Analysis of LRD Series with Time-Varying Hurst Parameter

Abstract

Abstract. It has been previously shown that actual network traffic exhibits long-range dependence. The Hurst parameter captures the degree of long-range dependence; however, because of the nature of computer network traffic, the Hurst parameter may not remain constant over a long period of time. An iterative method to compute the value of the Hurst parameter as a function of time is presented and analyzed. Experimental results show that the proposed method provides a good estimation of the Hurst parameter as a function of time. Additionally, this method allows the detection on changes of the Hurst parameter for long data series. The proposed method is compared with traditional methods for Hurst parameter estimation. Actual and synthetic traffic traces are used to validate our results. The proposed method allows detecting the changing points on the Hurst parameter, and better results can be obtained when modeling self-similar series using several values of the Hurst parameter instead of only one for the entire series. A new graphical tool to analyze long-range dependent series is proposed. Because of the nature of this plot, it is called the transition-variance plot. This tool may be helpful to distinguish between LAN and WAN traffic. Finally, the software LRD Lab* is deployed to analyze and synthesize long-range dependent series. The LRD Lab includes a simple interface to easily generate, analyze, visualize and save long-range dependent series.