Networks: An Introduction
Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo
Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo
Combinatorial approach to computing component importance indexes in coherent systems
Probability in the Engineering and Informational Sciences
Network Robustness under Large-Scale Attacks
Network Robustness under Large-Scale Attacks
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We consider two models of failure development in dependent networks. The first model assumes that there are two networks A and B, and some of the nodes of network A are connected to subsets of the node set VB of network B. The assumption is made that if a node i in A fails, and this node is connected to subset Vi of VB, then all nodes in Vi also fail. Node failure means that all edges incident to this node are erased. We compute, using Monte Carlo calculation of the spectra the probability that network B fails if nodes of A fail independently with given probability q. The second model considers one central network B whose nodes are "infected" in a random way by a collection of periphery networks σ = {A1,...,AK}. Each node of network Ai delivers with probability pi infection to a randomly chosen node in B. A node in B which gets infected at least once fails. Assuming that the number of infected nodes in B caused by network Ai has a Poisson distribution, we find out analytically the probability that network B will be DOWN as a result of joint infection originated from the periphery networks σ.