Ring network reliability-the probability that all operative nodes can communicate

The authors consider the reliability of fail-soft ring networks using as a measure the probability that all operative nodes can communicate P[C]. Although computing P[C] is in general an NP-hard problem, it is shown that, for ring networks, closed-form expressions can be derived in terms of the failure probabilities of nodes, links, and switches (the configuration components used in attempts to achieve fail-soft operation of the rings). The authors derive closed-form expressions of P[C] for five simplex rings: (1) the basic unidirectional ring, (2) rings with nodal bypass switches, (3) rings with both bypass switches and a standby ring, (4) rings with self-heal switches, and (5) star-shaped rings. The expressions for these five rings are evaluated under varying failure probability assumptions, and reliability comparisons are made