Calculating steady-state probabilities of single-channel queueing systems with changes of service times depending on the queue length

• Autorzy: Zhernovyi Yuriy , Kopytko Bohdan

Identyfikatory

DOI

10.17512/jamcm.2019.3.10

• Języki publikacji: EN

Abstrakty

EN

In this paper, we propose a method for calculating steady-state probabilities of the G/G/1/m and M/G/1/m queueing systems with service times changes depending of the number of customers in the system. The method is based on the use of fictitious phases and hyperexponential approximations with parameters of the paradoxical and complex type. A change in the service mode can only occur at the moment the service is started. We verified the obtained numerical results using the potential method and simulation models, constructed by means of GPSS World.

Słowa kluczowe

EN

single-channel queueing system; service times changes depending of the queue length; hyperexponential approximation

PL

rozkład hiperesponencjalny; czas obsługi; system kolejkowania jednokanałowy; długość kolejki

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2019
• Tom: Vol. 18, nr 3
• Strony: 107--117
• Opis fizyczny: Bibliogr. 8 poz., tab.

Twórcy

autor

Zhernovyi Yuriy

• Ivan Franko National University of Lviv, Lviv, Ukraine

autor

Kopytko Bohdan

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

Bibliografia

• [1] Finneran, M. (2008). Problems of the high-quality voice over IP-based networks: compression, delay and echo. Part 1. Elektronnyie Komponenty, 11, 83-85 (in Russian).
• [2] Sriram, K., & Lucantoni, D.M. (1989). Traffic smoothing effects of bit dropping in a packet voice multiplexer. IEEE Transactions on Communications, 37, 7, 703-712.
• [3] Dshalalow, D.H. (1996). Queueing systems with state dependent parameters. In: Frontiers in Queueing: Models and Applications in Science and Engineering. Boca Raton, Fl.: CRC Press, 61-116.
• [4] Zhernovyi, K.Yu. (2012). The Mθ/G/1/m queues with the time of service, depending on the length of the queue. Matematychni Studii, 38, 93-105 (in Ukrainian).
• [5] Ryzhikov, Yu.I., & Ulanov, A.V. (2016). Application of hyperexponential approximation in the problems of calculating non-Markovian queuing systems. Vestnik of Tomsk State University. Management, Computer Engineering and Informatics, 3(36), 60-65 (in Russian).
• [6] Zhernovyi, Yu.V. (2018). Calculating steady-state characteristics of single-channel queuing systems using phase-type distributions. Cybernetics and Systems Analysis, 54, 5, 824-832.
• [7] Zhernovyi, Yu., & Kopytko, B. (2019). Calculating steady-state probabilities of queueing systems using hyperexponential approximation. Journal of Applied Mathematics and Computational Mechanics, 18(2), 111-122.
• [8] 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 (2019).