Computing Diameter Constrained Reliability of a Network with Junction Points

We consider a network with unreliable communication channels and perfectly reliable nodes. The diameter constrained reliability for such a network is defined as the probability that between each pair of nodes, there exists a path consisting of operational edges whose number is upper bounded by a given integer. The problem of computing this characteristic is NP-hard, just like the problem of computing the probability of a network's connectivity. We propose a formula that lets one use junction points to compute the reliability of a two-pole system with diameter constraints, which makes the computations faster.