In this paper, we propose the multi-level Markov modulated Poisson process with arbitrary distribution of the packet length as a model of fractal traffic. For the total amount of information received in multi-level MMPP, we investigate the probability distribution and present the algorithm of calculating the first and the second moments. Using asymptotic analysis method, we build Gaussian approximation of aforementioned distribution. We show that the convergence time of the probability distribution to the Gaussian distribution forms the period where the Hurst parameter is stable and reflects the self-similarity of the multi-level MMPP.
Information Technologies and Mathematical Modelling. Queueing Theory and Applications : 19th International Conference, ITMM 2020, named after A. F. Terpugov, Tomsk, Russia, December 2–5, 2020 : revised selected papers. Cham, 2021. P. 61-77