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Tail Asymptotics for the Queue Size Distribution in an M/G/1 Retrial Queue

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Jerim Kim ,
Bara Kim  and
Sung-Seok Ko
Jerim Kim*
Affiliation:
Korea University
Bara Kim*
Affiliation:
Korea University
Sung-Seok Ko*
Affiliation:
Konkuk University
*
∗Postal address: Department of Mathematics, Korea University, 1 Anam-dong, Sungbuk-ku, Seoul 136-701, Korea.
∗Postal address: Department of Mathematics, Korea University, 1 Anam-dong, Sungbuk-ku, Seoul 136-701, Korea.
∗∗∗Postal address: Department of Industrial Engineering, Konkuk University, 1 Hwayang-dong, Gwangjin-Gu, Seoul 143-701, Korea. Email address: [email protected]
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Abstract

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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.

Keywords

M/G/1 retrial queuetail asymptoticsqueue size distribution

MSC classification

Secondary: 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 44 , Issue 4 , December 2007 , pp. 1111 - 1118
Copyright
Copyright © Applied Probability Trust 2007 

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