ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 4. Vol. 25. 2019

DOI: 10.17587/it.25.205-210

V. N. Tarasov, D. Sc., Professor, Head of Chair, e-mail: veniamin_tarasov@mal.ru, N. F. Bakhareva, D. Sc., Professor, Head of Chair, e-mail: nadin1956_04@inbox.ru, Kada Othmane, Postgraduate, Povolzhsky State University of Telecommunications and Informatics, Samara, 443010, Russian Federation

The Mathematical Model of Teletraffik Based on the HE₂/M/1 System

The article is devoted to the study of the HE₂/M/1 queuing system type G/M/1 with a second-order hypererlangian input distribution and an exponential service time law with the aim of obtaining a solution for the average waiting time in queue in the case of a stationary mode. For this, the classical method of spectral decomposition of the solution of the Lindley integral equation is used. For practical application of the obtained results, the method of moments is used. It turns out that the hyperelangian distribution law HE₂, like hyperexponential H₂, which is three-parameter, can be determined by both the first two moments and the first three moments. This characteristic feature of the hypererlangian distribution law must be used in the theory of mass service. The choice of such a law of probability distribution is due to the fact that it is the most common distribution of non-negative continuous random variables, since its coefficient of variation c_t>=1/2^1/2 covers a wider range than the hyperexponential distribution for which c_t>= 1 Determination of the main characteristic of QS — the average waiting time is an important task in the theory of teletraffic when analyzing traffic sensitive to delays. The method of spectral decomposition of the solution of the Lindley integral equation for the QS HE₂/M/1 allows one to obtain a solution in closed form.
Keywords: Hypererlangian distribution law, Lindley integral equation, spectral decomposition method, Laplace transform

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