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Calculating Steady-State Characteristics of Single-Channel Queuing Systems Using Phase-Type Distributions

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Cybernetics and Systems Analysis Aims and scope

Abstract

This paper analyzes the results of application of the hyperexponential and Erlang approximations with parameters of paradoxical and complex types for calculating steady-state characteristics of G /G /1/ m queuing systems by the fictitious phase method. The results are verified using simulation models.

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References

  1. M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models, The John’s Hopkins University Press, Baltimore (1981).

    MATH  Google Scholar 

  2. Yu. I. Ryzhikov and A. V. Ulanov, “A use of hyperexponential distribution in non-Markovian queuing systems analyses,” Tomsk State University Journal of Control and Computer Science, No. 3 (36), 60–65 (2016).

  3. Yu. I. Ryzhikov and A. V. Ulanov, “Application of hyperexponential approximation in problems of addition of flows,” Intellectual Technologies on Transport, No. 4, 34–39 (2015).

  4. Yu. I. Ryzhikov and A. V. Ulanov, “Calculation of the M/H 2/n–H 2 queuing system with impatient customers,” Tomsk State University Journal of Control and Computer Science, No. 2 (27), 47–53 (2014).

  5. G. Sh. Tsitsiashvili, “Synergetic effect in network with hyperexponential distributions of service times,” Tomsk State University Journal of Control and Computer Science, No. 1 (34), 65–68 (2016).

  6. A. A. Nazarov and V. I. Broner, “Inventory model with hyperexponential distribution of demands’s batch size,” Tomsk State University Journal of Control and Computer Science, No. 1(34), 43–49 (2016).

  7. D. R. Cox, “A use of complex probabilities in the theory of stochastic process,” in: Proc. Cambridge Phil. Soc., 313–323 (1955).

    Article  MathSciNet  Google Scholar 

  8. B. Bidabad and B. Bidabad, “Complex probability and Markov stochastic process,” in: Proc. 1st Iranian Statistics Conf. (Isfahan University of Technology, 1992). Isfahan (1992), pp. 1–8.

  9. Yu. Zhernovyi, Creating Models of Queuing Systems Using GPSS World: Programs, Detailed Explanations and Analysis of Results, LAP Lambert Academic Publishing, Saarbrucken (2015).

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Authors and Affiliations

  1. Ivan Franko National University of Lviv, Lviv, Ukraine

    Yu. V. Zhernovyi

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  1. Yu. V. Zhernovyi
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Correspondence to Yu. V. Zhernovyi.

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Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2018, pp. 160–169.

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Zhernovyi, Y.V. Calculating Steady-State Characteristics of Single-Channel Queuing Systems Using Phase-Type Distributions. Cybern Syst Anal 54, 824–832 (2018). https://doi.org/10.1007/s10559-018-0084-2

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  • DOI: https://doi.org/10.1007/s10559-018-0084-2

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