Bounds on expected performance of networks with links subject to failure

Upper and lower bounds on the expected maximum flows and benefits in capacitated networks with links subject to random failure are presented. Such bounds are of interest both because of the high or prohibitive cost of computing the exact expected values, and because the exact values will depend on the extent to which management avails itself of the opportunities for rerouting of flows in response to link failures. Algorithms for computing these bounds are discussed. These algorithms are sufficiently efficient to be applied to large networks having numerous possible failure states. An application to water‐network seismic risk analysis is described.