An Efficient Direct Algorithm for Computing the Reliability of a Multistate Flow Network Subject to Flow Loss

Multi-state flow network (MFN) reliability problem has attracted considerable interest in the past decades. MFN reliability subject to flow loss, defined as the probability that the demand at the destination can be met when flow undergoes loss during transmission, is an extension of the conventional MFN reliability problem. The current studies on MFN reliability subject to flow loss have been carried out under the assumption that flow and demand are integers, which means the existing algorithms are unavailable to the network with non-integer demand. Moreover, the existing algorithms would yield underestimated reliability values even if the demand is an integer, which limits their practical applications. This article goes one step forward to address the general case where flow and demand can be integers or non-integers, and presents an efficient direct algorithm to accurately compute MFN reliability subject to flow loss. The reported algorithm is not only available to more complex scenarios with non-integer flow and demand, but also indicates a performance advantage. Furthermore, a case study is analyzed to highlight the practical relevance of the algorithm.