It is well-known that fractal signals appear in many fields of science. LAN and WWW traces, wireless traffic, VBR resources, etc. are among the ones with this behavior in computer networks traffic flows. An important question in these applications is how long a measured trace should be to obtain reliable estimates of de Hurst index (H). This paper addresses this question by first providing a thorough study of estimator for short series based on the behavior of bias, standard deviation (s), Root-Mean-Square Error (RMSE), and convergence when using Gaussian H-Self-Similar with Stationary Increments signals (H-sssi signals). Results show that Whittle-type estimators behave the best when estimating H for short signals. Based on the results, empirically derived the minimum trace length for the estimators is proposed. Finally for testing the results, the application of estimators to real traces is accomplished. Immediate applications from this can be found in the real-time estimation of H which is useful in agent-based control of Quality of Service (QoS) parameters in the high-speed computer network traffic flows.

中文翻译：

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网络系统中精确分形分析的时间序列长度

众所周知，分形信号出现在许多科学领域。LAN和WWW跟踪，无线流量，VBR资源等在计算机网络流量中具有此行为。这些应用中的一个重要问题是，要获得可靠的de Hurst指数（H）估计值，应将测量的迹线测量多长时间。本文首先通过基于偏差，标准偏差，均方根误差（RMSE）和高斯H-Self-Similar的收敛性对短序列的估计量进行全面研究，从而解决了这个问题。固定增量信号（H-sssi信号）。结果表明，Whittle型估计器在估计短信号的H时表现最佳。基于结果，提出了经验估计的最小迹线长度。最后要测试结果，估计器在实际迹线上的应用已完成。可以在H的实时估计中找到对此的直接应用，这对高速计算机网络流量中基于代理的服务质量（QoS）参数的控制很有用。