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 \(c\) identical servers and can accommodate up to \(K\) jobs (including \(c\) 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.
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Acknowledgments
The authors would like to thank sincerely anonymous referees for very useful comments and suggestions. We would like also to acknowledge the financial support provided by EGIDE ECO-NET grant no.18933SL and the Program of Strategy development of Petrozavodsk State University in the framework of the research activity.
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Avrachenkov, K., Morozov, E. Stability analysis of GI/GI/c/K retrial queue with constant retrial rate. Math Meth Oper Res 79, 273–291 (2014). https://doi.org/10.1007/s00186-014-0463-z
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DOI: https://doi.org/10.1007/s00186-014-0463-z