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

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