A simple algorithm for reliability evaluation of stochastic-flow networks under distance limitation

. Various real-world systems, including computer and communication networks, transportation, and distribution systems, can be modeled as a stochastic/multistate flow network (MFN). Reliability indices are of great importance in evaluating the quality of service in MFNs. One such index is the two-terminal reliability (2TR), which represents the probability that the maximum flow in the network is not less than a certain demand level. Researchers have investigated the 2TR problem for MFNs, considering constraints such as budget, time, or distance limitations. Nevertheless, distance constraints have received relatively less attention in the literature, despite their significant role in optimizing the efficiency of some transmission networks. Hence, this study focuses on the 2TR problem with a distance constraint in an MFN and proposes a simple yet efficient algorithm to solve it. We demonstrate the effectiveness of our algorithm through a benchmark example.