This directory contains version 1.0 of an S program for synthesizing
approximate fractional Gaussian noise. The program consists of 3 routines:
ss.gen.fourier(n, H)
Returns a sample path of n synthesized points with Hurst
parameter H. n should be even.
FGN.spectrum(lambda, H)
Internal routine that returns an approximation to the power
spectrum of fractional Gaussian noise at the given
frequencies lambda and Hurst parameter H.
FGN.B.est <- (lambda, H)
Internal routine used in computing the approximation
to the power spectrum.
So an example of using it is just:
sample.path <- ss.gen.fourier(8192, .8)
Note that the mean and variance of the returned points is irrelevant,
because any linear transformation applied to the points preserves their
correlational structure (and hence their approximation to fractional
Gaussian noise); and by applying a linear transformation you can
transform the points to have any mean and variance you want.
If you're using the sample paths for simulating network arrival counts,
you'll want them to all be non-negative. Hopefully you have some notion of
the mean and variance of your desired traffic, and can apply the corresponding
transformation. If, after transforming, a fair number of the points are
still negative, then perhaps your traffic is not well-modeled using
fractional Gaussian noise. You might instead consider using an exponential
transformation. All of this is discussed in the technical report:
Fast Approximation of Self-Similar Network Traffic,
Vern Paxson, technical report LBL-36750/UC-405, April 1995.
URL:ftp://ftp.ee.lbl.gov/papers/fast-approx-selfsim.ps.Z
The program is covered by a U.C. Regents copyright, spelled out in
the file "COPYING".
Questions/comments to vern@ee.lbl.gov.