Reliability evaluation for overall-terminal multistate flow networks with bi-directed arcs

This article mainly studies the reliability evaluation of an overall-terminal multistate flow network whose arcs are all bi-directed in terms of MPs (minimal paths). The telephone-communication system (in which each node denoting a telephone station can either call or receive a phone) and computer-communication system are typical ones of such networks. Given the system demand (d;di,j∈B)(d;di,j∈B) where di,jdi,j is the required demand between the node pair (i, j) ∈ B with a specified set of node pairs B and d   the total demand requirement among all nodes, an algorithm is proposed first to find out all lower boundary points of (d;di,j∈B)(d;di,j∈B) (namely (d;di,j∈B)(d;di,j∈B)-MPs here) in terms of MPs. The system reliability can then be calculated in terms of the family of all (d;di,j∈B)(d;di,j∈B)-MPs. One example is illustrated to show how all its (d;di,j∈B)(d;di,j∈B)-MPs are generated and how the reliability nay be calculated.