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Evaluating Reliability of Stochastic Flow Networks

Published online by Cambridge University Press:  27 July 2009

George S. Fishman  and
Tien-Yi Danny Shaw
George S. Fishman
Affiliation:
Department of Operations ResearchUniversity of North Carolina Chapel Hill, North Carolina 27599
Tien-Yi Danny Shaw
Affiliation:
Department of Operations ResearchUniversity of North Carolina Chapel Hill, North Carolina 27599
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Abstract

This paper describes a highly efficient Monte Carlo sampling plan for evaluating the probability that the flow value in a stochastic flow network is greater than or equal to a prespecified level d. A stochastic flow network can characterize communication, transportation, and water or oil distribution systems. The paper first derives lower and upper bounds on the probability of interest and then describes how one can concentrate sampling in a specialized region of the arc capacity state space to increase the statistical efficiency of the resulting estimate. The paper also gives expressions for worst-case sample sizes needed to meet specified bounds on variances and coefficients of variation and illustrates the proposed sampling plan with an example.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 4 , October 1989 , pp. 493 - 509
Copyright
Copyright © Cambridge University Press 1989

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