Calculating steady-state probabilities of queueing systems using hyperexponential approximation

• Autorzy: Zhernovyi Yuriy , Kopytko Bohdan

Identyfikatory

DOI

10.17512/jamcm.2019.2.10

• Języki publikacji: EN

Abstrakty

EN

This article proposes an analysis of the results of the application of hyperexponential approximations with parameters of the paradoxical and complex type for calculating the steady-state probabilities of the G/G/n/m queueing systems with the number of channels n = 1, 2 and 3. The steady-state probabilities are solutions of a system of linear algebraic equations obtained by the method of fictitious phases. Approximation of arbitrary distributions is carried out using the method of moments. We verified the obtained numerical results using potential method and simulation models, constructed by means of GPSS World.

Słowa kluczowe

EN

non-Markovian queueing system; hyperexponential approximation; complex and paradoxical parameters of distribution

PL

system kolejkowy; aproksymacja; rozkład hiperesponencjalny

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2019
• Tom: Vol. 18, nr 2
• Strony: 111--122
• Opis fizyczny: Bibliogr. poz. 9, tab.

Twórcy

autor

Zhernovyi Yuriy

• Ivan Franko National University of Lviv, Lviv, Ukraine

autor

Kopytko Bohdan

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

Bibliografia

• [1] Neuts, M.F. (1981). Matrix-geometric Solutions in Stochastic Models. Baltimore: The John’s Hopkins University Press.
• [2] 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).
• [3] 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.
• [4] Ryzhikov, Yu.I. & Ulanov, A.V. (2015). Application of hyperexponential approximation in problems of summation of flows. Intelligent Technologies in Transport, 4, 34-39 (in Russian).
• [5] Ryzhikov, Yu.I. & Ulanov, A.V. (2014). Calculation of the M/H2/n-H2 hyperexponential system with customers impatient in the queue. Vestnik of Tomsk State University. Management, Computer Engineering and Informatics, 2(27), 47-53 (in Russian).
• [6] Tsitsiashvili, G.Sh. (2016). Synergistic effect in a network with hyperexponential distributions of service times. Vestnik of Tomsk State University. Management, Computer Engineering and Informatics, 1(34), 65-68 (in Russian).
• [7] Nazarov, A.A. & Broner, V.I. (2016). Inventory management system with hyperexponential distribution of resources consumption. Vestnik of Tomsk State University. Management, Computer Engineering and Informatics, 1(34), 43-49 (in Russian).
• [8] Bratiychuk, M. & Borowska, B. (2002). Explicit formulae and convergence rate for the system Mα/G/1/N as N →∞. Stochastic Models, 18, 1, 71-84.
• [9] 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).