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Upper bounds on the rate of convergence for constant retrial rate queueing model with two servers

Author

Listed:
  • Yacov Satin

    (Vologda State University)

  • Evsey Morozov

    (IAMR, KarRC RAS and Petrozavodsk State University)

  • Ruslana Nekrasova

    (IAMR, KarRC RAS and Petrozavodsk State University)

  • Alexander Zeifman

    (Vologda State University
    IPI FRC CSC RAS; VolSC RAS)

  • Ksenia Kiseleva

    (Vologda State University)

  • Anna Sinitcina

    (Vologda State University)

  • Alexander Sipin

    (Vologda State University)

  • Galina Shilova

    (Vologda State University)

  • Irina Gudkova

    (Peoples’ Friendship University of Russia (RUDN University), IPI FRC CSC RAS)

Abstract

The paper deals with a Markovian retrial queueing system with a constant retrial rate and two servers. We present the detailed description of the model as well as establish the sufficient conditions for null ergodicity and strong ergodicity of the corresponding process and obtain the upper bounds on the rate of convergence for both situations.

Suggested Citation

  • Yacov Satin & Evsey Morozov & Ruslana Nekrasova & Alexander Zeifman & Ksenia Kiseleva & Anna Sinitcina & Alexander Sipin & Galina Shilova & Irina Gudkova, 2018. "Upper bounds on the rate of convergence for constant retrial rate queueing model with two servers," Statistical Papers, Springer, vol. 59(4), pages 1271-1282, December.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:4:d:10.1007_s00362-018-1014-0
    DOI: 10.1007/s00362-018-1014-0
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    References listed on IDEAS

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    1. K. Avrachenkov & E. Morozov & R. Nekrasova & B. Steyaert, 2014. "Stability Analysis And Simulation Of N-Class Retrial System With Constant Retrial Rates And Poisson Inputs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-18.
    2. K. Avrachenkov & E. Morozov & B. Steyaert, 2016. "Sufficient stability conditions for multi-class constant retrial rate systems," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 149-171, February.
    3. Artalejo, J. R. & Gomez-Corral, A. & Neuts, M. F., 2001. "Analysis of multiserver queues with constant retrial rate," European Journal of Operational Research, Elsevier, vol. 135(3), pages 569-581, December.
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