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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 261568, 9 pages
Research Article

Poisson Shot Noise Traffic Model and Approximation of Significant Functionals

1Department of Statistic and Operation Research, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2Département de Mathématiques, Faculté des Sciences, Campus Universitaire 2092, Université de Tunis, El Manar, Tunisia

Received 24 November 2013; Accepted 31 December 2013; Published 23 February 2014

Academic Editor: Bessem Samet

Copyright © 2014 Wissem Jedidi. 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.


In Internet traffic modeling, many authors presented models based on particular fractal shot noise representations. The inconvenience of these approaches is the multitude of assumptions and the lack of tools to check them. In this paper we propose a unified model based on a general Poisson shot noise representation for the cumulative input process (CIP). We present a procedure of approximation of this process; then we give a procedure for controlling the bandwidth of Internet providers. The approximation and control go via limit theorems for functionals of the CIP, namely, the supremum process, the right inverse, and the storage mapping.