Fig. 1. Block diagram of the applied evaluation methodology. Based on a given Hurst parameter and a desired load the generator provides a sequence of packet arrival times. This is converted into a stochastic process used for the estimation to obtain the estimated Hurst parameter together with a confidence interval. The global error is .

Fig. 2. The conceptual image of a virtual first in first out queue fed by the arrival process and drained by a deterministic server of capacity μ.

Fig. 3. The arrival process associates a packet length with an arrival time, and uses the packet length series in the estimation.

Fig. 4. The arriving workload will instantaneously contribute to the filling of the queue. The queue will then drain at server capacity. The shaded area indicates the queue length. This will make the server alternate between its ON and OFF states, with switching times τ_k.

Fig. 5. The active indicator values {0,1} of the ON/OFF process model for the queue server are integrated over intervals of fixed length h to produce process values in the range [0,h] assigned to the end points of the intervals.

Fig. 6. The work process representing the amount of outstanding work relative to a zero starting point assuming that the server continuously drains the queue at full capacity.

Fig. 7. The interpolated work process derived from the work process of Section 4.7 by interpolating the process values with a cubic Spline.

Fig. 8. The errors of the Erramilli generator with the aggregated variance, the EBP and the Wavelet estimators for each of the Hurst values. The error bars show the 99% confidence intervals of the t-test. See Section 6.2 for an explanation of the results and Table 4 for the symbols.

Fig. 9. The results of the Erramilli generator estimated with the EBP estimator and the work process.

Fig. 10. The errors of the Mondragon generator with the aggregated variance, the EBP and the Wavelet estimators for each of the Hurst values. The error bars show the 99% confidence intervals of the t-test. See Section 6.3 for an explanation of the results and Table 4 for the symbols.

Fig. 11. The errors of the generator multiplexing 300 individual sources with the aggregated variance, the EBP and the Wavelet estimators for each of the Hurst values. The error bars show the 99% confidence intervals of the t-test. See Section 6.4 for an explanation of the results and Table 4 for the symbols.

Fig. 12. The errors of Opnet’s Raw Packet Generator with the aggregated variance, the EBP and the Wavelet estimators for each of the Hurst values. The error bars show the 99% confidence intervals of the t-test. See Section 6.5 for an explanation of the results and Table 4 for the symbols.

Fig. 13. The errors of the Erramilli map, the Mondragon map, and multiplexing 300 ON/OFF sources respectively. All errors obtained with the Wavelet estimator. The error bars show the 99% confidence intervals of the t-test. See Section 7.2 for an explanation of the results and Table 4 for the symbols.

Reported values of the Hurst parameter for the Bellcore pAug trace

A value in parentheses indicates a value identified from a figure in the article or from averaging numbers given in the article. The extremal values are taken from confidence intervals if available.

The different estimators applied to the result of filtering the pAug trace with the different process models

Used combinations are emphasised.

The effect of the sample time when using the count process with the aggregated variances estimator

Symbols used in the result diagrams to show the decisions of the tests regarding the validity of the default hypothesis, (31)