Load-Dependent Cascading Failures in Finite-Size Erdös-Rényi Random Networks

Large-scale cascading failures can be triggered by very few initial failures, leading to severe damages in complex networks. This paper studies load-dependent cascading failures in random networks consisting of a large but finite number of components. Under a random single-node attack, a framework is developed to quantify the damage at each stage of a cascade. Estimations and analyses for the fraction of failed nodes are presented to evaluate the time-dependent system damage due to the attack. The results provide guidelines for choosing the load margin to avoid a cascade of failures. Furthermore, the analysis reveals a phase transition behavior in the extent of the damage as the load margin grows, i.e., the fraction of the damaged components drops from near one to near zero over a slight change in the load margin. The critical value of the load margin and the short interval over which such an abrupt change occurs are derived to characterize the network reaction to small network load variations. Our findings provide design principles for enhancing the network resiliency in load-dependent complex networks with practical sizes.