Calculating steady-state probabilities of single-channel closed queueing systems using hyperexponential approximation

• Autorzy: Zhernovyi Yuriy , Kopytko Bohdan

Identyfikatory

DOI

10.17512/jamcm.2020.1.10

• Języki publikacji: EN

Abstrakty

EN

In this paper we propose a method for calculating steady-state probability distributions of the single-channel closed queueing systems with arbitrary distributions of customer generation times and service times. The approach based on the use of fictitious phases and hyperexponential approximations with parameters of the paradoxical and complex type by the method of moments. We defined conditions for the variation coefficients of the gamma distributions and Weibull distributions, for which the best accuracy of calculating the steady-state probabilities is achieved in comparison with the results of simulation modeling.

Słowa kluczowe

EN

single-channel closed queueing system; arbitrary distributions; hyperexponential approximation

PL

system kolejkowania; rozkład prawdopodobieństwa; aproksymacja wykładnicza

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2020
• Tom: Vol. 19, nr 1
• Strony: 113--120
• Opis fizyczny: Bibliogr. 10 poz., 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] Basharin, G.P., Kharkevich, A.D., & Shneps, M.A. (1968). Queueing in Telephony. Moscow: Nauka (in Russian).
• [2] Schwartz, M. (1987). Telecommunication Networks: Protocols, Modeling and Analysis. Reading: Addison Wesley.
• [3] Sovetov, B.Ya., & Yakovlev, S.A. (1990). Construction of Networks of Integral Service. Leningrad: Mashinostroenie (in Russian).
• [4] Tikhonenko, O. (2005). Generalized Engset formulas for queueing systems with limited memory. In: Queueing: flows, systems, networks, in Mathematical methods for an increase in the efficiency of communication networks, Proc. Int. Sci. Conf., Minsk, Feb. 22-24, 2005, 202-208 (in Russian).
• [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. (2019). Computing non-Markovian Queues Using Hyperexponential Distributions. Riga: LAP Lambert Academic Publishing.
• [9] Zhernovyi, Yu.V., & Zhernovyi, K.Yu. (2015). Method of potentials for a closed system with queue length dependent service times. Journal of Communications Technology and Electronics, 60(12), 1341-1347.
• [10] Zhernovyi, Yu. (2015). Creating Models of Queueing Systems Using GPSS World. Saarbrucken: LAP Lambert Academic Publishing.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).