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Impact of Nonparametric Density Estimation on the Approximation of the G∕G∕1 Queue by the M∕G∕1 One

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Functional Statistics and Applications

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

In this paper, we show the interest of nonparametric boundary density estimation to evaluate a numerical approximation of \(G/G/1\) and \(M/G/1\) queueing systems using the strong stability approach when the general arrivals law G in the \(G/G/1\) system is unknown. A numerical example is provided to support the results. We give a proximity error between the arrival distributions and an approximation error on the stationary distributions of the quoted systems.

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Author information

Authors and Affiliations

  1. Research Unit LaMOS (Modeling and Optimization of Systems), Faculty of Technology, University of Bejaia, Bejaia, 06000, Algeria

    Aïcha Bareche

  2. Research Unit LaMOS (Modeling and Optimization of Systems), Faculty of Exact Sciences, University of Bejaia, Bejaia, 06000, Algeria

    Djamil Aïssani

Authors
  1. Aïcha Bareche
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  2. Djamil Aïssani
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Corresponding author

Correspondence to Aïcha Bareche .

Editor information

Editors and Affiliations

  1. LMPA, Université du Littoral Côte d'Opale, Calais, France

    Elias Ould Saïd

  2. National School of Applied Sciences, Cadi Ayyad University, Marrakesh, Morocco

    Idir Ouassou

  3. Faculty of Science of Man and Society, Grenoble-Alpes University, Grenoble, France

    Mustapha Rachdi

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Bareche, A., Aïssani, D. (2015). Impact of Nonparametric Density Estimation on the Approximation of the G∕G∕1 Queue by the M∕G∕1 One. In: Ould Saïd, E., Ouassou, I., Rachdi, M. (eds) Functional Statistics and Applications. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-22476-3_7

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