  We study the reliability maximization problem in WDM networks with random
link failures. Reliability in these networks is defined as the probability that
the logical network is connected, and it is determined by the underlying
lightpath routing, network topologies and the link failure probability. By
introducing the notion of lexicographical ordering for lightpath routings, we
characterize precise optimization criteria for maximum reliability in the low
failure probability regime. Based on the optimization criteria, we develop
lightpath routing algorithms that maximize the reliability, and logical
topology augmentation algorithms for further improving reliability. We also
study the reliability maximization problem in the high failure probability
regime.
