IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v160y2008i1p3-1810.1007-s10479-007-0288-8.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-007-0288-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-007-0288-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dimitri frosinin & L. Breuer, 2006. "Threshold policies for controlled retrial queues with heterogeneous servers," Annals of Operations Research, Springer, vol. 141(1), pages 139-162, January.
    2. Andrzej Chydzinski & Pawel Mrozowski, 2016. "Queues with Dropping Functions and General Arrival Processes," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-23, March.
    3. Shaochuan Lu, 2012. "Markov modulated Poisson process associated with state-dependent marks and its applications to the deep earthquakes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 87-106, February.
    4. Casale, Giuliano & Sansottera, Andrea & Cremonesi, Paolo, 2016. "Compact Markov-modulated models for multiclass trace fitting," European Journal of Operational Research, Elsevier, vol. 255(3), pages 822-833.
    5. Peter Buchholz & Jan Kriege, 2017. "Fitting correlated arrival and service times and related queueing performance," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 337-359, April.
    6. Jane M. Lange & Rebecca A. Hubbard & Lurdes Y. T. Inoue & Vladimir N. Minin, 2015. "A joint model for multistate disease processes and random informative observation times, with applications to electronic medical records data," Biometrics, The International Biometric Society, vol. 71(1), pages 90-101, March.
    7. Nima Manafzadeh Dizbin & Barış Tan, 2019. "Modelling and analysis of the impact of correlated inter-event data on production control using Markovian arrival processes," Flexible Services and Manufacturing Journal, Springer, vol. 31(4), pages 1042-1076, December.
    8. Hautphenne, Sophie & Fackrell, Mark, 2014. "An EM algorithm for the model fitting of Markovian binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 19-34.
    9. Yera, Yoel G. & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2019. "Fitting procedure for the two-state Batch Markov modulated Poisson process," European Journal of Operational Research, Elsevier, vol. 279(1), pages 79-92.
    10. Pawel Mrozowski & Andrzej Chydzinski, 2018. "Queues with Dropping Functions and Autocorrelated Arrivals," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 97-115, March.
    11. Lin, Lei & Wang, Qian & Sadek, Adel W., 2014. "Border crossing delay prediction using transient multi-server queueing models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 64(C), pages 65-91.
    12. Liu, Baoliang & Cui, Lirong & Wen, Yanqing & Shen, Jingyuan, 2015. "A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 1-8.
    13. Mark, Brian L. & Ephraim, Yariv, 2013. "An EM algorithm for continuous-time bivariate Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 504-517.
    14. Ramírez-Cobo, Pepa & Carrizosa, Emilio & Lillo, Rosa E., 2021. "Analysis of an aggregate loss model in a Markov renewal regime," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    15. Jonas Hallgren & Timo Koski, 2016. "Testing for Causality in Continuous Time Bayesian Network Models of High-Frequency Data," Papers 1601.06651, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:160:y:2008:i:1:p:3-18:10.1007/s10479-007-0288-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.