Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 821215, 18 pages
Research Article

Abstract Description of Internet Traffic of Generalized Cauchy Type

1School of Information Science and Technology, East China Normal University, 500 Dong-Chuan Road, Shanghai 200241, China
2Department of Computer and Information Science, University of Macau, Avenue Padre Tomas Pereira, Taipa, Macau, China

Received 10 March 2011; Accepted 6 July 2011

Academic Editor: Zidong Wang

Copyright © 2012 Ming Li and Wei Zhao. 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.


Self-similar process with long-range dependence (LRD), that is, fractional Gaussian noise (fGn) with LRD is a widely used model of Internet traffic. It is indexed by its Hurst parameter HfGn that linearly relates to its fractal dimension DfGn. Note that, on the one hand, the fractal dimension D of traffic measures local self-similarity. On the other hand, LRD is a global property of traffic, which is characterized by its Hurst parameter H. However, by using fGn, both the self-similarity and the LRD of traffic are measured by HfGn . Therefore, there is a limitation for fGn to accurately model traffic. Recently, the generalized Cauchy (GC) process was introduced to model traffic with the flexibility to separately measure the fractal dimension DGC and the Hurst parameter HGC of traffic. However, there is a fundamental problem whether or not there exists the generality that the GC model is more conformable with real traffic than single parameter models, such as fGn, irrelevant of traffic traces used in experimental verification. The solution to that problem remains unknown but is desired for model evaluation in traffic theory or for model selection against specific issues, such as queuing analysis relating to the autocorrelation function (ACF) of arrival traffic. The key contribution of this paper is our solution to that fundamental problem (see Theorem 3.17) with the following features in analysis. (i) Set-valued analysis of the traffic of the fGn type. (ii) Set-valued analysis of the traffic of the GC type. (iii) Revealing the generality previously mentioned by comparing metrics of the traffic of the fGn type to that of the GC type.