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1

Finding the probabilistically-temporal characteristics of Markov G-network with batch removal of positive customers

Matalytski M., Naumenko V., Kopats D.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 4

125-136

EN

The investigation of a Markov queueing network with positive and negative customers and positive customers batch removal has been carried out in the article. The purpose of the research is analysis of such a network at the non-stationary regime, finding the time-dependent state probabilities and mean number of customers. In the first part of this article, a description of the G-network operation is provided with one-line queueing systems. When a negative customer arrives to the system, the count of positive customers is reduced by a random value, which is set by some probability distribution. Then for the non-stationary state probabilities a Kolmogorov system was derived of differencedifferential equations. A technique for finding the state probabilities and the mean number of customers of the investigated network, based on the use of an apparatus of multidimensional generating functions has been proposed. The theorem about the expression for the generating function has been given. A model example has been calculated.

2

Analysis of the queueing network with a random waiting time of negative customers at a non-stationary regime

Naumenko V., Matalytski M., Kopats D.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 3

111--122

EN

In the article a queueing network (QN) with positive customers and a random waiting time of negative customers has been investigated. Negative customers destroy positive customers on the expiration of a random time. Queueing systems (QS) operate under a heavy-traffic regime. The system of difference-differential equations (DDE) for state probabilities of such a network was obtained. The technique of solving this system and finding mean characteristics of the network, which is based on the use of multivariate generating functions was proposed.

3

Investigation of G-network with signals at transient behavior

Matalytski M., Naumenko V.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 1

75--86

EN

G-queueing network with positive messages and signals at transient behavior is considered. A system of difference-differential equations for the state probabilities of the network is obtained. To find them and the average characteristics of the network a technique was applied based on the use of apparatus of multivariate generating functions. An expression for the generating function was obtained. An example is calculated.

4

State probabilities of computer network models with dependent on time arrival and service parameters

Matałycki M., Koluzaewa K.

Informatyka Teoretyczna i Stosowana

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2008

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R. 8, nr 14

7-18

EN

In this article the method of multidimensional generating functions is observed. It can be applied for finding state probabilities of stochastic queueing models of computer and telecommunication networks (ICTN) of arbitrary topology, which functioning under condition of heavy loading. Investigations were carried out in transitional (nonsteady state); open Markovian queueing networks (QN) with dependent on time arrival process and service parameters are used as models. Expressions for state probabilities were obtained as multidimensional functional series.

5

Queueing networks with multi-type messages of multiple classes: analysis and applications

Matalycki M., Koluzaewa K.

Informatyka Teoretyczna i Stosowana

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2006

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R. 6, nr 10

19-26

EN

This paper provides the analysis and applications of networks with multi-type messages of multiple classes in systems. The network state is a vector, which components represent the number of messages in queues of the system. We obtained the sufficient conditions of representing the stationary distribution of the process, describing these networks, in the product form of factors characterizing separate systems.