Synthesis and MAVAR Characterization of Self-similar Traffic Traces from Chaotic Generators

Abstract

Experimental measurements show that many relevant processes in telecommunication engineering exhibit self-similarity and long-range dependence (LRD) characteristics. Internet traffic is a significant example. A traditional parameter used to characterize self-similarity and LRD is the Hurst parameter H. Recently, the Modified Allan Variance (MAVAR) has been proposed to estimate the power-law spectrum and thus the Hurst parameter of LRD series. Chaotic generators have been introduced in the last years to mimic time series derived both from sampled Internet or packet video traffic. They are built by means of optimized weighted sums of geometric characteristic sampled from Lorenz strange attractors. The optimization of the structure is obtained observing both the variation coefficients (i.e., a traditional long term feature well matched to the analysis of the error gap processes, related to the Variance-Time plot and to the Hurst parameter too), and, more recently, the logscale diagram. Then, it was quite natural to explore the MAVAR characterization of time series derived from the above chaotic generators, and to compare it to that exhibited by the mimicked process, looking for a fruitful inclusion of MAVAR terms in the optimization cost function.