IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v11y2009i2d10.1007_s11009-008-9081-7.html
   My bibliography  Save this article

Queuing Systems with Semi-Markov Flow in Average and Diffusion Approximation Schemes

Author

Listed:
  • V. S. Koroliuk

    (Ukrainian National Academy of Science)

  • V. V. Koroliuk

    (Ukrainian National Academy of Science)

  • N. Limnios

    (Université de Technologie de Compiègne)

Abstract

We study asymptotic average and diffusion approximation schemes for semi-Markov queuing systems by a random evolution approach and using compensating operator of the corresponding extended Markov renewal process. These results generalize Markov and renewal flow queuing systems.

Suggested Citation

  • V. S. Koroliuk & V. V. Koroliuk & N. Limnios, 2009. "Queuing Systems with Semi-Markov Flow in Average and Diffusion Approximation Schemes," Methodology and Computing in Applied Probability, Springer, vol. 11(2), pages 201-209, June.
    • Handle: RePEc:spr:metcap:v:11:y:2009:i:2:d:10.1007_s11009-008-9081-7
    DOI: 10.1007/s11009-008-9081-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-008-9081-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-008-9081-7?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. Ward Whitt, 2004. "A Diffusion Approximation for the G/GI/n/m Queue," Operations Research, INFORMS, vol. 52(6), pages 922-941, December.
    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. J. G. Dai & Tolga Tezcan, 2011. "State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 271-320, May.
    2. Ward Whitt, 2005. "Heavy-Traffic Limits for the G / H 2 */ n / m Queue," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 1-27, February.
    3. J B Atkinson, 2009. "Two new heuristics for the GI/G/n/0 queueing loss system with examples based on the two-phase Coxian distribution," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(6), pages 818-830, June.
    4. Gad Allon & Sarang Deo & Wuqin Lin, 2013. "The Impact of Size and Occupancy of Hospital on the Extent of Ambulance Diversion: Theory and Evidence," Operations Research, INFORMS, vol. 61(3), pages 544-562, June.
    5. Avishai Mandelbaum & Petar Momčilović, 2008. "Queues with Many Servers: The Virtual Waiting-Time Process in the QED Regime," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 561-586, August.
    6. Prahalad Venkateshan & Kamlesh Mathur, 2015. "A Heuristic for the Multisource Weber Problem with Service Level Constraints," Transportation Science, INFORMS, vol. 49(3), pages 472-483, August.
    7. Raj, G. & Roy, D. & de Koster, R. & Bansal, V., 2024. "Stochastic modeling of integrated order fulfillment processes with delivery time promise: Order picking, batching, and last-mile delivery," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1114-1128.
    8. Yunan Liu & Ward Whitt & Yao Yu, 2016. "Approximations for heavily loaded G/GI/n + GI queues," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(3), pages 187-217, April.
    9. Tolga Tezcan, 2008. "Optimal Control of Distributed Parallel Server Systems Under the Halfin and Whitt Regime," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 51-90, February.
    10. Narayanan C. Viswanath, 2022. "Transient study of Markov models with time-dependent transition rates," Operational Research, Springer, vol. 22(3), pages 2209-2243, July.
    11. Anatoly Nazarov & Alexander Moiseev & Svetlana Moiseeva, 2021. "Mathematical Model of Call Center in the Form of Multi-Server Queueing System," Mathematics, MDPI, vol. 9(22), pages 1-13, November.

    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:metcap:v:11:y:2009:i:2:d:10.1007_s11009-008-9081-7. 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.