Determination of minimal upper vectors for calculating flow network reliability

Abstract

When each edge in a planar network has two or multistate capacities depending on the degree of failure, the probability of successfully transmitting the required amount of information between two specified vertices are evaluated using the concept of minimal upper vectors. For the binary as well as multistate flow networks, the problem of finding the minimal upper vectors has not been sufficiently investigated. In this thesis, systematic procedures are developed to determine the minimal upper vectors and the efficiency of the proposed algorithm is evaluated for various type of networks.