Geodesic
On one application of fractional Levy motion to network traffic modeling
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2017), pp. 17-29

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Markovian theory effectively used in modeling of text and voice transmission is not able to reflect the high variability of packet traffic coupled with the presence of long memory. It leads to a substantial underestimation of the network load and a very non-accurate estimation of performance measures. Hence the construction of more adequate models of data flows and analysis of their properties remains a very important task. In this paper we found a non-asymptotic upper bound for queue length in the infinite buffer queue fed by a fractal Levy motion. The analysis follows a network calculus approach where traffic is characterized by envelope functions and do not assume a steady state, large buffer, or many sources regime.
Keywords: fractional Brownian motion, $\alpha$-stable subordinator, self-similar processes, envelope processes, queue length. 
@article{VTPMK_2017_1_a1,
     author = {O. I. Sidorova},
     title = {On one application of fractional {Levy} motion to network traffic modeling},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {17--29},
     publisher = {mathdoc},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2017_1_a1/}
}
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O. I. Sidorova. On one application of fractional Levy motion to network traffic modeling. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2017), pp. 17-29. http://geodesic.mathdoc.fr/item/VTPMK_2017_1_a1/