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Stability Analysis And Simulation Of N-Class Retrial System With Constant Retrial Rates And Poisson Inputs

Author

Listed:
  • K. AVRACHENKOV

    (Inria Sophia Antipolis, 2004 Route des Lucioles Sophia Antipolis, 06902, France)

  • E. MOROZOV

    (Institute of Applied Mathematical Research, Karelian Research Centre RAS, and Petrozavodsk State University, Russia)

  • R. NEKRASOVA

    (Institute of Applied Mathematical Research, Karelian Research Centre RAS, and Petrozavodsk State University, Russia)

  • B. STEYAERT

    (SMACS Research Group, Ghent University, St-Pietersnieuwstraat 41, B-9000 Gent, Belgium)

Abstract

In this paper, we study a new retrial queueing system with N classes of customers, where a class-i blocked customer joins orbit i. Orbit i works like a single-server queueing system with (exponential) constant retrial time (with rate $\mu_{0}^{(i)}$) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance wireless multi-access systems, and transmission control protocols. First, we present a review of some corresponding recent results related to a single-orbit retrial system. Then, using a regenerative approach, we deduce a set of necessary stability conditions for such a system. We will show that these conditions have a very clear probabilistic interpretation. We also performed a number of simulations to show that the obtained conditions delimit the stability domain with a remarkable accuracy, being in fact the (necessary and sufficient) stability criteria, at the very least for the 2-orbit M/M/1/1-type and M/Pareto/1/1-type retrial systems that we focus on.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:apjorx:v:31:y:2014:i:02:n:s0217595914400028
    DOI: 10.1142/S0217595914400028
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    Citations

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    Cited by:

    1. 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.
    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. Bara Kim & Jeongsim Kim, 2023. "Proof of the conjecture on the stability of a multi-class retrial queue with constant retrial rates," Queueing Systems: Theory and Applications, Springer, vol. 104(3), pages 175-185, August.
    4. Konstantin Avrachenkov, 2022. "Stability and partial instability of multi-class retrial queues," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 177-179, April.
    5. Dmitry Efrosinin & Natalia Stepanova & Janos Sztrik, 2023. "Robustness of the cμ -Rule for an Unreliable Single-Server Two-Class Queueing System with Constant Retrial Rates," Mathematics, MDPI, vol. 11(18), pages 1-14, September.

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