
ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 9. Vol. 25. 2019
DOI: 10.17587/it.25.531537
V. N. Tarasov, D. Sc., Professor, Head of Chair, email: veniamin_tarasov@mail.ru, N. F. Bakhareva, D. Sc., Professor, Head of Chair, email: nadin1956_04@inbox.ru,
Kada Othmane, Postgraduate, Povolzhsky State University of Telecommunications and Informatics, Samara, 443010, Russian Federation
The Mathematical Model of Teletraffic Based on the HE_{2}/H_{2}/1 System
The article is devoted to the study of the G/G/1 type HE_{2}/H_{2}/1 queuing system with a secondorder hypererlangian input distribution and a hyperexponential service time law with the aim of obtaining a solution for the average waiting time in queue in the case of 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 HE_{2}, like the hyperexponential H_{2}, which is threeparameter, can be determined by both the first two moments and the first three moments. The choice of such probability distribution laws is due to the fact that they are the most common distributions of nonnegative continuous random variables, since the coefficient of variation for the HE_{2} c_{t} >=1/2^{1/2} distribution covers a wider range than the hyperexponential distribution for which c_{t} >=1. Determination of the principal characteristic of QS G/G/1 — of the average waiting time in queue an important task due to the fact that for such a QS there is no solution in the general case. The method of spectral decomposition of the solution of the Lindley integral equation for the QS HE_{2}/H_{2}/1 allows one to obtain a solution in closed form.
Keywords: Hypererlangian and hyperexponential distribution laws, Lindley integral equation, method of spectral decomposition, Laplace transform
P.531537
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