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

• Autorzy: Matalytski M. , Naumenko V.
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

open G-network; positive and negative messages; expected incomes; z-transforms method

PL

dochody oczekiwane

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 1
• Strony: 61--73
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Matalytski M.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

autor

Naumenko V.

• Faculty of Mathematics and Computer Science, Grodno State University Grodno, Belarus

Bibliografia

• [1] Matalytski M., Some results of the analysis and optimization of Markov networks with incomes and their applications, Automation and Remote Control 2009, 10, 97-113 (in Russian).
• [2] Gelenbe E., Product form queueing networks with negative and positive customers, Journal of Applied Probability 1991, 28, 656-663.
• [3] Bocharov P., Vishnevsky V., G-networks: the development of the theory of multiplicative networks, Automation and Remote Control 2003, 5, 46-74 (in Russian).
• [4] Naumenko V., Matalytski M., Analysis networks with positive and negative messages at transition behavior. Herald of Tomsk State University. Management, Computer Science and Informatics 2013, 4, 61-70 (in Russian).
• [5] Naumenko V., Matalytski M., Analysis of Markov networks with incomes, positive and negative messages, Informatics 2014, 1, 36-44 (in Russian).
• [6] Kosareva E., Matalytski M., Rozov K., Finding incomes in HM-networks with limited waiting time messages by successive approximations, combined with the method of series, Herald of Grodno State University Yanka Kupala 2012, 2, 3, 125-130 (in Russian).
• [7] Naumenko V., Analysis of incomes in Markov G-networks by method of successive approximations, Herald of Grodno State UniversityYanka Kupala 2014, 2, 1 (in Russian).
• [8] Matalytski M., Tikhonenko O., Koluzaeva E., Systems and QN Networks: Analysis and Application, Grodno State University, Grodno 2011, 818 p. (in Russian).
• [9] Matalytski M., Koluzaeva E., Analysis of expected incomes in open network using z transforms, Herald of Grodno State UniversityYanka Kupala 2008, 2, 3, 11-19.
• [10] Koluzaeva E., Finding the expected incomes in the open two-node HM-network using z-transforms, Herald of Grodno State UniversityYanka Kupala 2010, 2, 1, 20-30.