SAT reliability evaluation of directed networks using disjointing technique

A method to generate disjoint spanning trees and hence to compute source to all terminal (SAT) reliability of acyclic directed networks is proposed in this paper. SAT reliability of a directed network is defined as the probability that there exists a minimal spanning tree from source node to all terminal nodes of the network. The method initiates with a specific directed spanning tree and produces all the disjoint spanning trees by exploiting the knowledge of the specific directed spanning tree. In literature various methods exist to determine SAT reliability of undirected networks with two step approach and most of the methods are arduous and lengthy so making these inefficient. The proposed method generates all the disjoint directed spanning trees in a simple and straightforward manner. The method is efficient as it involves minimum number of terms in reliability expression. Also, no duplicate spanning trees are formed during the process of spanning tree generation. The method is illustrated with the help of examples and its efficacy and simplicity has been demonstrated by comparing it with existing methods.