Multiscale Modeling and Queuing Analysis of Long-Range-Dependent
Network Traffic
Vinay Ribeiro (vinay@rice.edu)
Electrical and Computer Engineering, Rice University
Rudolf Riedi (riedi@rice.edu)
Electrical and Computer Engineering, Rice University
Matthew Crouse (mcrouse@ece.rice.edu)
Electrical and Computer Engineering, Rice University
Richard Baraniuk (richb@rice.edu)
Electrical and Computer Engineering, Rice University
We develop a simple multiscale model for the analysis and synthesis
of nonGaussian, long-range-dependent (LRD) network traffic loads.
The wavelet transform effectively decorrelates LRD signals and hence
is well-suited to model such data. However, traditional
wavelet-based models are Gaussian in nature which one may at the
most hope to match second order statistics of inherently nonGaussian
traffic loads. Using a multiplicative superstructure atop the Haar
wavelet tree, we retain the decorrelating properties of wavelets
while simultaneously capturing the positivity and ``spikiness'' of
nonGaussian traffic. This leads to a swift O(N) algorithm for
fitting and synthesizing N-point data sets. The resulting model
belongs to the class of multifractal cascades, a set of processes
with rich scaling properties which are better suited than LRD to
capture burstiness. We elucidate our model's ability to capture the
covariance structure of real data and then fit it to real traffic
traces. We derive approximate analytical queuing formulas for our
model, also applicable to other multiscale models, by exploiting its
multiscale construction scheme. Queuing experiments demonstrate the
accuracy of the model for matching real data and the precision of
our theoretical queuing results, thus revealing the potential use of
the model for numerous networking applications. Our results indicate
that a Gaussian assumption can lead to over-optimistic predictions
of tail queue probability even when taking LRD into account.