Tail asymptotics for the queue size distribution in AN M/G/1 retrial queue

Jerim Kim; Bara Kim; Sung Seok Ko

doi:10.1239/jap/1197908829

Tail asymptotics for the queue size distribution in AN M/G/1 retrial queue

Jerim Kim, Bara Kim, Sung Seok Ko

Department of Mathematics

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

25 Scopus citations

Abstract

We consider an M/G/1 retrial queue, where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. The result is obtained by investigating analytic properties of probability generating functions for the queue size and the server state.

Original language	English
Pages (from-to)	1111-1118
Number of pages	8
Journal	Journal of Applied Probability
Volume	44
Issue number	4
DOIs	https://doi.org/10.1239/jap/1197908829
State	Published - Dec 2007

Keywords

M/G/1 retrial queue
Queue size distribution
Tail asymptotics

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10.1239/jap/1197908829

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title = "Tail asymptotics for the queue size distribution in AN M/G/1 retrial queue",

abstract = "We consider an M/G/1 retrial queue, where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. The result is obtained by investigating analytic properties of probability generating functions for the queue size and the server state.",

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author = "Jerim Kim and Bara Kim and Ko, \{Sung Seok\}",

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AU - Kim, Bara

AU - Ko, Sung Seok

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N2 - We consider an M/G/1 retrial queue, where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. The result is obtained by investigating analytic properties of probability generating functions for the queue size and the server state.

AB - We consider an M/G/1 retrial queue, where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. The result is obtained by investigating analytic properties of probability generating functions for the queue size and the server state.

KW - M/G/1 retrial queue

KW - Queue size distribution

KW - Tail asymptotics

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JO - Journal of Applied Probability

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Tail asymptotics for the queue size distribution in AN M/G/1 retrial queue

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Keywords

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