Proof of the conjecture on the stability of a multiserver retrial queue

Bara Kim; Jeongsim Kim

doi:10.1016/j.orl.2015.02.007

Proof of the conjecture on the stability of a multiserver retrial queue

Bara Kim, Jeongsim Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper we solve the conjecture made by Avram, Matei and Zhao (2014), on stability condition of an M/M/s retrial queue with Bernoulli acceptance, abandonment and feedback. The Markov process describing this queueing system is positive recurrent if ^ρ∞<1 and transient if ^ρ∞>1, where ^ρ∞ is the traffic load under the saturation condition of the orbit. We also investigate the critical case when ^ρ∞=1 to see if it can be either stable or unstable.

Original language	English
Pages (from-to)	236-240
Number of pages	5
Journal	Operations Research Letters
Volume	43
Issue number	3
DOIs	https://doi.org/10.1016/j.orl.2015.02.007
Publication status	Published - 2015 May

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V.

Keywords

Lyapunov function
Markov process
Retrial queue
Stability

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2015.02.007

Cite this

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abstract = "In this paper we solve the conjecture made by Avram, Matei and Zhao (2014), on stability condition of an M/M/s retrial queue with Bernoulli acceptance, abandonment and feedback. The Markov process describing this queueing system is positive recurrent if ρ∞<1 and transient if ρ∞>1, where ρ∞ is the traffic load under the saturation condition of the orbit. We also investigate the critical case when ρ∞=1 to see if it can be either stable or unstable.",

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AB - In this paper we solve the conjecture made by Avram, Matei and Zhao (2014), on stability condition of an M/M/s retrial queue with Bernoulli acceptance, abandonment and feedback. The Markov process describing this queueing system is positive recurrent if ρ∞<1 and transient if ρ∞>1, where ρ∞ is the traffic load under the saturation condition of the orbit. We also investigate the critical case when ρ∞=1 to see if it can be either stable or unstable.

KW - Lyapunov function

KW - Markov process

KW - Retrial queue

KW - Stability

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JF - Operations Research Letters

IS - 3

ER -

Proof of the conjecture on the stability of a multiserver retrial queue

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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