Bounding algorithms for two-terminal network reliability

Abstract

Abstract Determining the exact reliability of a complex network involves extremely large amount of computation. Consequently, it is appropriate to discuss method for approximating network reliability. This paper develops methods for obtaining upper and lower bounds for two-terminal network reliability. Construction of different layers for a network is used to develop an algorithm to compute an upper bound for the reliability of a network. The nodes of this network are completely reliable and arcs fail statistically independently with known probabilities. A simple approach, to obtain a lower bound for the reliability of the network is also presented. Examples illustrate the use of the algorithms and show that the proposed bounds fare better than the well-known Esary and Proschan bounds.