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1

Application of HM-network with positive and negative claims for finding of memory volumes in information systems

Matalytski Mikhail, Zając Paweł

Journal of Applied Mathematics and Computational Mechanics

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2019

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Vol. 18, nr 1

41--51

EN

To solve the problem of determining the volume of memory of information systems (IS), it was suggested to use a stochastic model based on the use of HM (Howard-Matalytski) - a queueing network with revenues. This model allows you to take into account the dependencies of the processing times of messages (claims) on their volumes, the possibility of changing the volume of messages over time, and also the possibility of getting computer viruses into it. In such cases the processing of messages in nodes can be interrupted for some random time. Expressions are obtained for the mean (expected) values of the total message volumes in the IS nodes.

2

Finding of expected volumes of requests in systems of the queueing network with a limited amount of spaces of expectations

Zając P., Matalytski M.

Studia Informatica

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2017

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Vol. 38, nr 1B

89--104

EN

We present a method of finding the expected volume of requests in open HM-network with homogeneous requests, bypass of nodes the network service systems. Were considered a case where the changes in volumes associated with transitions between states of the network are deterministic functions dependent states of network and time, and service systems are single line. Assumed that the probability of state network systems, the parameters of entrance flow of messages and service depend on time.

PL

Opisano metodę znalezienia oczekiwanej objętości zgłoszeń w otwartej HM-sieci z jednorodnymi zgłoszeniami i obejściami węzłów sieci systemów obsługi. Rozpatrywano przypadek, gdy zmiany objętości związanych z przejściami między stanami sieci są deterministycznymi funkcjami, zależnymi od stanów sieci i czasu, a systemy obsługi są jednoliniowe. Zakłada się, że prawdopodobieństwo stanów systemów sieci, parametry strumienia wejściowego zgłoszeń i obsługi zależą od czasu.

3

Expected volumes of requests in systems of the queueing network with a limited number of waiting places

Zając P., Matalytski M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2017

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Vol. 22

141--160

EN

We present a method of finding the expected volume of requests in HM-network with homogeneous requests and bypass of the queueing systems of requests. The case was considered when the volume changes associated with the transitions between the states of the network are deterministic functions, depending on the state of the network and time, and the systems are single line. It is assumed that the probability of the states of the network systems, the parameters of the entrance flow of the requests and the service depend on the time.

4

Application of HM-networks with inpatient claims in finding the memory capacity in information systems

Matalytski M., Zajac P.

Journal of Applied Mathematics and Computational Mechanics

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2017

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Vol. 16, nr 3

47--59

EN

To solve the problem of determining the memory capacity of the information systems (IS), the use of the stochastic model is proposed, based on the use of НМ (Howard-Matalytski) - queueing networks with revenues. This model allows one to take into account time dependencies of the message processing from their capacities, the possibility changes of the messages capacities over time and also the possibility of leaving messages from queues in nodes of IS, without getting into them appropriate processing. The expressions for the mean (expected) values of total message capacities in the IS nodes have been obtained.

5

Zastosowanie HM-sieci kolejkowych dla wyznaczenia objętości pamięci systemów informacyjnych

Matalytski M., Naumenko V.

Studia Informatica

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2014

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Vol. 35, nr 3

63--69

PL

Dla rozwiązywania zagadnienia wyznaczenia objętości pamięci stochastycznych systemów informacyjnych (SI) proponowano nowy model matematyczny oparty na zastosowaniu HM (Howard-Matalytski) sieci kolejkowych z dochodami. Wskazany model pozwala na uwzględnienie zależności czasu opracowania komunikatu od jego objętości, a także możliwość zmiany objętości komunikatu z ciągiem czasu. Otrzymano wyrażenia dla wartości oczekiwanych objętości komunikatów w węzłach SI.

EN

To solve the problem of determining of memory volume of stochastic information (IS) systems of various configurations is proposed to use a new model based on the use of HM-queueing network, which takes into account the relationship between the volume of messages and the time of processing nodes in the system, the possibility of changing with time the volume of messages. It is obtained an expressions for the expected volumes of messages in the nodes IS.

6

O niektórych wynikach analizy i optymalizacji HM-sieci i ich zastosowaniach

Kiturko O., Kołuzajewa K., Matałycki M.

Studia Informatica

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2011

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Vol. 32, nr 3A

21-30

PL

W artykule przeprowadzono badanie HM-sieci kolejkowych z dochodami, w przypadku gdy intensywność wchodzącego strumienia zgłoszeń i intensywności obsługiwania zgłoszeń w systemach obsługi zależą od ich ilości w systemach i od czasu. Rozpatrywane są zadania optymalizacji i optymalnej kontroli dla tych sieci. Przedstawione zostały przykłady zastosowań HM-sieci do prognozowania dochodów różnych obiektów komputerowych.

EN

Investigation of HM queueing networks with incomes in case when arrival rate of messages and service rates of messages in queueing systems depend on their number and time is carried out. Optimization and optimal control problems for these networks are observed. Examples of HM-networks applications for income forecasting of different computer objects are presented.

7

Method of finding incomes in HM-Networks with time-dependent intensity of requests service

Matalytski M., Kiturko O., Czhornaja N.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2011

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Vol. 10, nr 2

169-178

EN

The article deals with an HM-network with time-dependent service rates of applications in the systems. The presented methods for finding the expected income systems: the direct method, Laplace transforms, the method of difference scheme, are implemented using the software package Mathematica. Expected earnings are important for solving problems of optimization and control of HM-networks, which are used in practice as stochastic models of various objects in computer technology, insurance, logistics, and medicine.

8

Analysis of HM-networks with stochastic incomes from transitions between states

Matalycki M., Koluzaewa K.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2009

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Vol. 8, nr 2

105-118

EN

In article method of finding of expected incomes in systems of HM-network of arbitrary topology when incomes from transitions between network states are stochastic variables with given mean values is proposed. For expected incomes the system of linear non-homogeneous ordinary differential equations was obtained, to solve it we can find incomes in network systems.

9

Analysis and optimization of Markov HM-networks with stochastic incomes from transitions between their states

Matalycki M., Koluzaewa K.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2008

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Vol. 7, nr 2

51-62

EN

Expressions for expected incomes and variations of incomes in systems of Markov HM-networks, when service rates of messages are depending or not depending of network's states are obtained. The case when incomes of transitions between network's states are random variables with the set moments of first two orders is considered. Solution of some optimization problems for HM-networks are resulted.