Recurrence relations for two-channel queueing systems with Erlangian service times and hysteretic strategy of random dropping of customers

• Autorzy: Zhernovyi Y. , Kopytko B.

Identyfikatory

DOI

10.17512/jamcm.2018.2.08

• Języki publikacji: EN

Abstrakty

EN

This article proposes a method of study the M/E_s/2/m and M/E_s/2/∞ queueing systems with a hysteretic strategy of random dropping of customers. Recurrence relations are obtained to compute the stationary distribution of the number of customers and steadystate characteristics. The constructed algorithms were tested on examples with the use of simulation models constructed with the help of GPSS World.

Słowa kluczowe

EN

two-channel queueing system; Erlangian service times; random dropping of customers; fictitious phase method; hysteretic strategy; recurrence relations; steady-state characteristics

PL

czas obsługi Erlanga; strategia histeretyczna; system kolejkowania dwukanałowy

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2018
• Tom: Vol. 17, nr 2
• Strony: 93--103
• Opis fizyczny: Bibliogr. 14 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

Bibliografia

• [1] Brockmeyer, E., Halstrom, H.L., & Jensen, A. (1948). The Life and Works of A.K. Erlang. Copenhagen: Danish Academy of Technical Sciences.
• [2] Neuts, M.F. (1981). Matrix-geometric Solutions in Stochastic Models. Baltimore: The John’s Hopkins University Press.
• [3] Bocharov, P.P., & Litvin, V.G. (1986). Methods of analysis and calculation of queuing systems with distributions of phase type, Avtomatika i Telemekhanika, 5, 5-23 (in Russian).
• [4] Takahashi, Y., & Takami, Y. (1976). A numerical method for the steady-state probabilities of a GI/G/c queueing system in a general class. J. Oper. Res. Soc. Japan, 19, 2, 147-157.
• [5] Ryzhikov, Yu.I. (1985). Recurrent calculation of multi-channel queueing systems with unlimited queue. Avtomatika i Telemekhanika, 6, 88-93 (in Russian).
• [6] Ryzhikov, Yu.I. (1980). Algorithm for calculating a multichannel system with Erlang service. Avtomatika i Telemekhanika, 5, 30-37 (in Russian).
• [7] Zhernovyi, K.Yu. (2017). Determining stationary characteristics of two-channel queueing systems with Erlangian distribution of service time. Cybernetics and Systems Analysis, 53, 1, 92-104.
• [8] Zhernovyi, Yu.V., & Zhernovyi K.Yu. (2017). Determination of steady-state characteristics of three-channel queuing systems with Erlangian service times. Cybernetics and Systems Analysis, 53, 2, 280-292.
• [9] Zhernovyi, Yu.V. (2017). Determining steady-state characteristics of some queuing systems with Erlangian distributions. Cybernetics and Systems Analysis, 53, 5, 776-784.
• [10] Kopytko, B., & Zhernovyi, K. (2016). Steady-state characteristics of three-channel queueing systems with Erlangian service times. JAMCM, 15(3), 75-87.
• [11] Chydziński, A. (2013). Nowe modele kolejkowe dla węzłów sieci pakietowych. Gliwice: Pracownia Komputerowa Jacka Skalmierskiego.
• [12] Tikhonenko, O., & Kempa, W.M. (2013). Queue-size distribution in M/G/1-type system with bounded capacity and packet dropping. Communications in Computer and Information Science, 356, 177-186.
• [13] Zhernovyi, Yu., Kopytko, B., & Zhernovyi K. (2014). On characteristics of the M /G/1/m and M /G/1 queues with queue-size based packet dropping. JAMCM, 13, 4, 163-175.
• [14] Zhernovyi, Yu. (2015). Creating Models of Queueing Systems Using GPSS World. Saarbrucken: LAP Lambert Academic Publishing.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).