On characteristics of the Mθ/G/1/m and Mθ/G/1 queues with queue-size based packet dropping

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

Abstrakty

EN

We study the Mθ/G/1/m and Mθ/G/1 queuing systems with the function of the random dropping of customers used to ensure the required characteristics of the system. Each arriving packet of customers can be rejected with a probability defined depending on the queue length at the service beginning of each customer. The Laplace transform for the distribution of the number of customers in the system on the busy period is found, the mean duration of the busy period is determined, and formulas for the stationary distribution of the number of customers in the system are derived via the approach based on the idea of Korolyuk’s potential method. The obtained results are verified with the help of a simulation model constructed with the assistance of GPSS World tools.

Słowa kluczowe

EN

queuing systems; packet arrival of customers; active queue management; random dropping of customers; busy period; distribution of the number of customersdistribution of the number of customers

PL

system kolejkowania; aktywne zarządzanie kolejką; przedział zajętości

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 4
• Strony: 163--175
• Opis fizyczny: Bibliogr. 12 poz., 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

autor

Zhernovyi K.

• Ivan Franko National University of Lviv, Lviv, Ukraine

Bibliografia

• [1] Chydziński A., Nowe modele kolejkowe dla węzłów sieci pakietowych, Pracownia Komputerowa Jacka Skalmierskiego, Gliwice 2013.
• [2] Floyd S., Jacobson V., Random early detection gateways for congestion avoidance, IEEE/ACM Transactions on Networking 1993, 1, 4, 397-413.
• [3] Bohacek S., Shah K., Arce G.R., Davis M., Signal processing challenges in active queue management, IEEE Signal Processing Magazine Transactions on Networking 2004, 21, 5, 69 79.
• [4] Bonald T., May M., Bolot J.-C., Analytic evaluation of RED performance, Proceedings of INFOCOM 2000, 3, 1415-1424.
• [5] Tikhonenko O., Kempa W.M., The generalization of AQM algorithms for queueing system with bounded capacity, Lecture Notes in Computer Sciences 2012, 7204, 242-251.
• [6] 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.
• [7] 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.
• [8] Zhernovyi Yu.V., The simplest models of queue management in the nodes of packet-switched networks, Informatsionnyie Protsessy 2014, 14, 2, 185-196 (in Russian).
• [9] Korolyuk V.S., The Boundary Problem for the Compound Poisson Processes, Naukova Dumka, Kyiv 1975 (in Russian).
• [10] Zhernovyi K.Yu., Zhernovyi Yu.V., Mθ/G/1/m and Mθ/G/1 queues with operating parameters depending on the queue length, Journal of Communications Technology and Electronics 2014, 59, 6, 605-613.
• [11] 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 Communications Technology and Electronics 2013, 58, 12, 1267-1275.
• [12] Zhernovyi K.Yu., Mθ/G/1/m-type systems with the service time dependent on the queue length, Math. Studii 2012, 38, 1, 93-105 (in Ukrainian).