Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
A closed exponential queueing G-network of unreliable multi-server nodes was studied under the asymptotic assumption of a large number of customers. The process of changing the number of functional servers in network nodes was considered as the birth-death process. The process of changing the number of customers at the nodes was considered as a continuous-state Markov process. It was proved that its probability density function satisfies the Fokker-Planck-Kolmogorov equation. The system of differential equations for the first-order and second-order moments of this process was derived. This allows us to predict the expectation, the variance and the pairwise correlation of the number of customers in the G-network nodes both in the transient and steady state.
Rocznik
Tom
Strony
91--102
Opis fizyczny
Bibliogr. 17 poz., rys.
Twórcy
autor
- Faculty of Mathematics and Informatics, Yanka Kupala State University of Grodno, Grodno, Belarus
Bibliografia
- [1] Gelenbe, E. (1991). Product form queueing networks with negative and positive customers. Journal of Applied Probability, 28(3), 656-663.
- [2] Gelenbe, E. (1993). G-networks with triggered customer movement. Journal of Applied Probability, 30(3), 742-748.
- [3] Gelenbe, E. (1993). G-networks with signals and batch removal. Probability in the Engineering and Informational Sciences, 7(3), 335-343.
- [4] Fourneau, J.M. (2016). G-networks of unreliable nodes. Probability in the Engineering and Informational Sciences, 30(3), 361-378.
- [5] Caglayan, M.U. (2017). G-networks and their applications to machine learning, energy packet networks and routing: introduction to the special issue. Probability in the Engineering and Informational Sciences, 31, 381-395.
- [6] Zhang, Y. (2021). Optimal energy distribution with energy packet networks. Probability in the Engineering and Informational Sciences, 35(1), 75-91.
- [7] Matalytski, M., & Naumenko, V. (2014). Investigation of G-network with signals at transient behaviour. Journal of Applied Mathematics and Computational Mechanics, 13(1), 75-86.
- [8] Matalytski, M., & Naumenko, V. (2017). Analysis of the queueing network with a random bounded waiting time of positive and negative customers at a non-stationary regime. Journal of Applied Mathematics and Computational Mechanics, 16(1), 97-108.
- [9] Gelenbe, E. (1989). Random neural networks with negative and positive signals and product form solution. Neural Computation, 1(4), 502-510.
- [10] Gelenbe, E. (1990). Stability of the random neural network model. Neural Computation, 2(2), 239-247.
- [11] Gelenbe, E. (1993). Learning in the recurrent random neural network. Neural Computation, 5(1), 154-164.
- [12] Gelenbe, E. (2009). Steps toward self-aware networks. Communications of the ACM, 52(7), 66-75.
- [13] Medvedev, G.A. (1975). Closed queueing systems and their optimization. Proceedings of the USSR Academy of Sciences. Engineering Cybernetic, 6, 65-73 (In Russian).
- [14] Matalytski, M., Rusilko T., & Pankov A. (2013). Asymptotic analysis of the closed queueing structure with time-dependent service parameters and single-type messages. Journal of Applied Mathematics and Computational Mechanics, 12(2), 73-80.
- [15] Rusilko, T.V. (2021). The first two orders moments of determination method for the state vector of the queueing network in the asymptotic case. Vesnik of Yanka Kupala State University of Grodno. Series 2. Mathematics. Physics. Informatics, Computer Technology and its Control, 11(2), 152-161 (In Russian).
- [16] Gardiner, K.V. (1986). Stochastic Methods in Natural Sciences. Moscow: Mir (In Russian).
- [17] Rusilko, T.V. (2021). Network stochastic call centre model. CEUR Workshop Proceedings: Selected Papers of the 6th International Scientific and Practical Conference Distance learning technologies (Vol. 3057). Yalta, Crimea, 91-101.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c577ca7b-7750-4beb-aa96-d5364c4a4f30