On the Time Series Length for an Accurate Fractal Analysis in Network Systems

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.