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Stability Analysis and Simulation of N-class Retrial System with Constant Retrial Rates and Poisson Inputs

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 mu0i) 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.
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https://hal.inria.fr/hal-01092341
Contributor : Konstantin Avrachenkov <>
Submitted on : Monday, December 8, 2014 - 3:41:08 PM
Last modification on : Thursday, September 24, 2020 - 10:22:03 AM

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Konstantin Avrachenkov, Evsey Morozov, Ruslana Nekrasova, Bart Steyaert. Stability Analysis and Simulation of N-class Retrial System with Constant Retrial Rates and Poisson Inputs. Asia-Pacific Journal of Operational Research, World Scientific Publishing, 2014, 31 (02), pp.18. ⟨10.1142/S0217595914400028⟩. ⟨hal-01092341⟩

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