Reliability estimation of stochastic flow networks using pre-ordered minimal cuts

Flow networks in which each component is associated with multiple capacities are known as Stochastic flow networks. These networks are prone to partial or complete failures and are often subjected to unavailability. To estimate two-terminal reliability for such stochastic flow networks several algorithms exists in literature. Most of these algorithms takes huge computational time to compute network reliability even for moderate sized networks. The known efficient cutset based stochastic flow network reliability estimation algorithm developed till date can be presented as follows (1) Maximal flows for demand d, of the network are generated using the minimal cuts and capacities of the components. (2) Removes the non-maximal flows to obtain the set of upper boundary flows for demand d. (3) Determines unreliability from the upper boundary flows from which reliability is calculated as 1-unreliability of the network. In this work, we present an algorithm that preorders the minimal cuts and calculates the network unreliability using the ordered minimal cuts. Our algorithm reduces the computational time compared to the existing algorithm. We provide an example to illustrate the proposed method. Matlab simulation is performed to compare the proposed method with the existing methods using the standard benchmark networks available in literature. Simulation results show that the proposed method takes lesser computation time and memory.