Tail asymptotics of the queue size distribution in the MMm retrial queue

Jerim Kim; Jeongsim Kim; Bara Kim

doi:10.1016/j.cam.2012.03.027

Tail asymptotics of the queue size distribution in the MMm retrial queue

Jerim Kim, Jeongsim Kim, Bara Kim

Department of Mathematics

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

17 Citations (Scopus)

Abstract

We consider an MMm retrial queue and investigate the tail asymptotics for the joint distribution of the queue size and the number of busy servers in the steady state. The stationary queue size distribution with the number of busy servers being fixed is asymptotically given by a geometric function multiplied by a power function. The decay rate of the geometric function is the offered load and independent of the number of busy servers, whereas the exponent of the power function depends on the number of busy servers. Numerical examples are presented to illustrate the result.

Original language	English
Pages (from-to)	3445-3460
Number of pages	16
Journal	Journal of Computational and Applied Mathematics
Volume	236
Issue number	14
DOIs	https://doi.org/10.1016/j.cam.2012.03.027
Publication status	Published - 2012 Aug

Bibliographical note

Funding Information:
The second author’s research was supported by the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) ( 2009-0076674 ). The third author’s research was supported by the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) ( 2009-0076600 ).

Keywords

Censored Markov process
Karamata Tauberian theorem
MMm retrial queue
Queue size distribution
Riemann-Lebesgue lemma
Tail asymptotics

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2012.03.027

Cite this

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abstract = "We consider an MMm retrial queue and investigate the tail asymptotics for the joint distribution of the queue size and the number of busy servers in the steady state. The stationary queue size distribution with the number of busy servers being fixed is asymptotically given by a geometric function multiplied by a power function. The decay rate of the geometric function is the offered load and independent of the number of busy servers, whereas the exponent of the power function depends on the number of busy servers. Numerical examples are presented to illustrate the result.",

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AB - We consider an MMm retrial queue and investigate the tail asymptotics for the joint distribution of the queue size and the number of busy servers in the steady state. The stationary queue size distribution with the number of busy servers being fixed is asymptotically given by a geometric function multiplied by a power function. The decay rate of the geometric function is the offered load and independent of the number of busy servers, whereas the exponent of the power function depends on the number of busy servers. Numerical examples are presented to illustrate the result.

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KW - Karamata Tauberian theorem

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Tail asymptotics of the queue size distribution in the MMm retrial queue

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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