Geodesic
Investigation in non-stationary mode of $G$-network with signal and group removal customers by successive approximation method
Problemy fiziki, matematiki i tehniki, no. 4 (2018), pp. 85-89.

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A study was conducted in the $G$-network transition mode with positive customers and signals, when they move the customers to another system or destroy a group of positive customers in it, reducing their number by a random amount, which is specified by some probability distribution. A signal arriving at a system in which there are no positive applications does not have any influence on the queuing network and immediately disappears from it. Streams of positive applications and signals coming to each of the network systems are independent. For nonstationary probabilities of network states, a system of Kolmogorov difference-differential equations is derived. A method for finding them is proposed. It is based on the use of a modified method of successive approximations, combined with the method of series. The properties of successive approximations are considered.
Keywords: Markov $G$-network, positive and negative customers, signals, group removal, non-stationary mode, non-stationary state probability. 
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D. Y. Kopats; M. A. Matalytski. Investigation in non-stationary mode of $G$-network with signal and group removal customers by successive approximation method. Problemy fiziki, matematiki i tehniki, no. 4 (2018), pp. 85-89. http://geodesic.mathdoc.fr/item/PFMT_2018_4_a14/

[1] E. Gelenbe, “Product form queueing networks with negative and positive customers”, Journal of Applied Probability, 28 (1991), 656–663 | DOI | MR | Zbl

[2] E. Gelenbe, “G-networks with triggered customer movement”, Journal of Applied Probability, 30 (1993), 742–748 | DOI | MR | Zbl

[3] E. Gelenbe, “G-networks with signals and batch removal”, Probability in the Engineering and Informational Sciences, 7 (1993), 335–342 | DOI

[4] M.A. Matalytskii, V.V. Naumenko, Stokhasticheskie seti s nestandartnymi peremescheniyami zayavok, GrGU, Grodno, 2016, 348 pp.

[5] M. Matalytski, V. Naumenko, “Investigation of G-network with signals at transient behavior”, Journal of Applied Mathematics and Computational Mechanics, 13:1 (2014), 75–86 | DOI | MR

[6] D.Ya. Kopat, M.A. Matalytskii, “Analiz seti s polozhitelnymi i otritsatelnymi zayavkami razlichnykh tipov v perekhodnom rezhime”, Vestnik GrGU. Seriya 2, 2017, no. 3, 150–162

[7] L.D. Kudryavtsev, Kurs matematicheskogo analiza, v 3 t., v. 2, Vysshaya shkola, M., 2006, 720 pp.