Abstract
In this paper, a stochastic network is an undirected graph with unreliable edges and absolutely reliable nodes. Its connectedness probability is determined by reliability preserving network reduction. The principle of this method consists in splitting the underlying deterministic graph of the stochastic network into two edge-disjoint subgraphs via a separating node set. One of the subgraphs is replaced with a simpler structured graph (replacement graph) in such a way that the interesting reliability criterion of the original stochastic network is retained. Special attention is given to the construction of suitable replacement graphs. The case of a 3-point separating node set is considered in more detail.
Highlights
Network reliability analysis arises in many important engineering areas, in particular communication networks, computer networks, monitoring and military systems as well as transportation and electrical power systems
It is imperative that effective tools are being developed for the reliability analysis of complex networks with a general topological structure
A stochastic network is an undirected graph with unreliable edges and absolutely reliable nodes
Summary
Network reliability analysis arises in many important engineering areas, in particular communication networks, computer networks, monitoring and military systems as well as transportation and electrical power systems. A stochastic network is an undirected graph with unreliable edges and absolutely reliable nodes. The terminology used throughout the paper refers to communication networks. If an edge is not available, no direct transmission of information between its end nodes is possible. The paper only deals with the connectedness probability of a stochastic network, i.e. with the probability that there is a path between any node pair of the network, which only consists of http://orion.journals.ac.za/. For the sake of convenience, the connectedness probability of a stochastic network is referred to as its reliability. Stochastic network under discussion l q G = (N, E) G underlying deterministic graph with node set N = 1, 2,.., n and edge. Set E any stochastic network with underlying deterministic graph G' connectedness probability (reliability) of G~ '
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