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

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  • B. Houdt
  • J. Velthoven
  • C. Blondia

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

Suggested Citation

  • B. Houdt & J. Velthoven & C. Blondia, 2008. "QBD Markov chains on binomial-like trees and its application to multilevel feedback queues," Annals of Operations Research, Springer, vol. 160(1), pages 3-18, April.
    • Handle: RePEc:spr:annopr:v:160:y:2008:i:1:p:3-18:10.1007/s10479-007-0288-8
    DOI: 10.1007/s10479-007-0288-8
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    References listed on IDEAS

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    1. Lothar Breuer, 2002. "An EM Algorithm for Batch Markovian Arrival Processes and its Comparison to a Simpler Estimation Procedure," Annals of Operations Research, Springer, vol. 112(1), pages 123-138, April.
    2. Ryden, Tobias, 1996. "An EM algorithm for estimation in Markov-modulated Poisson processes," Computational Statistics & Data Analysis, Elsevier, vol. 21(4), pages 431-447, April.
    3. L. E. Schrage, 1967. "The Queue M/G/1 With Feedback to Lower Priority Queues," Management Science, INFORMS, vol. 13(7), pages 466-474, March.
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