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Article Dans Une Revue Queueing Systems Année : 2016

Sufficient Stability Conditions for Multi-class Constant Retrial Rate Systems

Résumé

We study multi-class retrial queueing systems with Poisson inputs, general service times, and an arbitrary numbers of servers and waiting places. A class-i blocked customer joins orbit i and waits in the orbit for retrial. Orbit i works like a single-server ·/M/1 queueing system with exponential retrial time regardless of the orbit size. Such retrial systems are referred to as retrial systems with constant retrial rate. Our model is motivated by several telecommunication applications, such as wireless multi-access systems, optical networks and transmission control protocols, but represents independent theoretical interest as well. Using a regenerative approach, we provide sufficient stability conditions which have a clear probabilistic interpretation. We show that the provided sufficient conditions are in fact also necessary, in the case of a single-server system without waiting space and in the case of symmetric classes. We also discuss a very interesting case, when one orbit is unstable, whereas the rest of the system is stable.
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Dates et versions

hal-01402744 , version 1 (25-11-2016)

Identifiants

Citer

Konstantin Avrachenkov, E. Morozov, B. Steyaert. Sufficient Stability Conditions for Multi-class Constant Retrial Rate Systems. Queueing Systems, 2016, 82 (1-2), pp.149 - 171. ⟨10.1007/s11134-015-9463-9⟩. ⟨hal-01402744⟩

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