Title
QBD Markov chains on binomial-like trees and its application to multilevel feedback queues QBD Markov chains on binomial-like trees and its application to multilevel feedback queues
Author
Faculty/Department
Faculty of Sciences. Physics
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Basel ,
Subject
Mathematics
Source (journal)
Annals of operations research. - Basel
Volume/pages
160(2008) :1 , p. 3-18
ISSN
0254-5330
ISI
000253211100002
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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¡Ý0}, 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.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/aa8161/4686.pdf
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