Abstract Description of Internet Traffic of Generalized Cauchy Type
نویسندگان
چکیده
Self-similar process with long-range dependence (LRD), i.e., fractional Gaussian noise (fGn) with LRD is a widely used model of the Internet traffic. It is indexed by its Hurst parameter HfGn that linearly relates to its fractal dimension DfGn. Note that, on the one side, the fractal dimension D of traffic measures local self-similarity. On the other side, 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, which 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 ACF of arrival traffic. The key contribution of this paper is our solution to that fundamental problem (see Theorem 2) with the following features in analysis. • Set-valued analysis of the traffic of the fGn type. • Set-valued analysis of the traffic of the GC type. • Revealing the generality previously mentioned by comparing metrics of the traffic of the fGn type to that of the GC type.
منابع مشابه
Cauchy-Rassias Stability of linear Mappings in Banach Modules Associated with a Generalized Jensen Type Mapping
متن کامل
Non-Archimedean stability of Cauchy-Jensen Type functional equation
In this paper we investigate the generalized Hyers-Ulamstability of the following Cauchy-Jensen type functional equation$$QBig(frac{x+y}{2}+zBig)+QBig(frac{x+z}{2}+yBig)+QBig(frac{z+y}{2}+xBig)=2[Q(x)+Q(y)+Q(z)]$$ in non-Archimedean spaces
متن کاملRSVP-TE Extensions in Support of End-to-End Generalized Multi-Protocol Label Switching (GMPLS) Recovery
Status of This Memo This document specifies an Internet standards track protocol for the Internet community, and requests discussion and suggestions for improvements. Please refer to the current edition of the "Internet Official Protocol Standards" (STD 1) for the standardization state and status of this protocol. Distribution of this memo is unlimited. Abstract This document describes protocol...
متن کاملGeneralized Cauchy Type
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 parameterHfGn that linearly relates to its fractal dimensionDfGn. Note that, on the one hand, the fractal dimensionD of traffic measures local self-similarity. On the other hand, LRD is a global property of traffic, which is...
متن کاملA Novel Description of Multifractal Phenomenon of Network Traffic Based on Generalized Cauchy Process
Let D(n) and H(n) be the fractal dimension and the Hurst parameter of traffic in the nth interval, respectively. Thus, this paper gives the experimental variance analysis of D(n) and H(n) of network traffic based on the generalized Cauchy (GC) process on an interval-by-interval basis. We experimentally infer that traffic has the phenomenon Var[D(n)] > Var[H(n)]. This suggests a new way to descr...
متن کامل