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

16 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

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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title = "Tail asymptotics of the queue size distribution in the MMm retrial queue",

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.",

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

author = "Jerim Kim and Jeongsim Kim and Bara Kim",

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N2 - 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.

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.

KW - Censored Markov process

KW - Karamata Tauberian theorem

KW - MMm retrial queue

KW - Queue size distribution

KW - Riemann-Lebesgue lemma

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

Abstract

Keywords

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