Network reliability with arc failures and repairs

Arc repair probabilities are incorporated into network calculations for directed networks with independent arc failures. A discrete-time Markov chain with one absorbing state is constructed for the problem. The transition probability matrix is used to determine the probability of source-to-sink conductivity in a given time interval, the mean time to source-to-sink connectivity, the fraction of time a node is blocked, and the fraction of time the network is blocked (disconnected). Blockage probabilities aid in repair-crew allocation to the nodes of the network