ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 5. Vol. 24. 2018

DOI: 10.17587/it.24.306-312

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, L. V. Lipilina, Postgradulate Student, e-mail: mila199113@gmail.com, Povolzhsky State University of Telecommunications and Informatics, Samara, 443010, Russia

Analysis of Non-Markov Queuing Networks on the Basis of the Equations Balance of Flows

The article proposes models of mathematical multiplexing and demultiplexing of flows, as well as expressions for determining the numerical characteristics of the distribution of the outflow intervals from the queuing system (QS). Together, they allow us to write the equilibrium equations for the mean and variance of the distribution of time intervals between consecutive requirements in
queuing networks with arbitrary laws receipts and services. On the place of nodes of a queuing network are considered QS M^-/M^-/1 with delay in time, H₂/H₂/1 and H₂/M/1. Under general assumptions about the probability distribution of time intervals between requirements in the input flows and the time of service in the nodes, the proposed approach makes it possible to determine the average
values and variances of time intervals between the requirements of all queuing network flows, as well as all the main indicators of the functioning of such networks. Such an approach can also be extended, if necessary, for third-order moments, which from the point of view of probability theory is more accurate than the calculation at the level of two moments of the distributions. Such an approach can also be extended, if necessary, for third-order moments. From the point of view of probability theory, this will be more
accurate than calculating at the level of two moments of distribution. Under incomplete information on the laws of flows distributions, the proposed approach to analyzing the performance of non-Markov queuing networks is currently acceptable.
Keywords: queuing networks, queuing systems M^-/M^-/1 with delay in time, H₂/H₂/1 and H₂/M/1, aggregation and rarefaction of flows

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