PERMUTATIONAL METHODS FOR PERFORMANCE ANALYSIS OF STOCHASTIC FLOW NETWORKS. Issue 1 (19th November 2013)

• Record Type: Journal Article
• Authors: Gertsbakh, Ilya; Rubinstein, Reuven; Shpungin, Yoseph; Vaisman, Radislav
• Is Part Of: Probability in the engineering and informational sciences. Volume 28:Issue 1(2014)
• Page Start: 21
• Page End: 38
• Publication Date: 2013-11-19
• Subjects: Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S0269964813000302
• Languages: English
• ISSNs: 0269-9648

Abstract

<abstract abstract-type="normal"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>In this paper we show how the permutation Monte Carlo method, originally developed for reliability networks, can be successfully adapted for stochastic flow networks, and in particular for estimation of the probability that the maximal flow in such a network is above some fixed level, called the <italic>threshold</italic>. A stochastic flow network is defined as one, where the edges are subject to random failures. A failed edge is assumed to be erased (broken) and, thus, not able to deliver any flow. We consider two models; one where the edges fail with the same failure probability and another where they fail with different failure probabilities. For each model we construct a different algorithm for estimation of the desired probability; in the former case it is based on the well known notion of the D-spectrum and in the later one—on the permutational Monte Carlo. We discuss the convergence properties of our estimators and present supportive numerical results.</p> </abstract>