Generalized Cauchy Type
نویسندگان
چکیده
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 characterized by its Hurst parameterH. 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 dimensionDGC and the Hurst parameterHGC 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 Setvalued 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.
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تاریخ انتشار 2014