Finding the expected revenues in Markov networks with positive and negative customers at a stationary regime

• Autorzy: Matalytski M. , Kopats D.

Identyfikatory

DOI

10.17512/jamcm.2018.1.05

• Języki publikacji: EN

Abstrakty

EN

Finding the expected revenues in the queueing systems (QS) of open Markov G-networks of two types, with positive and negative customers and with positive customers and signals, has been described in the paper. A negative customer arriving to the system destroys one positive customer if at least one is available in the system, thus reducing the number of positive customers in the system by one. The signal, coming into an empty system (where there are no positive customers), does not have any impact on the network and immediately disappears from it. Otherwise, if the system is not empty, when it receives a signal, the following events can occur: the incoming signal instantly moves the positive customer from one QS into another with a certain probability, or with the other probability, the signal is triggered as a negative customer.

Słowa kluczowe

EN

G-network; positive and negative customers; signals; expected revenues; stationary regime

PL

sieć G; pozytywny klient; negatywny klient; system kolejkowy

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2018
• Tom: Vol. 17, nr 1
• Strony: 49--60
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Matalytski M.

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

autor

Kopats D.

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

Bibliografia

• [1] Crabill, T. (1972). Optimal control of a service facility with variable exponential service times and constant arrival rate. Management Science, 18, 560-566.
• [2] Foschini, G. (1977). On heavy traffic diffusion analysis and routing in packet switched networks. Computer Performance, 9, 499-514.
• [3] Stidham, S., & Weber, R. (1993). A survey of Markov decision models for control of networks of queue. Queueing Systems, 3, 291-314.
• [4] Matalytski, M., & Pankov, A. (2003). Analysis of stochastic model of the changing of incomes in the open banking network. Vestnik GrSU, 3, 5, 19-29.
• [5] Matalytski, M., & Pankov, A. (2003). Incomes probabilistic models of banking network. Scientific Research of the Institute of Mathematics and Computer Science of Czestochowa University of Technology, 11, 2, 99-104.
• [6] Matalytski, M. (2009). On some results in analysis and optimization of Markov networks with incomes and their application. Automation and Remote Control, 70, 10, 1683-1697.
• [7] Koluzaeva, E., & Matalytski, M. (2011). Analysis and Optimization of Queueing Networks. Saarbrucken: LAPLAMBERT Academic Publishing.
• [8] Howard, R. (1964). Dynamic Programming and Markov Processes. Moscow: Soviet Radio.
• [9] Matalytski, M. (2015). Analysis and forecasting of expected incomes in Markov network with bounded waiting time for the claims. Automation and Remote Control, 76, 6, 1005-1017.
• [10] Matalytski, M. (2015). Analysis and forecasting of expected incomes in Markov network with unreliable servicing systems. Automation and Remote Control, 15, 11, 2179-2189.
• [11] Matalytski, M., & Naumenko, V. (2016). Stochastic Networks with Non-Standard Customers Movement. Grodno: GrSU.
• [12] Gelenbe, E. (1991). Product form queuing networks with negative and positive customers. Journal of Applied Probability, 28, 656-663.
• [13] Gelenbe, E. (1993). G-networks with triggered customer movement. Journal of Applied Probability, 30, 742-748.
• [14] Prokhorov, Y.V., & Rozanov, U.A. (1973). The Theory of Probability. Moscow: Science.
• [15] Bocharov, P.P., & Vishnevsky, V.M. (2003). G-networks: the development of the theory of multiplicative network. Automation and Remote Control, 5, 46-74.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).