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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Article dans une revue
Asia-Pacific Journal of Operational Research, World Scientific Publishing, 2014, 31 (02), pp.18. 〈http://www.worldscientific.com/doi/abs/10.1142/S0217595914400028〉. 〈10.1142/S0217595914400028〉
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https://hal.inria.fr/hal-01092341
Contributeur : Konstantin Avrachenkov <>
Soumis le : lundi 8 décembre 2014 - 15:41:08
Dernière modification le : samedi 27 janvier 2018 - 01:31:41

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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. 〈http://www.worldscientific.com/doi/abs/10.1142/S0217595914400028〉. 〈10.1142/S0217595914400028〉. 〈hal-01092341〉

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