The queueing system M₂^X/M/n with hysteretic control of the input flow intensity

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

Abstrakty

EN

We consider a multi-channel queueing system with unlimited queue and with exponentially distributed service time and the intervals between the arrival of customers batches, which uses a hysteretic control mechanism of the input flow intensity. The system receives two independent flows of customers, one of which is blocked in an overload mode. An algorithm for finding the stationary distribution of the number of customers and stationary characteristics (the mean queue length, the mean waiting time in the queue, the probability of customers loss) is proposed. The obtained results are verified with the help of a simulation model constructed with the assistance of GPSS World tools.

Słowa kluczowe

EN

multi-channel queueing system; batch arrival of customers; hysteretic control of the input flow intensity; stationary characteristics

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 1
• Strony: 149--161
• Opis fizyczny: Bibliogr. 11 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] Abaev P.O., Gaidamaka Yu.V., Samouylov K.E., Hysteretic control of signaling load in the SIP server network, Viestnik of the Russian Peoples Friendship University. Mathematics. Computer Science. Physics 2011, 4, 54-71 (in Russian).
• [2] Abaev P., Gaidamaka Yu., Samouylov K., Queuing model for loss-based overload control in a SIP server using a hysteretic technique, Lecture Notes in Computer Science 2012, 7469, 371-378.
• [3] Abaev P., Gaidamaka Yu., Samouylov K., Modeling of hysteretic signaling load control in next generation networks, Lecture Notes in Computer Science 2012, 7469, 440-452.
• [4] Pechinkin A.V., Razumchik R.V., Stationary characteristics of the system M2 |G|1|r with hysteretic policy of control of the input flow intensity, Informatsionnyie Protsessy 2013, 13, 3, 125-140 (in Russian).
• [5] Dshalalow J.H., Queueing systems with state dependent parameters, Frontiers in Queueing: Models and Applications in Science and Engineering 1997, 61-116.
• [6] Kitaev M.Yu., Rykov V.V., Controlled Queueing Systems, CRC-Press, New York 1995.
• [7] Zhernovyi K.Yu., Zhernovyi Yu.V., System M theta/G/1/m with two-threshold hysteretic strategy of service intensity switching, Informatsionnyie Protsessy 2012, 12, 2, 127-140 (in Russian).
• [8] Zhernovyi Yu.V., Stationary characteristics of M X/M/1 systems with hysteretic switching of the service intensity, Journal of Communications Technology and Electronics 2013, 58, 6, 613-627.
• [9] Bocharov P.P., Pechinkin A.V., Queueing Theory, RUDN, Moskow 1995 (in Russian).
• [10] Boyev V.D., Systems Modeling. Tools of GPSS World, BHV-Petersburg, St. Petersburg 2004 (in Russian).
• [11] Zhernovyi Yu.V., Simulation of Queuing Systems, Vydavnychyi Tsentr LNU im. Ivana Franka, Lviv 2007 (in Ukrainian).