The busy period for the M^θ /G/1/m system with service time dependent of the queue length

• Autorzy: Zhernovyi Y. , Kopytko B. , Zhernovyi K.
• Języki publikacji: EN

Abstrakty

EN

We consider the M^θ/G/1/m system wherein the service time depends on the queuelength and it is determined at the beginning of customer service. Using an approach basedon the potential method proposed by V. Korolyuk, the Laplace transforms for the distribution f the number of customers in the system on the busy period and for the distribution function of the busy period are found.

Słowa kluczowe

EN

queueing system; group arrival of customers; service time dependent on the queue length

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2013
• Tom: Vol. 12, nr 4
• Strony: 127--133
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Zhernovyi Y.

• Ivan Franko National University of Lviv, Lviv, Ukraine

autor

Kopytko B.

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

autor

Zhernovyi K.

• Ivan Franko National University of Lviv, Lviv, Ukraine

Bibliografia

• [1] Zhernovyi K.Yu., Zhernovyi Yu.V., The M theta/G/1/m and M theta/G/1 systems with service times dependent on the queue length, Informatsionnyie Protsessy 2013, 13, 2, 76-90 (in Russian).
• [2] Zhernovyi K.Yu., The M theta/G/1/m systems with service times dependent on the queue length, Matematychni Studii 2012, 38, 1, 93-105 (in Ukrainian).
• [3] Ivnitskiy V.A., A stationary regime of a queueing system with parameters dependent on the queue length and with nonordinary flow, Eng. Cybernetics 1975, 13, 85-90.
• [4] Dudin A.N., Optimal control for an M X/G/1 queue with two operation modes, Probability in Engin. and Inform. Sciences 1997, 11, 2, 255-265.
• [5] Dudin A.N., Medvedev G.A., Melenets Yu.V., Workshop on Computers on Queueing Theory, Universitetskoye, Minsk 2000 (in Russian).
• [6] Choi B.D., Kim Y.Ch., Shin Y., Pearce C.E.M., The M X/G/1 queue with length – dependent service times, J. of Appl. Math. and Stoch. Anal. 2001, 14, 4, 399-419.
• [7] Korolyuk V.S., The Boundary Problem for the Compound Poisson Processes, Naukova Dumka, Kyiv 1975 (in Russian).