Network reliability problem and its efficient solution by Subset Simulation

Complex technological networks designed for distribution of some resource or commodity are a pervasive feature of modern society. Moreover, the dependence of our society on modern technological networks constantly grows. As a result, there is an increasing demand for these networks to be highly reliable. The degree to which a network is able to provide the required service needs to be quantitatively estimated. This quantitative assessment of network reliability is a very important aspect of network design, optimization, and operation. In this paper, we propose a framework for quantitative assessment of network reliability, formulate a general network reliability problem within this framework, and propose an efficient Markov chain Monte Carlo method for solving this problem, which is based on Subset Simulation, a very efficient stochastic simulation method originally developed for estimation of small failure probabilities of complex civil engineering structures such as tall buildings and bridges at risk from earthquakes. The efficiency of the method is demonstrated with an illustrative example where two small-world network models are compared in terms of reliability of networks they produce.