IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i3p1713-1734.html
   My bibliography  Save this article

The correlation function of a queue with Lévy and Markov additive input

Author

Listed:
  • Berkelmans, Wouter
  • Cichocka, Agata
  • Mandjes, Michel

Abstract

Let (Qt)t∈R be a stationary workload process, and r(t) the correlation coefficient of Q0 and Qt. In a series of previous papers (i) the transform of r(⋅) has been derived for the case that the driving process is spectrally-positive (sp) or spectrally-negative (sn) Lévy, (ii) it has been shown that for sp-Lévy and sn-Lévy input r(⋅) is positive, decreasing, and convex, (iii) in case the driving Lévy process is light-tailed (a condition that is automatically fulfilled in the sn case), the decay of the decay rate agrees with that of the tail of the busy period distribution.

Suggested Citation

  • Berkelmans, Wouter & Cichocka, Agata & Mandjes, Michel, 2020. "The correlation function of a queue with Lévy and Markov additive input," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1713-1734.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:3:p:1713-1734
    DOI: 10.1016/j.spa.2019.05.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918307488
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2019.05.015?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. A. B. Dieker & M. Mandjes, 2011. "Extremes of Markov-additive Processes with One-sided Jumps, with Queueing Applications," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 221-267, June.
    2. Ivanovs, Jevgenijs, 2017. "Splitting and time reversal for Markov additive processes," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2699-2724.
    3. Rajeeva L. Karandikar & Vidyadhar G. Kulkarni, 1995. "Second-Order Fluid Flow Models: Reflected Brownian Motion in a Random Environment," Operations Research, INFORMS, vol. 43(1), pages 77-88, February.
    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. Nigel Bean & Angus Lewis & Giang T. Nguyen & Małgorzata M. O’Reilly & Vikram Sunkara, 2022. "A Discontinuous Galerkin Method for Approximating the Stationary Distribution of Stochastic Fluid-Fluid Processes," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2823-2864, December.
    2. Gábor Horváth & Miklós Telek, 2017. "Matrix-analytic solution of infinite, finite and level-dependent second-order fluid models," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 325-343, December.
    3. Bean, Nigel G. & Nguyen, Giang T. & Nielsen, Bo F. & Peralta, Oscar, 2022. "RAP-modulated fluid processes: First passages and the stationary distribution," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 308-340.
    4. Przemysław Klusik & Zbigniew Palmowski, 2014. "A Note on Wiener–Hopf Factorization for Markov Additive Processes," Journal of Theoretical Probability, Springer, vol. 27(1), pages 202-219, March.
    5. Nicole Bäuerle, 1998. "The advantage of small machines in a stochastic fluid production process," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(1), pages 83-97, February.
    6. Lyu, Hanbaek & Sivakoff, David, 2019. "Persistence of sums of correlated increments and clustering in cellular automata," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1132-1152.
    7. Horton, Graham & Kulkarni, Vidyadhar G. & Nicol, David M. & Trivedi, Kishor S., 1998. "Fluid stochastic Petri nets: Theory, applications, and solution techniques," European Journal of Operational Research, Elsevier, vol. 105(1), pages 184-201, February.
    8. Ivanovs, Jevgenijs & Boxma, Onno & Mandjes, Michel, 2010. "Singularities of the matrix exponent of a Markov additive process with one-sided jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1776-1794, August.
    9. Søren Asmussen & Patrick J. Laub & Hailiang Yang, 2019. "Phase-Type Models in Life Insurance: Fitting and Valuation of Equity-Linked Benefits," Risks, MDPI, vol. 7(1), pages 1-22, February.
    10. Ivanovs, Jevgenijs, 2017. "Splitting and time reversal for Markov additive processes," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2699-2724.
    11. Guy Latouche & Matthieu Simon, 2018. "Markov-Modulated Brownian Motion with Temporary Change of Regime at Level Zero," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1199-1222, December.
    12. M. Gribaudo & D. Manini & B. Sericola & M. Telek, 2008. "Second order fluid models with general boundary behaviour," Annals of Operations Research, Springer, vol. 160(1), pages 69-82, April.
    13. Nail Akar & Omer Gursoy & Gabor Horvath & Miklos Telek, 2021. "Transient and First Passage Time Distributions of First- and Second-order Multi-regime Markov Fluid Queues via ME-fication," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1257-1283, December.
    14. Marco Gribaudo & Illés Horváth & Daniele Manini & Miklós Telek, 2020. "Modelling large timescale and small timescale service variability," Annals of Operations Research, Springer, vol. 293(1), pages 123-140, October.

    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:eee:spapps:v:130:y:2020:i:3:p:1713-1734. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.