Combinatorial Approach to Reliability Evaluation of Network with Unreliable Nodes and Unreliable Edges

Estimating the reliability of a computer network has been a subject of great interest. It is a well known fact that this problem is NP-hard. In this paper we present a very efficient combinatorial approach for Monte Carlo reliability estimation of a network with unreliable nodes and unreliable edges. Its core is the computation of some network combinatorial invariants. These invariants, once computed, directly provide pure and simple framework for computation of network reliability. As a specific case of this approach we obtain tight lower and upper bounds for distributed network reliability (the so called residual connectedness reliability). We also present some simulation results. Keywords—Combinatorial invariants, Monte Carlo simulation, reliability, unreliable nodes and unreliable edges.

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