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Bull. Korean Math. Soc. 2013; 50(5): 1659-1671

Printed September 1, 2013

https://doi.org/10.4134/BKMS.2013.50.5.1659

Copyright © The Korean Mathematical Society.

Waiting time distribution in the M/M/m retrial queue

Jeongsim Kim and Jerim Kim

Chungbuk National University, Yongin University

Abstract

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In this paper, we are concerned with the analysis of the waiting time distribution in the M/M/m retrial queue. We give expressions for the Laplace-Stieltjes transform (LST) of the waiting time distribution and then provide a numerical algorithm for calculating the LST of the waiting time distribution. Numerical inversion of the LSTs is used to calculate the waiting time distribution. Numerical results are presented to illustrate our results.

Keywords: M/M/m retrial queue, waiting time, Laplace-Stieltjes transform, first passage time

MSC numbers: Primary 60K25

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