Communication networks are becoming increasingly dominant in business, industrial and governmental applications. There has been considerable recent interest in the performance of communication networks, with connectivity, speed, cost and security issues carefully considered, individually and in tandem. Various forms of approximate optimality have been examined. In this paper, we address fundamental questions about network topologies. We examine the utility of analytical tools such as “dominations” and “signatures” in assessing the reliability of a given network and in comparing two competing network designs. The traditional approach to treating the question of whether there exists a uniformly optimal network design of a given size (i.e., with v vertices and n edges for fixed v and n) is examined, and certain weaknesses in the approach are noted. An alternative approach is proposed and is shown to provide rather striking results in a context in which the traditional approach had been shown to fail. A scenario which treats the tension between performance and cost is also considered, and the optimality of a network under a “performance per unit cost” criterion is studied. An agenda for further research in this area is outlined.

Keywords: Network reliability; Network signatures; Stochastic order relations; Optimality under various criteria

Biography: Francisco J. Samaniego is a Distinguished Professor of Statistics at the University of California, Davis. His research interests include Mathematical Statistics, Reliability and Survival Analysis, Sampling Techniques, Bayesian Inference and applications of Statistics in Education, Engineering and Public Health. He is a Fellow of the American Statistical Association, the Institute of Mathematical Statistics and the Royal Statistical Society and is a member of the International Statistical Institute. He is the author of two recent monographs, “System Signatures and their Applications in Engineering Reliability” (2007) and “System Signatures and their Applications in Engineering Reliability” (2010), both published by Springer.