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### The system M2θ/G/1/m with threshold control of the arrival rate and service time

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Języki publikacji
EN
Abstrakty
EN
We consider a M2θ/G/1/m queueing system with arrival of customer batches, which uses a threshold control mechanism of the service time and arrival rate. The system receives two independent flows of customers, one of which is blocked in an overload mode (under the condition that the number of customers in the system exceeds a given threshold value h). Full blocking of the input flow is carried out from the moment when the queue length reaches the number m until the beginning of the service of the first customer, for which the number of customers in the system does not exceed h. From the beginning of the service of the first customer during the excess of number of customers in the system of h until the completion of full blocking the time of service of customer is distributed under the law of F(x) (an increased service rate is used). Rest of the time the system applies the normal service rate with the distribution function F(x) of service time. Laplace transforms for the distributions of the number of customers in the system during the busy period and for the distribution function of the busy period are found. The average duration of the busy period is obtained. Formulas for the stationary distribution of the number of customers in the system, for the probability of service and for the stationary characteristics of the system are established. The obtained results are verified with the help of a simulation model constructed with the assistance of GPSS World tools.
Słowa kluczowe
EN
Rocznik
Strony
149--163
Opis fizyczny
Bibliogr. 13 poz., tab.
Twórcy
autor
• Ivan Franko National University of Lviv, Lviv, Ukraine
autor
• Institute of Mathematics, Czestochowa University of Technology Czestochowa, 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 2 M |G|1|r with hysteretic policy of control of the input flow intensity, Informatsionnyie Protsessy 2013, 13, 3, 125-140 (in Russian).
• [5] Zhernovyi K.Yu., Investigation of the M /G/1/m _ system with service regime switchings and reducing blocking of the flow of customers, Informatsionnyie Protsessy 2011, 11, 2, 203-224 (in Russian).
• [6] Zhernovyi K.Yu., Zhernovyi Yu,V., An M /G/1/m _ system with two-threshold hysteresis strategy of service intensity switching, Journal of Communications Technology and Electronics 2012, 57, 12, 1340-1349.
• [7] Zhernovyi Yu.V., Stationary characteristics of X M /M/1 systems with hysteretic switching of the service intensity, Journal of Communications Technology and Electronics 2013, 58, 6, 613-627.
• [8] Zhernovyi Yu., Kopytko B., The queueing system X2M /M/n with hysteretic control of the input flow intensity, Journal of Applied Mathematics and Computational Mechanics 2014, 13(1), 149-161.
• [9] Bocharov P.P., Pechinkin A.V., Queueing Theory, RUDN, Moscow 1995 (in Russian).
• [10] Korolyuk V.S., The Boundary Problem for the Compound Poisson Processes, Naukova Dumka, Kyiv 1975 (in Russian).
• [11] Zhernovyi K.Yu., Zhernovyi Yu.,V., System M /G/1/m _ with two-threshold hysteretic strategy of service intensity switching, Informatsionnyie Protsessy 2012, 12, 2, 127-140 (in Russian).
• [12] Ivchenko G.I., Kashtanov V.A., Kovalenko I.N., Queueing Theory, Vysshaya Shkola, Moscow 1982 (in Russian).
• [13] Boyev V.D., Systems Modeling. Tools of GPSS World, BHV-Petersburg, St. Petersburg 2004 (in Russian).
Typ dokumentu
Bibliografia