Abstract
We propose a method to analyze M/G/1/m queuing systems with the function of random dropping of customers and service time distribution dependent on the queue length. We obtain formulas to determine the Laplace transforms of the distribution of the number of customers in the system during busy period and of the distribution function of the busy period and to calculate the stationary characteristics. The relations for the stationary characteristics are tested using simulation models constructed with the use of the GPSS World tools. The results of the use of various control tools of system parameters are compared in the example.
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References
A. N. Dudin and V. I. Klimenok, “BMAP/G/1 queueing system with alternating operating mode,” Avtom. i Telemekhanika, No. 10, 97–107 (1999).
A. Chydziński, Nowe modele kolejkowe dla wezlow sieci pakietowych [in Polish], Pracownia Komputerowa Jacka Skalmierskiego, Gliwice (2013).
K. Sriram and D. M. Lucantoni, “Traffic smoothing effects of bit dropping in a packet voice multiplexer,” IEEE Trans. Comm., 37, No. 7, 703–712 (1989).
K. Yu. Zhernovyi and Yu.V. Zhernovyi, “Mθ/G/1/m and Mθ/G/1 systems with the service time dependent on the queue length,” J. of Communic. Technology and Electronics, 58, No. 12, 1267–1275 (2013).
K. Yu. Zhernovyi, “Stationary characteristics of the Mθ/G/1/m system with the threshold functioning strategy,” J. of Communic. Technology and Electronics, 56, No. 12, 1585–1596 (2011).
K. Yu. Zhernovyi and Yu. V. Zhernovyi, “Mθ/G/1/m and Mθ/G/1 queues with operating parameters depending on the queue length,” J. of Communic. Technology and Electronics, 59, No. 6, 605–613 (2014).
Yu. Zhernovyi and K. Zhernovyi, The Potentials Method for Threshold Service Strategies [in Russian], LAP Lambert Academic Publishing, Saarbrucken (2015).
M. Bratiychuk and B. Borowska, “Explicit formulae and convergence rate for the system Mα/G/1/N as N → ∞,” Stochastic Models, 18, No. 1, 71–84 (2002).
V. S. Korolyuk, “Boundary problems for complex Poisson processes,” Naukova Dumka, Kyiv (1975).
Yu. Zhernovyi, B. Kopytko, and K. Zhernovyi, “On characteristics of the Mθ/G/1/m and Mθ/G/1 queues with queue-size based packet dropping,” J. of Applied Math. and Computational Mechanics, No. 13(4), 163–175 (2014).
E. S. Ventsel and L. A. Ovcharov, Theory of Random Processes and its Engineering Applications, Vysshaya Shkola, Moscow (2000).
Yu. Zhernovyi, Creating Models of Queueing Systems using GPSS World: Programs, Detailed Explanations, and Analysis of Results, Lambert Academic Publishing, Saarbrucken (2015).
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Translated from Kibernetika i Sistemnyi Analiz, No. 3, May–June, 2016, pp. 170–181.
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Zhernovyi, Y.V., Zhernovyi, K.Y. Potentials Method for M/G/1/m Systems with Threshold Operating Strategies. Cybern Syst Anal 52, 481–491 (2016). https://doi.org/10.1007/s10559-016-9849-7
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DOI: https://doi.org/10.1007/s10559-016-9849-7