Abstract
The authors propose a mathematical model for a multi-channel queueing system with feedback in which one part of calls instantaneously enters the system for repeated service and the other part either retries in some random time or finally leaves the system. The behavior of the serviced calls is randomized. Both exact and asymptotic methods are developed to calculate the characteristics of the proposed model. The results of numerical experiments are presented.
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References
M. H. Lee, A. Birukou, A. Dudin, V. Klimenok, O. Kostyukova, and C. H. Choe, “Queueing model of a single-level single-mediator with cooperation of the agents,” in: N. T. Nguyen (ed.), Agent and Muli-Agent Systems: Technology and Applications, Springer, Heidelberg–Dordrecht (2007), pp. 447–455.
N. Gnanasambandam, S. Lee, N. Gautam, S. R. T. Kumara, W. Peng, V. Manikonda, M. Brinn, and M. Greaves, “Reliable MAS performance prediction using queueing models,” in: Proc. IEEE 1st Symp. on Multi-Agent Security and Survivability, Philadelphia, Pennsylvania at Drexel University, Aug. 30–31 (2004), pp. 55–64.
N. Gnanasambandam, S. Lee, and S. R. T. Kumara, “An autonomous performance control framework for distributed multi-agent systems: A queueing theory based approach,” in: Proc. AAMAS’05, Utrecht, Netherlands, July 25–29 (2005), pp. 1313–1314.
L. Takacs, “A single-server queue with feedback,” Bell System Technical J., 42, 505–519 (1963).
L. Takacs, “A queueing model with feedback,” Operations Research, 11, No. 4, 345–354 (1977).
A. A. Nazarov, S. P. Moiseeva, and A. S. Morozova, “Examination of QS with repeated service and unlimited number of servicing instruments by the method of ultimate decomposition,” Vychisl. Tekhnologii, 13, Issue 5, 88–92 (2008).
S. P. Moiseeva and I. A. Zahorolnaya, “Mathematical model of parallel service of multiple demands with retrials,” Avtometriya, 47, Issue 6, 51–58 (2011).
A. N. Dudin, A. V. Kazimirsky, V. I. Klimenok, L. Breuer, and U. Krieger, “The queueing model MAP/PH/1/N with feedback operating in a Markovian random environment,” Austrian J. of Statistics, 34, No. 2, 101–110 (2005).
M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, John Hopkins University Press, Baltimore (1981).
J. R. Artalejo and A. Gomez-Corral, Retrial Queueing. A Computational Approach, Springer, Heidelberg–Dordrecht (2008).
L. M. Abolnikov and E. A. Dzhalalov, “A queueing system with feedback. The duality principle and optimization,” Avtom. i Telemekhanika, No. 1, 17–28 (1978).
A. I. Gromov, “A two-phase queueing system with feedback,” Avtom. i Telemekhanika, No. 12, 93–97 (1988).
R. W. Wolff, “Poisson arrivals see time averages,” Oper. Research, 30, No. 2, 223–231 (1992).
E. A. Pekoz and N. Joglekar, “Poisson traffic flow in a general feedback,” J. of Applied Probability, 39, No. 3, 630–636 (2002).
V. S. Korolyuk and V. V. Korolyuk, Stochastic models of Systems, Kluwer, Boston (1999).
L. Ponomarenko, C. S. Kim, and A. Melikov, Performance Analysis and Optimization of Multi-Traffic on Communication Networks, Springer, Heidelberg–Dordrecht–London–New York (2010).
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, January–February, 2016, pp. 64–77.
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Koroliuk, V.S., Melikov, A.Z., Ponomarenko, L.A. et al. Methods for Analysis of Multi-Channel Queueing System with Instantaneous and Delayed Feedbacks. Cybern Syst Anal 52, 58–70 (2016). https://doi.org/10.1007/s10559-016-9800-y
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DOI: https://doi.org/10.1007/s10559-016-9800-y