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

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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$c$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>c</mi> </math> </EquationSource> </InlineEquation> identical servers and can accommodate up to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$K$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>K</mi> </math> </EquationSource> </InlineEquation> jobs (including <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$c$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>c</mi> </math> </EquationSource> </InlineEquation> 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