A Modified Universal Generating Function Algorithm for the Acyclic Binary-State Network Reliability

Network reliability is an important part of planning, designing, and controlling networks. Now, the most general binary-state network (BSN) reliability evaluation methods are based on Minimal Paths (MPs), or Minimal Cuts (MCs). The universal generating function method (UGFM) is a novel, efficient scheme for determining network reliability. Because the current best-known UGFM can only search for all MPs, it needs to be coupled with another routine such as Sum-of-Disjoint-Product method to calculate the final flow network reliability in terms of obtained MPs. In this study, a straightforward, novel UGFM is presented for calculating the acyclic BSN (ABSN) reliability between the source node and the sink node (i.e. one-to-one reliability). The proposed method is the first UGFM for the ABSN reliability problem without searching for all MPs in advance, which can reduce computational complexity. The computational complexity of the proposed algorithm is analysed, and its efficiency is well illustrated by a numerical example.