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GI/G/1/∞ batch arrival queueing system with a single exponential vacation

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Abstract

In the article the queueing system of GI/G/1 type with batch arrival of customers and a single exponentially distributed vacation period at the end of every busy period is considered. Basic characteristics of transient state of the system are investigated: the first busy period, the first vacation period and the number of customers served during the first busy period. New results for the Laplace transform of the joint distribution of these three variables are obtained in dependence on the initial conditions of the system.

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Authors and Affiliations

  1. Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

    Wojciech M. Kempa

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  1. Wojciech M. Kempa
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Correspondence to Wojciech M. Kempa.

Additional information

This material is based upon work supported by the Polish Ministry of Scientific Research and Information Technology under Grant No. 3 T11C 014 26.

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Kempa, W.M. GI/G/1/∞ batch arrival queueing system with a single exponential vacation. Math Meth Oper Res 69, 81–97 (2009). https://doi.org/10.1007/s00186-008-0212-2

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  • DOI: https://doi.org/10.1007/s00186-008-0212-2

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