QBD Markov chains on binomial-like trees and its application to multilevel feedback queues

B. Houdt (), J. Velthoven and C. Blondia

Annals of Operations Research, 2008, vol. 160, issue 1, 3-18

Abstract: A matrix analytic paradigm, termed Quasi-Birth-Death Markov chains on binomial-like trees, is introduced and a quadratically converging algorithm to assess its steady state is presented. In a bivariate Markov chain {(X t ,N t ),t≥0}, the values of the variable X t are nodes of a binomial-like tree of order d, where the ith child has i children of its own. We demonstrate that it suffices to solve d quadratic matrix equations to yield the steady state vector, the form of which is matrix geometric. We apply this framework to analyze the multilevel feedback scheduling discipline, which forms an essential part in contemporary operating systems. Copyright Springer Science+Business Media, LLC 2008

Keywords: QBD Markov chains; Tree-like processes; Matrix-analytic methods; Multilevel feedback queues (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10479-007-0288-8

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