Computing the Reliability of a Multistate Flow Network with Flow Loss Effect

Multistate flow networks (MFNs) and their reliability problem have been studied extensively. However, most of the research on MFN reliability assumes that flow into and out of any arc is equal. In practical applications, flow may experience loss during transmission such that flow into and out of an arc may not be equal. Thus, this article concentrates on the reliability of an MFN with flow loss effect, defined as the probability that the sink node can receive a flow of at least
d
units when the flow experiences loss without replenishment during transmission. Using minimal paths, a simple method is put forth to compute this reliability index, and the solution procedure is illustrated via a simple network example. Finally, computational experiments are provided to investigate the impact of flow loss on network reliability.