Abstract
A method for determination of the time dependence of the anticipated income in the systems of Markov queuing networks with incomes and positive and negative customers was proposed. Subject to this proviso, the incomes from the transitions between the network states are deterministic functions depending on its state and time, and the system incomes in a time unit when they do not change their states depend only on these states. An illustrative example of calculations was given which shows that the anticipated incomes of the network systems can be both increasing and decreasing time functions assuming positive and negative values.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Crabill, T., Optimal Control of a Service Facility with Variable Exponential Service Times and Constant Arrival Rate, Manage. Sci., 1972, no. 18, pp. 560–566.
Foschini, G., On Heavy Traffic Diffusion Analysis and Dynamic Routing in Packet Switched Networks, Comput. Manage., 1977, no. 10, pp. 499–514.
Stidham, S. and Weber, R., A Survey of Markov Decision Models for Control of Networks of Queue, Queuing Syst., 1993, no. 3, pp. 291–314.
Matalytski, M. and Pankov, A., Analysis of the Stochastic Model of the Changing of Incomes in the Open Banking Network, Comput. Sci., 2003, vol. 3, no. 5, pp. 19–29.
Matalytski, M. and Pankov, A., Incomes Probabilistic Models of the Banking Network, Sci. Res. Inst. Math. Comput. Sci. Czestochowa Univ. Technol., 2003, vol. 1, no. 2, pp. 99–104.
Matalytski, M., On Some Results in Analysis and Optimization of Markov Networks with Incomes and Their Applications, Autom. Remote Control, 2009, vol. 70, no. 10, pp. 1683–1697.
Koluzaeva, E.V. and Matalytski, M.A., Analysis and Optimization of the Queuing Networks, Saarbrucken: LAP LAMBERT Acad. Publishing, 2011.
Khovard, R., Dinamicheskoe programmirovanie i markovskie protsessy (Dynamic Programming and Markov Processes), Moscow: Sovetskoe Radio, 1964.
Matalytski, M., Analysis and Forecasting of Expected Incomes in Markov Networks with Bounded Waiting Time for the Claims, Autom. Remote Control, 2015, vol. 76, no. 6, pp. 1005–1017.
Matalytski, M., Analysis and Forecasting of Expected Incomes in Markov Networks with Unreliable Servicing Systems, Autom. Remote Control, 2015, vol. 76, no. 12, pp. 2179–2189.
Gelenbe, E., Product Form Queuing Networks with Negative and Positive Customers, J. Appl. Probab., 1991, vol. 28, pp. 656–663.
Bocharov, P.P. and Vishnevskii, V.M., G-Networks: Development of the Theory of Multiplicative Networks, Autom. Remote Control, 2003, vol. 63, no. 5, pp. 946–974.
Valeev, K.G. and Zhautykov, O.A., Beskonechnye sistemy differentsial’nykh uravnenii (Infinite Systems of Differential Equations), Almaty: Nauka, 1974.
Korobeinik, Yu.F., Differential Equations of Infinite Order and Infinite Systems of Differential Equations, Izv. Akad. Nauk SSSR, Mat., 1970, vol. 31, no. 4, pp. 881–922.
Matalytski, M. and Naumenko, V., Simulation Modeling of HM-Networks with Consideration of Positive and Negative Messages, J. Appl. Math. Comput. Mechan., 2015, vol. 14, no. 2, pp. 49–60.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.A. Matalytski, 2017, published in Avtomatika i Telemekhanika, 2017, No. 5, pp. 56–70.
Rights and permissions
About this article
Cite this article
Matalytski, M.A. Forecasting anticipated incomes in the Markov networks with positive and negative customers. Autom Remote Control 78, 815–825 (2017). https://doi.org/10.1134/S0005117917050046
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117917050046