or in three-dimensional space. For example, airline and Internet networks, as well as friendship networks where the nodes are the residences of friends, are embedded in the two-dimensional surface of the earth, whereas the neuronal network in the brain is embedded in a complex three-dimensional structure. If in a d-dimensional lattice, the links connect only neighbouring nodes (in space), then the dimension of the network is trivially identical to the dimension of the embedding space. In most cases, however, links are not short ranged, their length distribution is broad, connecting also distant nodes. The question we pose here is: Is there a finite dimension that characterizes such a spatially embedded network and how can we determine it? The knowledge of the dimension is not only important for a structural characterization of the network, but is also crucial for understanding the function of the network, as the dimension governs the dynamical processes in the network.

Transportation systems

A critical phenomenon is an intrinsic feature of traffic dynamics, during which transition between isolated local flows and global flows occurs. However, very little attention has been given to the question of how the local flows in the roads are organized collectively into a global city flow. We characterize this organization process of traffic as “traffic percolation,” where the giant cluster of local flows disintegrates when the second largest cluster reaches its maximum. We find in real-time data of city road traffic that global traffic is dynamically composed of clusters of local flows, which are connected by bottleneck links. This organization evolves during a day with different bottleneck links appearing in different hours, but similar in the same hours in different days. A small improvement of critical bottleneck roads is found to benefit significantly the global traffic, providing a method to improve city traffic with low cost. Answers to those issues would provide insights on the relation between traffic dynamics and percolation, which can be useful for efficient transportation, epidemic control, and emergency evacuation.