  Recent network traffic studies argue that network arrival processes are much
more faithfully modeled using statistically self-similar processes instead of
traditional Poisson processes [LTWW94,PF95]. One difficulty in dealing with
self-similar models is how to efficiently synthesize traces (sample paths)
corresponding to self-similar traffic. We present a fast Fourier transform
method for synthesizing approximate self-similar sample paths for one type of
self-similar process, Fractional Gaussian Noise, and assess its performance and
validity. We find that the method is as fast or faster than existing methods
and appears to generate close approximations to true self-similar sample paths.
We also discuss issues in using such synthesized sample paths for simulating
network traffic, and how an approximation used by our method can dramatically
speed up evaluation of Whittle's estimator for H, the Hurst parameter giving
the strength of long-range dependence present in a self-similar time series.
