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Stability analysis of GI/GI/c/K retrial queue with constant retrial rate

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  • Konstantin Avrachenkov
  • Evsey Morozov

Abstract

We consider a finite buffer capacity GI/GI/c/K-type retrial queueing system with constant retrial rate. The system consists of a primary queue and an orbit queue. The primary queue has $$c$$ c identical servers and can accommodate up to $$K$$ K jobs (including $$c$$ c jobs under service). If a newly arriving job finds the primary queue to be full, it joins the orbit queue. The original primary jobs arrive to the system according to a renewal process. The jobs have i.i.d. service times. The head of line job in the orbit queue retries to enter the primary queue after an exponentially distributed time independent of the length of the orbit queue. Telephone exchange systems, medium access protocols, optical networks with near-zero buffering and TCP short-file transfers are some telecommunication applications of the proposed queueing system. The model is also applicable in logistics. We establish sufficient stability conditions for this system. In addition to the known cases, the proposed model covers a number of new particular cases with the closed-form stability conditions. The stability conditions that we obtained have clear probabilistic interpretation. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Konstantin Avrachenkov & Evsey Morozov, 2014. "Stability analysis of GI/GI/c/K retrial queue with constant retrial rate," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(3), pages 273-291, June.
    • Handle: RePEc:spr:mathme:v:79:y:2014:i:3:p:273-291
    DOI: 10.1007/s00186-014-0463-z
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    5. Efrosinin, Dmitry & Winkler, Anastasia, 2011. "Queueing system with a constant retrial rate, non-reliable server and threshold-based recovery," European Journal of Operational Research, Elsevier, vol. 210(3), pages 594-605, May.
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    Cited by:

    1. Tuan Phung-Duc & Wouter Rogiest & Yutaka Takahashi & Herwig Bruneel, 2016. "Retrial queues with balanced call blending: analysis of single-server and multiserver model," Annals of Operations Research, Springer, vol. 239(2), pages 429-449, April.
    2. 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.

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