On the superimposition of heterogeneous traffic at large time scales
L. Lopez-Oliveros and S.I. Resnick
Empirical and theoretical studies indicate that cumulative
network traffic is a Gaussian process. However, depending on whether
the intensity at which sessions are initiated is large or small
relative to the session duration tail,
it is known that traffic at large time scales
can be approximated by either fractional Brownian motion (fBm) or
stable Levy motion. We study distributional properties of
cumulative traffic that consists of a finite number of independent
streams and give an explanation of why Gaussian examples abound in
practice but not stable Levy motion. We offer an explanation of how
much vertical aggregation is needed for the Gaussian approximation to
hold. Our results are expressed as limit theorems for a sequence of
cumulative traffic processes whose session initiation intensities
satisfy growth rates.