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Interest of Boundary Kernel Density Techniques in Evaluating an Approximation Error of Queueing Systems Characteristics

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  • Aïcha Bareche
  • Djamil Aïssani

Abstract

We show the interest of nonparametric methods taking into account the boundary correction techniques for a numerical evaluation of an approximation error between the stationary distributions of and queueing systems, when the density function of the general arrivals law in the system is unknown and defined on a bounded support. To compute this error, we use two kinds of norms: the norm and the weight norm. Numerical examples based on simulation studies are presented for the two cases of considered norms. A comparative study of the results has been provided.

Suggested Citation

  • Aïcha Bareche & Djamil Aïssani, 2014. "Interest of Boundary Kernel Density Techniques in Evaluating an Approximation Error of Queueing Systems Characteristics," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-8, August.
    • Handle: RePEc:hin:jijmms:871357
    DOI: 10.1155/2014/871357
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    References listed on IDEAS

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    1. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
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    1. F. R. B. Cruz & M. A. C. Santos & F. L. P. Oliveira & R. C. Quinino, 2021. "Estimation in a general bulk-arrival Markovian multi-server finite queue," Operational Research, Springer, vol. 21(1), pages 73-89, March.

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