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International Journal of Mathematics and Mathematical Sciences
Volume 2014, Article ID 871357, 8 pages
http://dx.doi.org/10.1155/2014/871357
Research Article

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

Research Unit LaMOS (Modeling and Optimization of Systems), University of Bejaia, 06000 Bejaia, Algeria

Received 11 February 2014; Revised 9 July 2014; Accepted 23 July 2014; Published 14 August 2014

Academic Editor: Vladimir Mityushev

Copyright © 2014 Aïcha Bareche and Djamil Aïssani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.