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ANALYSIS OF THE NETWORK WITH MULTIPLE CLASSES OF POSITIVE CUSTOMERS AND SIGNALS AT A NON-STATIONARY REGIME

Published online by Cambridge University Press:  13 July 2018

M. Matalytski  and
D. Kopats
M. Matalytski
Affiliation:
Czestochowa University of Technology, Institute of Mathematics, Czestochowa, Poland E-mail: m.matalytski@gmail.com
D. Kopats
Affiliation:
Faculty of Mathematics and Computer Science, Grodzenskij dzyarzhauny universitat imya Yanki Kupaly, Grodno, Belarus E-mail: dk80395@mail.ru
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Abstract

The object of research is G-network with positive customers and signals of multiple classes. The present paper describes an analysis of this network at a non-stationary regime, also provided a description of method for finding non-stationary state probabilities.

At the beginning of the article, a description of the network with positive customers and signals is given. A signal when entering the system destroys a positive customer of its type or moves the customer of its type to another system. Streams of positive customers and signals arriving to each of the network systems are independent. Selection of positive customers of all classes for service – randomly. For non-stationary state probabilities of the network, the system of Kolmogorov difference-differential equations (DDE) has been derived. It is solved by a modified method of successive approximations, combined with the method of series. The convergence of successive approximations with time has been proved to the stationary distribution of probabilities, the form of which is indicated in the article, and the sequence of approximations converges to the unique solution of the DDE system. Any successive approximation is representable in the form of a convergent power series with an infinite radius of convergence, the coefficients of which satisfy recurrence relations, which is convenient for computer calculations.

The obtained results can be applied for modeling behavior of computer viruses and attack in computer systems and networks, for example, as model impact of some file viruses on server resources.

Keywords

classescombined with the method of seriesG-networkmethod of successive approximationsnon-stationary regimepositive customers and signals of multiple
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 3 , July 2019 , pp. 404 - 416
Copyright
Copyright © Cambridge University Press 2018 

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