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PERMUTATIONAL METHODS FOR PERFORMANCE ANALYSIS OF STOCHASTIC FLOW NETWORKS

Published online by Cambridge University Press:  19 November 2013

Ilya Gertsbakh ,
Reuven Rubinstein ,
Yoseph Shpungin  and
Radislav Vaisman
Ilya Gertsbakh
Affiliation:
Department of Mathematics, Ben Gurion University, Beer-Sheva 84105, Israel. E-mail: elyager@bezeqint.net
Reuven Rubinstein
Affiliation:
Department of Mathematics, Ben Gurion University, Beer-Sheva 84105, Israel. E-mail: elyager@bezeqint.net
Yoseph Shpungin
Affiliation:
Department of Software Engineering, Shamoon College of Engineering, Beer-Sheva 84105, Israel. E-mail: yosefs@sce.ac.il
Radislav Vaisman
Affiliation:
Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology, Haifa, Israel. E-mail: slvaisman@gmail.com
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Abstract

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 threshold. 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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 1 , January 2014 , pp. 21 - 38
Copyright
Copyright © Cambridge University Press 2013 

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