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The analysis of the three-level HM-network and its application for the incomes forecasting of a logistic transport system

Matalytski M., Kiturko O.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 3

141--153

EN

Investigation of the closed three-level HM-network, which is the model of the production transportation in a logistic transport system, is conducted in this article. The approximated expression for the expected income of the central system and the system of the nonhomogeneous differential equations for an average number of messages in network systems, when the incomes from transitions between network’s states are random variables with the set moments of the first two orders, is received. The relation for variance of the income of the central system of network (system of the top level) is also received.

2

Application of a z-transforms method for investigation of Markov G-networks

Matalytski M., Naumenko V.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 1

61--73

EN

The purpose of this research paper is to find the expected incomes in open Markov queueing networks with incomes, positive and negative messages at any time by the multidimensional transformations. Investigations were carried out in cases when incomes from the network transitions between the states are deterministic functions not dependent on network states and time. It is assumed that all network systems are one-line. It was proved the theorem on the expression for the multidimensional z-transform. An algorithm was proposed for calculation of expected incomes. It is calculated an example on the PC.

3

On analytical investigation and simulation of HM-networks with priority requests

Bekish N., Kiturko O., Matalytski M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2012

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Vol. 11, nr 1

5-14

EN

This paper describes finding the expected incomes HM (Howard-Matalytski) - networks with priority requests both analytically and through simulation. The analytical results for the study of such networks can be used as stochastic models for the prediction of income of enterprises and banking information networks, logistics systems, transportation and other facilities. The basic principles of simulation networks using discrete-event simulation, using the open software library SimPy (Simulation in Python) package of Python. This library allows for the simulation of different processes in parallel, and describes the logic of interaction between processes. The application of simulation for solving the problems of finding the expected incomes the logistics transport system is considered.

4

Finding of incomes of HM-network with limited waiting times in queues by means of the successive approximations method

Kosarava K., Matalytski M., Rozau K.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2012

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Vol. 11, nr 1

41-52

EN

The article is devoted to the successive approximations method combined with the series method and its application for finding of expected incomes in HM-network systems with limited waiting times in queues and one-type messages. The properties of successive approximations were researched. The example of implementation of the described method is calculated.

5

Finding of expected incomes in open exponential networks of arbitrary architecture

Matalycki M., Koluzaewa K.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2007

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Vol. 6, nr 1

179-190

EN

Investigation of the open exponential queueing network of arbitrary architecture with incomes is carry out in paper. The incomes of transitions between network's states are random variables with specified moments of two first orders. The expressions for expected incomes and variances of incomes are received.