Skip to Main content Skip to Navigation
Journal articles

Sufficient Stability Conditions for Multi-class Constant Retrial Rate Systems

Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [30 references]  Display  Hide  Download

https://hal.inria.fr/hal-01402744
Contributor : Konstantin Avrachenkov <>
Submitted on : Friday, November 25, 2016 - 10:11:22 AM
Last modification on : Thursday, September 24, 2020 - 10:22:03 AM
Long-term archiving on: : Monday, March 20, 2017 - 8:51:18 PM

File

StabilityConditionsRevision2.p...
Files produced by the author(s)

Identifiers

Collections

Citation

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

Share

Metrics

Record views

230

Files downloads

374