Modelling Fractal Internet Traffix: Additive Dyadic Superposition of Lognormal Distributions

J. Potemans, J. Theunis, B. Van den Broeck, Y. Guan, E. Van Lil, and A. Van de Capelle (Belgium)


Modelling, fractal traffic, queuing, network performance


In this paper we present a major enhancement to our multifractal traffic model, which we introduced at ICC'03 and further extended at Globecom'03. Our discrete model consisted of a dyadic superposition of ON/OFF sources whose parameters are chosen to fit the variances and third order moments of the desired trace at the corresponding aggregation levels. By replacing these simple sources by continuous lognormally distributed sources and by adjusting the procedure to fit the mean of the trace, our model can also be used to generate more general fractal traffic, whose second and third order moments are no longer restricted to follow a simple power-law decay when aggregating the trace. We will prove with some examples that both the marginal distribution and the queuing behaviour of the traffic are very well approximated by our model. The advantages of the previous versions of the model remain: the limited computational complexity allows generating very long traces, which can even be performed on-line. Unlike other multifractal models, our model is an additive model which limits the mathematical complexity.

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