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1
Content available Finding the expected revenues in Markov networks with positive and negative customers at a stationary regime
Matalytski M., Kopats D.
Journal of Applied Mathematics and Computational Mechanics
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2018
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Vol. 17, nr 1
49--60
EN
Finding the expected revenues in the queueing systems (QS) of open Markov G-networks of two types, with positive and negative customers and with positive customers and signals, has been described in the paper. A negative customer arriving to the system destroys one positive customer if at least one is available in the system, thus reducing the number of positive customers in the system by one. The signal, coming into an empty system (where there are no positive customers), does not have any impact on the network and immediately disappears from it. Otherwise, if the system is not empty, when it receives a signal, the following events can occur: the incoming signal instantly moves the positive customer from one QS into another with a certain probability, or with the other probability, the signal is triggered as a negative customer.
2
Content available Application of HM-networks with unreliable systems for finding the memory capacity in the information systems
Matalytski M., Zajac P., Kopats D.
Journal of Applied Mathematics and Computational Mechanics
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2018
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Vol. 17, nr 2
51--63
EN
To solve the problem of determining the memory capacity of the information systems (IS), it was proposed to use a stochastic model, based on the use of HM (Howard-Matalytski) - queueing networks with incomes. This model takes into account the servicing of requests along with their volumes, the ability to change the volumes of the requests over time and the possibility of damaging IS nodes and their repairs, so servicing of demands can be interrupted randomly. The expressions are generated for the mean (expected) values of total requests volumes in the IS nodes.
3
Content available 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.
4
Content available Diffusion approximation of the network with limited number of same type customers and time dependent service parameters
Matalytski M., Kopats D.
Journal of Applied Mathematics and Computational Mechanics
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2016
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Vol. 15, nr 2
77--84
EN
The article presents research of an open queueing network (QN) with the same types of customers, in which the total number of customers is limited. Service parameters are dependent on time, and the route of customers is determined by an arbitrary stochastic transition probability matrix, which is also dependent on time. Service times of customers in each line of the system is exponentially distributed. Customers are selected on the service according to FIFO discipline. It is assumed that the number of customers in one of the systems is determined by the process of birth and death. It generates and destroys customers with certain service times of rates. The network state is described by the random vector, which is a Markov random process. The purpose of the research is an asymptotic analysis of its process with a big number of customers, obtaining a system of differential equations (DE) to find the mean relative number of customers in the network systems at any time. A specific model example was calculated using the computer. The results can be used for modelling processes of customer service in the insurance companies, banks, logistics companies and other organizations.
5
Content available 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.
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