The potentials method for the M/G/1/m queue with customer dropping and hysteretic strategy of the service time change

• Autorzy: Zhernovyi Y. , Kopytko B.

Identyfikatory

DOI

10.17512/jamcm.2016.1.20

• Języki publikacji: EN

Abstrakty

EN

We propose a method for determining the probabilistic characteristics of the M/G/1/m queueing system with the random dropping of arrivals and distribution of the service time depending on the queue length. Two sets of service modes, with the service time distribution functions F_n (x) and F_n (x) respectively, are used according to the twothreshold hysteretic strategy. The Laplace transforms for the distribution of the number of customers in the system during the busy period and for the distribution function of the length of the busy period are found. The developed algorithm for calculating the stationary characteristics of the system is tested with the help of a simulation model constructed with the assistance of GPSS World tools.

Słowa kluczowe

EN

single-channel queueing system; random dropping of customers; hysteretic strategy for service time; potentials method; stationary characteristics

PL

system kolejkowania jednokanałowy; metoda potencjałów; charakterystyka stacjonarna; czas obsługi

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 1
• Strony: 197--210
• Opis fizyczny: Bibliogr. 12 poz., rys., tab.

Twórcy

autor

Zhernovyi Y.

• Ivan Franko National University of Lviv Lviv, Ukraine

autor

Kopytko B.

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

Bibliografia

• [1] Chydziński A., Nowe modele kolejkowe dla węzłów sieci pakietowych, Pracownia Komputerowa Jacka Skalmierskiego, Gliwice 2013.
• [2] Tikhonenko O., Kempa W.M., Queue-size distribution in M/G/1-type system with bounded capacity and packet dropping, Communications in Computer and Information Science 2013, 356, 177-186.
• [3] Kempa W.M., A direct approach to transient queue-size distribution in a finite-buffer queue with AQM, Applied Mathematics and Information Sciences 2013, 7, 3, 909-915.
• [4] Zhernovyi K.Yu., Zhernovyi Yu.V., Mθ/G/1/m and Mθ/G/1 systems with the service time dependent on the queue length, Journal of Communicat. Technology and Electronics 2013, 58, 12, 1267-1275.
• [5] Zhernovyi Yu., Zhernovyi K., Potentials Method for Threshold Strategies of Queueing, LAP Lambert Academic Publishing, Saarbrücken 2015 (in Russian).
• [6] Zhernovyi K.Yu., Stationary characteristics of the Mθ/G/1/m system with the threshold functioning strategy, Journal of Communicat. Technology and Electronics 2011, 56, 12, 1585-1596.
• [7] Zhernovyi Yu., Kopytko B., The potentials method for a closed queueing system with hysteretic strategy of the service time change, Journal of Applied Mathematics and Computational Mechanics 2015, 14(2), 131-143.
• [8] Zhernovyi Yu.V., Zhernovyi K.Yu., Method of potentials for a closed system with queue length dependent service times, J. of Communicat. Technology and Electronics 2015, 60, 12, 1341-1347.
• [9] Zhernovyi Yu., Kopytko B., Zhernovyi K. On characteristics of the Mθ/G/1/m and Mθ/G/1 queues with queue-size based packet dropping, Journal of Applied Mathematics and Computational Mechanics 2014, 13(4), 163-175.
• [10] Wentzel E.S., Ovcharov L.A., Theory of Stochastic Processes and its Engineering Applications, Vysshaya Shkola, Moscow 2000 (in Russian).
• [11] Zhernovyi Yu., Creating Models of Queueing Systems Using GPSS World, LAP Lambert Academic Publishing, Saarbrücken 2015.
• [12] Boyev V.D., Systems Modeling, Tools of GPSS World, BHV-Petersburg, St. Petersburg 2004 (in Russian).

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.