ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 12. Vol. 27. 2021

DOI: 10.17587/it.27.634-641

V. N. Tarasov, Dr. of Tech. Sc., Professor, Head of Department of POUTS, e-mail: veniamin_tarasov@mail.ru, N. F. Bakhareva, Dr. of Tech. Sc., Professor, Head of Department of ICT, e-mail: nadin1956_04@inbox.ru, Volga State University of Telecommunications and Informatics, Samara, 443010, Russian Federation

Mathematical Model of the Delay in Communication Networks Based on QS with a Time Lag

In the mathematical modeling of modern computer networks, telecommunication networks, traffic flows, logistics and many others, the methods of queuing theory are widely used. In turn, in studies of queuing systems (QS) G/G/1 with arbitrary distribution laws of intervals between adjacent requirements of the incoming flow and their service time, the spectral decomposition method (MSD) of solving the Lindley integral equation is often used. This method is based on the search for zeros and poles of the constructed spectral decomposition in the form of some fractional-rational function using numerical methods to determine the roots of polynomials. In this case, the coefficients of the polynomial in the numerator of the expansion are expressed through the unknown parameters of the distribution laws used to describe the QS. In the case of teletraffic research, usually these unknown parameters of the distribution laws can be determined through the numerical characteristics of the intervals between traffic packets by the method of moments. The purpose of this article is to present a fundamentally new mathematical model of a system formed by two flows with distribution laws shifted to the right. This is possible only for those probability distribution laws whose density functions are Laplace transformable. The main advantages of such systems, let us call them time lag systems, are that they provide less queue latency compared to conventional systems, and that they extend the range of traffic parameters. The article presents the results obtained on the average delay of requests in the queue for a system with exponential and hyper-Erlang distributions, an algorithm for calculating the average delay and the results of computational experiments in the Mathcad package.
Keywords: queuing system, average delay, Lindley integral equation, Laplace transform, spectral decomposition method

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