Static Network Reliability Estimation under the Marshall-Olkin Copula

• DOI: 10.1145/2775106
• Publication Date: 2016-01-14T02:18:38Z
• Authors: Zdravko I. Botev; Pierre L'Ecuyer; Richard Simard; Bruno Tuffin
• Keywords: [INFO.INFO-RO]Computer Science [cs]/Operations Research [math.OC]; [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO]; 0101 mathematics; 01 natural sciences; [INFO.INFO-RO] Computer Science [cs]/Operations Research [math.OC]

In a static network reliability model, one typically assumes that the failures of components are independent. This simplifying assumption makes it possible to estimate efficiently via specialized Monte Carlo algorithms. Hence, natural question consider is whether this independence can be relaxed while still attaining an elegant and tractable model permits efficient algorithm for unreliability estimation. article, we provide answer by considering with dependent link failures, based on Marshall-Olkin copula, which models dependence shocks take down subsets at exponential times, propose collection adapted versions permutation (PMC, conditional method), its refinement called turnip method , generalized splitting (GS) methods very small unreliabilities accurately under model. The PMC estimators have bounded relative error when topology fixed failure probabilities converge 0, whereas GS does not property. But size (or number shocks) increases, eventually fail, works nicely (empirically) large networks, over 5,000 in our examples.