Finding the probabilistically-temporal characteristics of Markov G-network with batch removal of positive customers

• Autorzy: Matalytski M. , Naumenko V. , Kopats D.

Identyfikatory

DOI

10.17512/jamcm.2016.4.14

• Języki publikacji: EN

Abstrakty

EN

The investigation of a Markov queueing network with positive and negative customers and positive customers batch removal has been carried out in the article. The purpose of the research is analysis of such a network at the non-stationary regime, finding the time-dependent state probabilities and mean number of customers. In the first part of this article, a description of the G-network operation is provided with one-line queueing systems. When a negative customer arrives to the system, the count of positive customers is reduced by a random value, which is set by some probability distribution. Then for the non-stationary state probabilities a Kolmogorov system was derived of differencedifferential equations. A technique for finding the state probabilities and the mean number of customers of the investigated network, based on the use of an apparatus of multidimensional generating functions has been proposed. The theorem about the expression for the generating function has been given. A model example has been calculated.

Słowa kluczowe

EN

G-network; positive and negative customers; customers batch removal; nonstationary regime; generation function; state probabilities

PL

teoria kolejek; systemy kolejkowe; pozytywny klient

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 4
• Strony: 125--136
• Opis fizyczny: Bibliogr. 8 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

autor

Kopats D.

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

Bibliografia

• [1] Gelenbe E., Product form queueing networks with negative and positive customers, Journal of Applied Probability 1991, 28, 656-663.
• [2] Naumenko V., Pankov A., Kopats D., Investigation of Markov G-network with positive customers batch removal in transient regime. [In Russian: Issledovaniye markovskoy G-seti s gruppovym udaleniyem polozhitel'nykh zayavok v perekhodnom rezhime]. Vestnik of GrSU. Ser 2, 2016, 3.
• [3] Matalytski M., Naumenko V., Stochastic networks with non-standard customers movement. [In Russian: Stokhasticheskiye seti s nestandartnymi peremeshcheniyami zayavok], Monograph, GrSU, Grodno 2016.
• [4] Naumenko V., Matalytski M., Network analysis with positive and negative requests in transitional mode. [In Russian: Analiz seti s polozhitel'nymi i otritsatel'nymi zaiavkami v perekhodnom rezhime], Vestnik of GrSU, Ser 2. 2016, 3(159), 135-142.
• [5] Matalytski M., Naumenko V., Non-stationary analysis of queueing network with positive and negative messages, Journal of Applied Mathematics and Computational Mechanics 2013, 12(2), 61-71.
• [6] 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.
• [7] Matalytski M., Naumenko V., Investigation of G-network with random delay of signals at nonstationary behavior, Journal of Applied Mathematics and Computational Mechanics 2014, 13(3), 155-166.
• [8] Gelenbe E., G-networks with signals and batch removal, Probability in the Engineering and Informational Sciences 1993, 7, 335-342.

Uwagi

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