# On probability estimation of buffer overflow for communication networks

## DOI:

https://doi.org/10.17721/1812-5409.2022/2.8## Keywords:

Gaussian process, fractional Brownian motion, Hurst index, probability estimation, random process, self-similar traffic, statistical simulation modeling, telecommunication traffic## Abstract

*In recent years, a large number of research of telecommunications traffic have been conducted. It was found that traffic has a number of specific properties that distinguish it from ordinary traffic. Namely: it has the properties of self-similarity, multifractality, long-term dependence and distribution of the amount of load coming from one source.*

*At present, many other models of traffic with self-similarity properties and so on have been built in other researched works on this topic. Such models are investigated in this paper, which considers traffic in telecommunications networks, the probability of overflow traffic buffer. Statistical models are built to analyze traffic in telecommunications networks, in particular to research the probability of buffer overflow for communication networks. *

*The article presents the results of the analysis of processes in telecommunication networks, in particular traffic; research of possibilities of representation of real processes in the form of random processes on the basis of use of statistical simulation model; the necessary mathematical and statistical models are selected and analyzed; software-implemented models using the Matlab environment; visual graphs for comparison of the received data are given; the analysis of the received models is carried out.*

* Pages of the article in the issue*: 64 - 69

**Language of the article**: Ukrainian

## References

PASHKO A., ROZORA I. (2018) Analysis of the accuracy of fractional Brownian motion modeling in a uniform metric / Bulletin of the Taras Shevchenko National University. Series Physics and Mathematics, vol. 1, pp. 60-65.

GAUTAM. N. (2003) Stochastic Models in Telecommunications for Optimal Design, Control and Performance Evaluation , chapter 7, Handbook of Statistics, Elsevier, Vol. 21., p. 243-284. https://doi.org/10.1016/S0169-7161(03)21009-9.

NOMOS I. (1995). On the Use of Fractional Brownian Motion in the Theory of Connectionless Networks / IEEE journal on selected areas in communications, Vol. 13, No. 6, p.953-962.

PASHKO A., ROZORA I. (2021) Estimation of the Probability of Buffer overflow for self-similar Traffic / 2021 IEEE 8th International Conference on Problems of Infocommunications, Science and Technology, PIC S and T 2021.–2021.– P.28-32.

KOZACHENKO YU., PASHKO A., VASILYK O. (2017) Modeling of fractional Brownian motion in space Lp ([0, T]) / Probability theory and mathematical statistics, Vol. 97, p.97-108.

DIEKER T. (2004). Simulation of fractional Brownian motion. Master thesis, University of Twente, Amsterdam. http://www.columbia.edu/~ad3217//fbm/thesis.pdf

VOROPAEVA V., BESSARAB V., TURUPALOV V. (2011). Theory of teletraffic: textbook. Donetsk: DonNTU, 202 p.

MATLAB Documentation [Electronic resource] / https://ch.mathworks.com/help

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## How to Cite

*Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics*, (2), 64–69. https://doi.org/10.17721/1812-5409.2022/2.8

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