About one method of finding expected incomes in HM-queueing network with positive customers and signals

• Autorzy: Matalytski M.

Identyfikatory

DOI

10.17512/jamcm.2016.1.09

• Języki publikacji: EN

Abstrakty

EN

In the paper an open Markov HM(Howard-Matalytski)-Queueing Network (QN) with incomes, positive customers and signals (G(Gelenbe)-QN with signals) is investigated. The case is researched, when incomes from the transitions between the states of the network are random variables (RV) with given mean values. In the main part of the paper a description is given of G-network with signals and incomes, all kinds of transition probabilities and incomes from the transitions between the states of the network. The method of finding expected incomes of the researched network was proposed, which is based on using of found approximate and exact expressions for the mean values of random incomes. The variances of incomes of queueing systems (QS) was also found. A calculation example, which illustrates the differences of expected incomes of HM-networks with negative customers and QN without them and also with signals, has been given. The practical significance of these results consist of that they can be used at forecasting incomes in computer systems and networks (CSN) taking into account virus penetration into it and also at load control in such networks.

Słowa kluczowe

EN

HM-queueing network; positive and negative customers; signals; expected incomes; ransient regime

PL

kolejkownie sieci; systemy kolejkowe; pozytywny klient; negatywny klient; teoria kolejek

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 1
• Strony: 87--98
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Matalytski M.

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

Bibliografia

• [1] Gelenbe E., G-networks with triggered customer movement, Journal of Applied Probability 1993, 30, 742-748.
• [2] Matalytski M., Naumenko V., Investigation of G-network with signals at transient behavior, Journal of Applied Mathematics and Computational Mechanics 2014, 13(1), 75-86.
• [3] Naumenko V., Matalytski M., Finding the expected incomes in the Markov G-network with signals, Vestnik of GrSU. A Series of Mathematics, Physics, Computer Science, Computer Facilities and Management 2014, 2, 134-143.
• [4] Naumenko V., Matalytski M., Investigation and application of G-networks with incomes and signals with random time activation Vestnik of GrSU. A Series of Mathematics, Physics, Computer Science, Computer Facilities and Management 2014, 3, 142-152.
• [5] Matalytski M., On some results in analysis and optimization of Markov networks with incomes and their application, Automation and Remote Control 2009, 70(10), 1683-1697.
• [6] Naumenko V., Matalytski M., Analysis of Markov net with incomes, positive and negative customers, Informatics 2014, 1, 5-14.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.