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The Virtual Waiting Time in a Finite-Buffer Queue with a Single Vacation Policy

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Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7314))

Abstract

A finite-buffer queueing system with Poisson arrivals and generally distributed service times is considered. Every time when the system empties, a single vacation is initialized, during which the service process is blocked. A system of integral equations for the transient distributions of the virtual waiting time v(t) at a fixed moment t, conditioned by the numbers of packets present in the system at the opening, is derived. A compact formula for the 2-fold Laplace transform of the conditional distribution of v(t) is found and written down using a special-type sequence called a potential. From this representation the stationary distribution of v(t) as t → ∞ and its mean can be easily obtained. Theoretical results are illustrated by numerical examples as well.

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Author information

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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Editor information

Editors and Affiliations

  1. Faculty of Advanced Technology, University of Glamorgan, Pontypridd, UK

    Khalid Al-Begain

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

    Dieter Fiems

  3. LIG Laboratory - INRIA MESCAL Project,, Joseph Fourier University, 51, avenue Jean Kuntzmann, F-38330, Montbonnot, France

    Jean-Marc Vincent

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Kempa, W.M. (2012). The Virtual Waiting Time in a Finite-Buffer Queue with a Single Vacation Policy. In: Al-Begain, K., Fiems, D., Vincent, JM. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2012. Lecture Notes in Computer Science, vol 7314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30782-9_4

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  • DOI: https://doi.org/10.1007/978-3-642-30782-9_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30781-2

  • Online ISBN: 978-3-642-30782-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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