Reliability and Survivability of Communication Networks

Abstract

Abstract : For an (n,m)-graph G (on n vertices and m edges) representing a communications network with each vertex representing a processor and each edge a communications link the majority of studies of reliability and survivability were concerned with global reliability (the probability that the graph remains connected) or with 2-terminal reliability (the probability that the graph remains connected). The common model assumed the vertices are fail-safe but each edge is inoperable independently with probability q = 1-p. In another publication we introduced a general formula that encompassed the various known reliability/survivability measures and that made clear the probabilistic rating of component failure and the penalty function aspect of measuring the amount of disruption that is created by the failure of certain elements. We introduced the pair-connected measure of reliability, letting (PC(G) denote the expected number of pairs of vertices that remain connected. (This concept was independently introduced by Colbourn who used the term resilience). We have shown that determining PC(G;p) is NP-hard even for the case where G is planar of maximum degree four, and have produced linear algorithms for its determination in special cases (for example, for series-parallel graphs). Indeed, exact formulas have been produced for certain classes of graphs, and in general we have the following theorem. Theorem. For a fixed value h, the coefficients A1, A2, ..., Ah in PC(G;p) can be computed in time polynomial in n. (rrh)