A method for maximizing the reliability coefficient of a communications network

The most common idea of network reliability in the literature is a numerical parameter calledoverall network reliability, which is the probability that the network will be in a successful state in which all nodes can mutually communicate. Most papers concentrate on the problem of calculating the overall network reliability which is known to be an NP hard problem. In the present paper, the question asked is how to find a method for determining a reliable subnetwork of a given network. Givenn terminals and one central computer, the problem is to construct a network that links each terminal to the central computer, subject to the following conditions: (1) each link must be economically feasible; (2) the minimum number of links should be used; and (3) the reliability coefficient should be maximized. We argue that the network satisfying condition (2) is a spanning arborescence of the network defined by condition (1). We define the idea of thereliability coefficient of a spanning arborescence of a network, which is the probability that a node at average distance from the root of the arborescence can communicate with the root. We show how this coefficient can be calculated exactly when there are no degree constraints on nodes of the spanning arborescence, or approximately when such degree constraints are present. Computational experience for networks consisting of up to 900 terminals is given.This report was prepared as part of the activities of the Management Science Research Group, Carnegie-Mellon University, under Contract No. N00014-82-K-0329 NR 047–048 with the U.S. Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.