Characterization of linear scale invariant system input/output relationships and synthesis of network traffic traces

It has been shown that discrete-time self-similar processes can be synthesized by the discrete-time linear scale invariant system (DLSI) models proposed by Zhao and Rao. This paper reports results of subsequent studies on the DLSI systems to characterize properties such as long-range dependency. This paper also shows that self-similar processes generated by these systems have fractional Gaussian characteristics regardless of the marginal distribution of the white noise input. This property can be verified by comparing the autocovariance functions of the fractional Gaussian noise and the system outputs. It is also shown that the system is able to generate statistically self-similar signals whose parameters coincide with those observed in network traffic traces.