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Output Process in Batch-Arrival Queue with N-Policy and Multiple Vacations

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Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7984))

Abstract

In the paper the M X/G/1-type queueing system with the N-policy and multiple vacations is considered. The output process, counting successive departures, is studied using the approach consisting of two main stages. Firstly, introducing an auxiliary model with the N-policy and multiple vacations, and applying the formula of total probability, the analysis is brought to the case of the corresponding system without restrictions in the service process, on its first busy cycle. Next, defining a delayed renewal process of successive vacation cycles, the general results are obtained. The explicit formula for the probability generating function of the Laplace transform of the distribution of the number of packets completely served before a fixed moment t is derived and written using transforms of “input” distributions of the system, and components of the Wiener-Hopf-type factorization identity connected with them. Moreover, illustrative numerical results are presented.

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Authors and Affiliations

  1. Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23, 44-100, Gliwice, Poland

    Wojciech M. Kempa

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  1. Wojciech M. Kempa
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Editors and Affiliations

  1. Belarusian State University, Nezavisimosti Ave. 4, 220030, Minsk, Belarus

    Alexander Dudin

  2. Department of Telecommunications and Information Processing, Ghent University, Sint-Pietersnieuwstraat 41, 9000, Gent, Belgium

    Koen De Turck

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Kempa, W.M. (2013). Output Process in Batch-Arrival Queue with N-Policy and Multiple Vacations. In: Dudin, A., De Turck, K. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2013. Lecture Notes in Computer Science, vol 7984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39408-9_18

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  • DOI: https://doi.org/10.1007/978-3-642-39408-9_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39407-2

  • Online ISBN: 978-3-642-39408-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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