IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v19y2011i2p233-299.html
   My bibliography  Save this article

Light tail asymptotics in multidimensional reflecting processes for queueing networks

Author

Listed:
  • Masakiyo Miyazawa

Abstract

No abstract is available for this item.

Suggested Citation

  • Masakiyo Miyazawa, 2011. "Light tail asymptotics in multidimensional reflecting processes for queueing networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 233-299, December.
    • Handle: RePEc:spr:topjnl:v:19:y:2011:i:2:p:233-299
    DOI: 10.1007/s11750-011-0179-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11750-011-0179-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11750-011-0179-7?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. Yiqiang Q. Zhao & Wei Li & W. John Braun, 2003. "Censoring, Factorizations, and Spectral Analysis for Transition Matrices with Block-Repeating Entries," Methodology and Computing in Applied Probability, Springer, vol. 5(1), pages 35-58, March.
    2. P. Lieshout & M. Mandjes, 2007. "Tandem Brownian queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 275-298, October.
    3. Anatolii A. Puhalskii & Alexander A. Vladimirov, 2007. "A Large Deviation Principle for Join the Shortest Queue," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 700-710, August.
    4. David Gamarnik, 2002. "On Deciding Stability of Constrained Homogeneous Random Walks and Queueing Systems," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 272-293, May.
    5. Jiashan Tang & Yiqiang Zhao, 2008. "Stationary tail asymptotics of a tandem queue with feedback," Annals of Operations Research, Springer, vol. 160(1), pages 173-189, April.
    6. Dupuis, Paul & Ramanan, Kavita, 2002. "A time-reversed representation for the tail probabilities of stationary reflected Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 253-287, April.
    7. Alsmeyer, Gerold, 1994. "On the Markov renewal theorem," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 37-56, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Toshihisa Ozawa, 2022. "Tail asymptotics in any direction of the stationary distribution in a two-dimensional discrete-time QBD process," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 227-267, October.
    2. Ioannis Dimitriou, 2021. "On partially homogeneous nearest-neighbour random walks in the quarter plane and their application in the analysis of two-dimensional queues with limited state-dependency," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 95-143, June.
    3. Yanting Chen & Richard J. Boucherie & Jasper Goseling, 2016. "Invariant measures and error bounds for random walks in the quarter-plane based on sums of geometric terms," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 21-48, October.
    4. Yanting Chen & Richard J. Boucherie & Jasper Goseling, 2020. "Necessary conditions for the compensation approach for a random walk in the quarter-plane," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 257-277, April.
    5. Yiqiang Q. Zhao, 2022. "The kernel method tail asymptotics analytic approach for stationary probabilities of two-dimensional queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 100(1), pages 95-131, February.
    6. Mihail Bazhba & Chang-Han Rhee & Bert Zwart, 2022. "Large deviations for stochastic fluid networks with Weibullian tails," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 25-52, October.
    7. Arnaud Devos & Joris Walraevens & Herwig Bruneel, 2024. "Analysis of A Two-queue Discrete-time Model with Random Alternating Service Under High Occupancy in One Queue," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-21, December.
    8. Kamil Demirberk Ünlü & Ali Devin Sezer, 2020. "Excessive backlog probabilities of two parallel queues," Annals of Operations Research, Springer, vol. 293(1), pages 141-174, October.
    9. Ioannis Dimitriou, 2022. "Stationary analysis of certain Markov-modulated reflected random walks in the quarter plane," Annals of Operations Research, Springer, vol. 310(2), pages 355-387, March.
    10. Toshihisa Ozawa & Masahiro Kobayashi, 2018. "Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 351-403, December.
    11. Toshihisa Ozawa, 2021. "Asymptotic properties of the occupation measure in a multidimensional skip-free Markov-modulated random walk," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 125-161, February.

    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. Ernst, Philip A. & Franceschi, Sandro & Huang, Dongzhou, 2021. "Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 634-670.
    2. Plinio S. Dester & Christine Fricker & Danielle Tibi, 2017. "Stationary analysis of the shortest queue problem," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 211-243, December.
    3. Rosario Delgado, 2010. "State space collapse and stability of queueing networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(3), pages 477-499, December.
    4. Alsmeyer, Gerold, 1996. "Superposed continuous renewal processes A Markov renewal approach," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 311-322, February.
    5. Biswas, Anup & Budhiraja, Amarjit, 2011. "Exit time and invariant measure asymptotics for small noise constrained diffusions," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 899-924.
    6. David Gamarnik, 2007. "On the Undecidability of Computing Stationary Distributions and Large Deviation Rates for Constrained Random Walks," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 257-265, May.
    7. 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.
    8. Basrak, Bojan & Conroy, Michael & Olvera-Cravioto, Mariana & Palmowski, Zbigniew, 2022. "Importance sampling for maxima on trees," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 139-179.
    9. Jiashan Tang & Yiqiang Zhao, 2008. "Stationary tail asymptotics of a tandem queue with feedback," Annals of Operations Research, Springer, vol. 160(1), pages 173-189, April.
    10. Krzysztof Dȩbicki, 2022. "Exact asymptotics of Gaussian-driven tandem queues," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 285-287, April.
    11. Ruth Sagron & Uri Yechiali, 2024. "Inter-Departure Time Correlations in PH / G /1 Queues," Mathematics, MDPI, vol. 12(9), pages 1-23, April.
    12. Gobet, Emmanuel & Menozzi, Stéphane, 2010. "Stopped diffusion processes: Boundary corrections and overshoot," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 130-162, February.
    13. Gobet, Emmanuel & Menozzi, Stéphane, 2004. "Exact approximation rate of killed hypoelliptic diffusions using the discrete Euler scheme," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 201-223, August.
    14. Paul Dupuis & Kevin Leder & Hui Wang, 2009. "Importance Sampling for Weighted-Serve-the-Longest-Queue," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 642-660, August.
    15. Hansen, Niels Richard & Jensen, Anders Tolver, 2005. "The extremal behaviour over regenerative cycles for Markov additive processes with heavy tails," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 579-591, April.
    16. Alsmeyer, Gerold & Hoefs, Volker, 2002. "Markov renewal theory for stationary (m+1)-block factors: convergence rate results," Stochastic Processes and their Applications, Elsevier, vol. 98(1), pages 77-112, March.
    17. Danielle Tibi, 2019. "Martingales and buffer overflow for the symmetric shortest queue model," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 153-190, October.
    18. Fuh, Cheng-Der, 2021. "Asymptotic behavior for Markovian iterated function systems," Stochastic Processes and their Applications, Elsevier, vol. 138(C), pages 186-211.
    19. Zbigniew Michna, 2018. "Ruin probabilities for two collaborating insurance companies," Papers 1804.06598, arXiv.org, revised Dec 2018.
    20. Masuyama, Hiroyuki, 2011. "Subexponential asymptotics of the stationary distributions of M/G/1-type Markov chains," European Journal of Operational Research, Elsevier, vol. 213(3), pages 509-516, September.

    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:topjnl:v:19:y:2011:i:2:p:233-299. 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.