Survival reliabilities of double loop networks

A reliability model of double loop networks which assumes that each link independently has probability p to fail and that the network fails if and only if there exist two nodes u and v with every path from u and v containing a failed link is extended to the more difficult survival reliability model for both isolated and nonisolated cutsets. The survival reliability model assumes that every node independently has probability p to fail and that the network fails if and only if there exist two surviving nodes u and v with every path from u to v containing a failed node. It is shown that many results from the reliability model can be carried over to the survival reliability model, and that for even n, G(1, 1+n/2) is the most reliable double loop network in survival reliability. The reliability model is only extended to the nonisolated cases for a small number of cutsets.<>