Modeling self-similar traffic using matrix exponentials.

摘要

This dissertation explores the question of whether it is possible to accurately represent self-similar network traffic exhibiting long-range dependence using a matrix exponential approach. A method for generating synthetic traffic traces which accurately captures both first-order and second-order properties of empirical traces is presented. A matrix exponential distribution, inversely derived from the moments of an empirical trace, was used as the basis for generating random variables whose marginal distribution is indistinguishable from that of the original traffic stream. The autocorrelation structure of the original trace was also preserved through the use of an AR(p) model. This approach provides a numerically accurate, non-heuristic approach to generating a traffic stream whose first and second order statistics match those of a known self-similar traffic trace.;Simulation studies showed that the synthetic traffic produced conservative estimates of both average and maximum buffer usage in infinite buffer systems and for the number of lost packets in finite buffer systems. Although performance does not match that of the empirical trace exactly, it is a vast improvement over the traditional exponential model which dramatically underestimates the buffering requirements for real traffic traces.;Long-range dependence was clearly present in the synthetically generated traffic traces, with more than 1000 lags of significant autocorrelations present in one of the synthetic traces. The heavy-tail of the distribution of the original interarrival times was also successfully captured. Traffic was highly bursty as shown by the aggregated interval counts and that burstiness was preserved across several time scales, an attribute of self-similarity. However, variance-time plots of the data did not show the presence of slowly decaying variances, suggesting that self-similarity was not present. No definitive conclusion was drawn on the presence or absence of self-similarity in the synthetic traces.