GE-MBAT: An efficient algorithm for reliability assessment in multi-state flow networks

Multi-state flow networks are increasingly critical across diverse applications such as network resilience, Internet of Things (IoT), and facility networks. These networks provide a more realistic representation of operational environments compared to binary-state models. Ensuring reliable network performance is crucial for the continuous and effective operation of these multi-state flow networks, especially as they grow in complexity. However, assessing reliability presents significant challenges due to the computational complexity involved. This paper introduces the "Greater than or Equal to" Multi-State Binary-Addition-Tree (GE-MBAT), designed to identify all vectors X of which (the maximum flow in the subgraph resulting from X) ≥ d rather than generating all possible multi-state vectors to enhance the efficiency and accuracy of reliability calculations in multi-state networks. The GE-MBAT reduces the generation of infeasible vectors, outperforming traditional methods in computational efficiency. This research contributes to the development of more reliable and robust network systems, with significant implications for critical infrastructure and advanced network technologies.