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A Batch-Service Queueing Model with a Discrete Batch Markovian Arrival Process

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Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6148))

Abstract

Queueing systems with batch service have been investigated extensively during the past decades. However, nearly all the studied models share the common feature that an uncorrelated arrival process is considered, which is unrealistic in several real-life situations. In this paper, we study a discrete-time queueing model, with a server that only initiates service when the amount of customers in system (system content) reaches or exceeds a threshold. Correlation is taken into account by assuming a discrete batch Markovian arrival process (D-BMAP), i.e. the distribution of the number of customer arrivals per slot depends on a background state which is determined by a first-order Markov chain. We deduce the probability generating function of the system content at random slot marks and we examine the influence of correlation in the arrival process on the behavior of the system. We show that correlation merely has a small impact on the threshold that minimizes the mean system content. In addition, we demonstrate that correlation might have a significant influence on the system content and therefore has to be included in the model.

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Authors and Affiliations

  1. Stochastic Modelling and Analysis of Communication Systems (SMACS) Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University, Sint-Pietersnieuwstraat 41, B-9000, Gent, Belgium

    Dieter Claeys, Joris Walraevens, Koenraad Laevens, Bart Steyaert & Herwig Bruneel

Authors
  1. Dieter Claeys
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  2. Joris Walraevens
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  3. Koenraad Laevens
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  4. Bart Steyaert
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  5. Herwig Bruneel
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Editor information

Editors and Affiliations

  1. Faculty of Advanced Technology, University of Glamorgan, CF37 1DL, Pontypridd, UK

    Khalid Al-Begain

  2. Department TELIN, Ghent University, Sint-Pietersnieuwstraat 41, 9000, Gent, Belgium

    Dieter Fiems

  3. Department of Computing,, Imperial College London, South Kensington Campus, SW7 2AZ, London, United Kingdom

    William J. Knottenbelt

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Claeys, D., Walraevens, J., Laevens, K., Steyaert, B., Bruneel, H. (2010). A Batch-Service Queueing Model with a Discrete Batch Markovian Arrival Process. In: Al-Begain, K., Fiems, D., Knottenbelt, W.J. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2010. Lecture Notes in Computer Science, vol 6148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13568-2_1

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  • DOI: https://doi.org/10.1007/978-3-642-13568-2_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13567-5

  • Online ISBN: 978-3-642-13568-2

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