Design of reliable networks

The author considers a reliable network synthesis problem. It is assumed that in a computer network, denoted as G_n,e, the number of nodes n, the number of edges e, and the operational probability of each edge are known. The system reliability of the network is defined to be the probability that every pair of nodes can communicate with each other. The problem is to find a network G *_n,e that maximizes system reliability over the class of all networks having n nodes and e edges. The optimal networks are found for the classes of networks G_n,n-1, G_n,n and G_n,n+1, respectively. In addition, an upper bound of maximum reliability for networks with n-nodes and e-edges is derived in terms of node degrees. Computational results for the reliability upper bound are also presented. The results show that the proposed reliability upper bound is effective