Adaptive Hurst Index Estimator Based on Wavelet

[Abstract] Measurement studies show that the burstiness of packet traffic in LAN as well as WAN is associated with self-similar and long-range dependency. The Hurst index is the key value of this model. With the analysis in discrete wavelet domain, the nature of the wavelet coefficients and their statistical properties are proposed. Then an adaptive, efficient unbiased estimator of Hurst index based on multiresolution wavelet analysis and weighted regression, is presented. Simulation results based on fractal Gaussian noise and real traffic data reveal the proposed approach shows more adaptiveness, accuracy, and robustness than traditional estimators, which have only O(N) computation. Thus this estimator can be applied to traffic management and real-time control in high-speed networks. [Keywords] Self-similar, long-range dependent (LRD); wavelet; Hurst index; adaptive Introduction When modeling the burstiness of packet traffic in high-speed networks, it is usually assumed that traffic arrival process is Poisson's Points. However, both Bellcore's monitor over packet traffic in LAN and analysis of Internet data and VBR video traffic in WAN made by many institutes showed that the burstiness of the arrival process complies with asymptotic or strict self-similar model in a better way. The Hurst index is a significant parameter for representing burstiness of self-similar traffic. Usually, the Hurst index of burstiness of packet traffic falls between 0.5 and 1, which means that the network structure is positively correlated. The larger the Hurst index is, the more dramatic the network traffic burstiness will be. Therefore, evaluation of Hurst index will directly influence the accuracy of network traffic model, and the performance of both traffic control and statistical division multiplexing in high-speed network traffic. Today, the method used in literatures can be classified into two categories, time domain and frequency domain. All the methods need a large amount of data samples to analyze network traffic in comparatively long time and have a higher computational complexity. In addition, they cannot represent exactly the time-variation of Hurst index. As a result, wavelet transform is introduced by many scholars into the study of the self-similarity and long-range dependency of network traffic and evaluation of Hurst index (Leland et al., 1994; Paxson & Floyd, 1995; Garrett & Willinger, 1994; Abry & Veitch, 1998, 1999, 2000, 2002; Xue, 2000). Studies show that the evaluation results in wavelet domain depend on which scale intervals of wavelet is chosen. Chen et al (1998) provides performance evaluation for the method and shows the influence of scale intervals choice on the evaluator of Hurst index, as well as a choice method for small Hurst index. Hence the adaptive choice of scale intervals remains open. In this thesis, the self-similar model are briefly described in a mathematical way, and the nature of wavelet transform coefficients in self-similar process and its related statistical properties are proposed. Then, for the purpose of perfecting wavelet-based estimators for Hurst index, an efficient method, which can help people make an adaptive choice of scale interval, is proposed. Simulation based on fractal Gaussian noise and real traffic data reveal that this method is easier, faster, and more accurate than traditional methods. In addition, it allows the choice of the optimal scale interval of wavelet. As a result, it is appropriate for realtime control in high-speed network. Adaptive Approach to Parameter Evaluation As mentioned above, the Hurst index is a significant parameter for representing burstiness of traffic with long-range dependence. Evaluation based on monitoring data of network traffic within a certain time has showed that the Hurst index is very important for both modeling self-similar network and traffic control. Today, existing methods of evaluating the Hurst index fall into two categories: time-domain and frequency domain. …