Busy period distribution of a batch arrival retrial queue

Jeongsim Kim

doi:10.4134/CKMS.c160106

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2017; 32(2): 425-433

Online first article January 18, 2017 Printed April 30, 2017

https://doi.org/10.4134/CKMS.c160106

Busy period distribution of a batch arrival retrial queue

Jeongsim Kim

Chungbuk National University

Abstract

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Abstract

This paper is concerned with the analysis of the busy period distribution in a batch arrival $M^X/G/1$ retrial queue. The expression for the Laplace-Stieltjes transform of the length of the busy period is well known, but from this expression we cannot compute the moments of the length of the busy period by direct differentiation. This paper provides a direct method of calculation for the first and second moments of the length of the busy period.

Keywords: retrial queue, batch arrivals, busy period

MSC numbers: 60K25