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

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

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Article ID: iaor2014917
Volume: 79
Issue: 3
Start Page Number: 273
End Page Number: 291
Publication Date: Jun 2014
Journal: Mathematical Methods of Operations Research
Authors: ,
Keywords: queues: theory, communications, networks
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 equ1 identical servers and can accommodate up to K equ2 jobs (including c equ3 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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