Title: Limits of Predictability of Cascading Overload Failures in Spatially-Embedded Networks with Distributed Flows,
Abstract: Cascading failures are a critical vulnerability of complex information or
infrastructure networks. Here we investigate the properties of load-based
cascading failures in real and synthetic spatially-embedded network structures,
and propose mitigation strategies to reduce the severity of damages caused by
such failures. We introduce a stochastic method for optimal heterogeneous
distribution of resources (node capacities) subject to a fixed total cost.
Additionally, we design and compare the performance of networks with N-stable
and (N-1)-stable network-capacity allocations by triggering cascades using
various real-world node-attack and node-failure scenarios. We show that failure
mitigation through increased node protection can be effectively achieved
against single node failures. However, mitigating against multiple node
failures is much more difficult due to the combinatorial increase in possible
failures. We analyze the robustness of the system with increasing protection,
and find that a critical tolerance exists at which the system undergoes a phase
transition, and above which the network almost completely survives an attack.
Moreover, we show that cascade-size distributions measured in this region
exhibit a power-law decay. Finally, we find a strong correlation between
cascade sizes induced by individual nodes and sets of nodes. We also show that
network topology alone is a weak factor in determining the progression of
cascading failures.