High-reliability 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, and we consider both statistically independent and 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. 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 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.