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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

2019

Vol. 18, nr 1

41--51

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.

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

2018

Vol. 17, nr 2

51--63

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.

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

2017

Vol. 22

141--160

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.