Cascading Failures and Stochastic Analysis for Mitigation in Spatially-Embedded Random Networks

In complex information or infrastructure networks, even small localized disruptions can give rise to congestion, large-scale correlated failures [1], or cascades, -- a critical vulnerability of these systems. Recent studies have demonstrated that flow-driven cascading overload failures in spatial graphs, such as the power grid, are non-self-averaging, hence predictability is poor and conventional mitigation strategies are largely ineffective [2]. In particular, we have shown that protecting all nodes (or edges) by the same additional capacity (tolerance) can actually lead to larger global failures, i.e., ``paying more can result in less'', in terms of robustness [2]. Here, we explore stochastic methods for optimal heterogeneous distribution of resources (node or edge capacities) subject to a fixed total cost. In addition to random geometric graphs, we also investigate cascading failures on the UCTE European electrical power transmission network. [1] A. Bernstein, D. Bienstock, D. Hay, M. Uzunoglu, and G. Zussman, http://arxiv.org/abs/1206.1099 (2011). [2] A. Asztalos, S. Sreenivasan, B.K. Szymanski, and G. Korniss, PLOS One 9(1): e84563 (2014).