Moments of the queue size distribution in the MAP/G/1 retrial queue

Jeongsim Kim; Bara Kim; Jerim Kim

doi:10.1016/j.cor.2009.04.007

Moments of the queue size distribution in the MAP/G/1 retrial queue

Jeongsim Kim, Bara Kim, Jerim Kim

Department of Mathematics

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

5 Scopus citations

Abstract

We consider an MAP/G/1 retrial queue. A necessary and sufficient condition is obtained for the existence of the moments of the queue size distribution. The condition is expressed in terms of the moment condition for a service time distribution. In addition, we provide recursive formulas for the moments of the queue size distribution. Numerical examples are given to illustrate our results.

Original language	English
Pages (from-to)	1212-1219
Number of pages	8
Journal	Computers and Operations Research
Volume	37
Issue number	7
DOIs	https://doi.org/10.1016/j.cor.2009.04.007
State	Published - Jul 2010

Keywords

MAP/G/1 retrial queue
Perron-Frobenius eigenvalue
Perron-Frobenius eigenvector
Queue size distribution

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10.1016/j.cor.2009.04.007

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abstract = "We consider an MAP/G/1 retrial queue. A necessary and sufficient condition is obtained for the existence of the moments of the queue size distribution. The condition is expressed in terms of the moment condition for a service time distribution. In addition, we provide recursive formulas for the moments of the queue size distribution. Numerical examples are given to illustrate our results.",

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AU - Kim, Bara

AU - Kim, Jerim

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N2 - We consider an MAP/G/1 retrial queue. A necessary and sufficient condition is obtained for the existence of the moments of the queue size distribution. The condition is expressed in terms of the moment condition for a service time distribution. In addition, we provide recursive formulas for the moments of the queue size distribution. Numerical examples are given to illustrate our results.

AB - We consider an MAP/G/1 retrial queue. A necessary and sufficient condition is obtained for the existence of the moments of the queue size distribution. The condition is expressed in terms of the moment condition for a service time distribution. In addition, we provide recursive formulas for the moments of the queue size distribution. Numerical examples are given to illustrate our results.

KW - MAP/G/1 retrial queue

KW - Perron-Frobenius eigenvalue

KW - Perron-Frobenius eigenvector

KW - Queue size distribution

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DO - 10.1016/j.cor.2009.04.007

M3 - Article

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EP - 1219

JO - Computers and Operations Research

JF - Computers and Operations Research

IS - 7

ER -

Moments of the queue size distribution in the MAP/G/1 retrial queue

Abstract

Keywords

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