A survey and introduction to network reliability theory

The author surveys some of the basic analysis and synthesis results in network reliability theory. The model considered is an undirected simple graph with independent probabilities that edges operate. The reliability is defined as the probability that the network has some path between each pair of nodes. The analysis problem is to calculate the reliability, given the graph and the probabilities. The author introduces a parameter known as the reliability domination of a graph and shows its role in calculating the reliability. A number of interesting synthesis problems concerning the reliability model are illustrated for the case in which the edge probabilities are all equal. Two specific synthesis problems are discussed in detail, giving the known results and the outstanding questions. The author shows how the topology of the optimal network might change as a function of the edge probabilities