Efficient algorithm and discrete‐event solver for stochastic flow networks with converging flows

An efficient algorithm is proposed for determining the quantity of transferred flow and the losses from failures of repairable stochastic networks with converging flows. We show that the computational speed related to determining the variation of the flow through a stochastic flow network can be improved enormously if the topology of the network is exploited directly. The proposed algorithm is based on a new result related to maximising the flow in networks with converging flows. An efficient discrete‐event solver for repairable networks with converging flows has also been developed, based on the proposed algorithm. The solver handles repairable networks with multiple sources of production flow, multi‐commodity flows, overlapping failures, multiple failure modes, redundant components and redundant branches of components. The solver is capable of tracking the cumulative distribution of the potential losses from failures associated with the whole network and with each component in the network.