Factorization and exact evaluation of the source‐terminal diameter‐constrained reliability

In classical network reliability, the system under study is a network with perfect nodes and imperfect links that fail randomly and independently. The probability that a given subset K of terminal nodes belongs to the same connected component is called classical or K-Terminal reliability. Although (and because) the classical reliability computation belongs to the class of N P-Hard problems, the literature offers many methods for this purpose, given the importance of the models. This article deals with diameter-constrained reliability, where terminal nodes are further required to be connected by d hops or fewer (d is a given strictly positive parameter of the metric called its diameter). This metric was defined in 2001, inspired by delay-sensitive applications in telecommunications. Factorization theory is fundamental for the classical network reliability evaluation, and today it is a mature area. However, its extension to the diameter-constrained context requires at least the recognition of irrelevant links, which is an open problem. In this article, irrelevant links are efficiently determined in the most used case, where |K|=2, thus providing a first step toward a Factorization theory in diameter-constrained reliability. We also analyze the metric in series-parallel and composition graphs. The article closes with a Factoring algorithm and a discussion of trends for future work. © 2017 Wiley Periodicals, Inc. NETWORKS, 2017