Internet Traffic Modelling -Variance Based Markovian Fitting of Fractal Point Process from Self-Similarity Perspective

Abstract

Most of the proposed self-similar traffic models could not address fractal onset time at which self-similar behavior actually begins. This parameter has considerable impact on network performance. Fractal point process (FPP) emulates self-similar traffic and involves fractal onset time (FOT). However, this process is asymptotic in nature and has less effective in queueing based performance. In this paper, we propose a model of variance based Markovian fitting. The proposed method is to match the variance of FPP and superposed Markov modulated Poisson Process (MMPP) while taking FOT into consideration. Superposition consists of several interrupted Poisson processes (IPPs) and Poisson process. We present how well resultant MMPP could approximate FPP which emulates self-similar traffic. We investigate queueing behavior of resultant queueing system in terms of a packet loss probability. We demonstrate how FOT affects the fitting model and queueing behavior. We conclude from the numerical example that network nodes with a self-similar input traffic can be well represented by a queueing system with MMPP input