摘要
Multistate flow networks with multiple sources are essential in systems that integrate data from diverse origins, enabling comprehensive analysis and coordinated operation of complex infrastructure. Assessing the reliability of such networks is vital for ensuring data consistency and operational accuracy. Although the reliability of multistate flow networks has been extensively studied in the two-terminal case, the multi-source setting has received significantly less attention. Indirect methods typically start by identifying all relevant state vectors and computing their probabilities using established techniques such as the inclusion-exclusion principle. Many of these approaches convert multi-source networks into equivalent single-source models by introducing artificial nodes and arcs, which can increase network complexity. In this work, we introduce a new reliability index and propose an algorithm that determines all relevant state vectors directly on the original multi-source networks, considering transmission costs. We prove the algorithm's correctness, analyze its computational complexity, and validate its performance through extensive experiments on benchmark and synthetic instances. The results show substantial improvements, with our method achieving speedups exceeding 2800 times compared to existing techniques. © 2025