Abstract
This paper proposes a multifractal model, with the aim of providing a possible explanation for the locality phenomenon that appears in the estimation of the Hurst exponent in stationary second order temporal series representing self-similar traffic flows in current high-speed computer networks. It is shown analytically that this phenomenon occurs if the network flow consists of several components with different Hurst exponents.
Highlights
The properties that evidence the nature of the fractal origin of traffic flows in high-speed computer networks have been extensively studied and reported in the literature during the last twenty years, and it is generally accepted that their rescaled dynamic behavior must be carefully considered in performance analyses
On the other hand, admitting that the localities of a fractal process can only be analyzed from the standpoint of multifractal analysis, in view of their construction from multiplicative cascades that ensure an exact characterization as a result of the high frequency analysis [9, 10], it is accepted that the traffic flows present in current high-speed computer networks are of a multifractal nature, and this gives rise to a new flow model that attempts to explain the locality phenomenon present in the estimation of the Hurst exponent [4, 8, 10]
The above shows in a simple manner that if a traffic process is formed from two independent self-similar additive components with different Hurst exponents, the locality phenomenon is seen in the estimation of the H exponent using cumulants
Summary
The properties that evidence the nature of the fractal origin of traffic flows in high-speed computer networks have been extensively studied and reported in the literature during the last twenty years, and it is generally accepted that their rescaled dynamic behavior must be carefully considered in performance analyses. On the other hand, admitting that the localities of a fractal process can only be analyzed from the standpoint of multifractal analysis, in view of their construction from multiplicative cascades that ensure an exact characterization as a result of the high frequency analysis [9, 10], it is accepted that the traffic flows present in current high-speed computer networks are of a multifractal nature, and this gives rise to a new flow model that attempts to explain the locality phenomenon present in the estimation of the Hurst exponent [4, 8, 10]. From the results obtained by the use of computational simulations, it is inferred that the model contributes to the knowledge of the actual dynamics of the traffic in current high-speed computer networks, and that it can be used to simulate realistic traffic flow from real networks
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