High-reliability topological architectures for networks under stress

In this paper, we consider the design of a physical network topology that meets a high level of reliability using unreliable network elements. We are motivated by the use of networks and, in particular, all-optical networks, for high-reliability applications which involve unusual and catastrophic stresses. Our network model is one in which nodes are invulnerable and links are subject to failure - a good approximation for optical networks with passive nodes and vulnerable fiber under stress of disconnection - and we focus on statistically independent link failures with initial steps taken toward generalization to dependent link failures. Our reliability metrics are the all-terminal connectedness measure and the less commonly considered two-terminal connectedness measure. We compare in the low and high stress regimes, via analytical approximations and simulations, common commercial architectures designed for all-terminal reliability when links are very reliable with alternative architectures which are mindful of both of our reliability metrics and regimes of stress. We derive new results especially for one of these alternative architectures, Harary graphs, which have been shown to possess attractive reliability properties. Furthermore, we show that for independent link failures network design should be optimized with respect to reliability under high stress, as reliability under low stress is less sensitive to graph structure; and that under high stress, very high node degrees and small network diameters are required to achieve moderate reliability performance. Finally, in our discussion of correlated failure models, we show the danger in relying on an independent failure model and the need for the network architect to minimize component failure dependencies.