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On Two Interacting Markovian Queueing Systems

Author

Listed:
  • Valeriy A. Naumov

    (Service Innovation Research Institute, 8 A Annankatu, Helsinki 00120, Finland)

  • Yuliya V. Gaidamaka

    (Department of Applied Informatics and Probability, Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya St. 6, Moscow 117198, Russian
    Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilov St. 44-2, Moscow 119333, Russian)

  • Konstantin E. Samouylov

    (Department of Applied Informatics and Probability, Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya St. 6, Moscow 117198, Russian
    Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilov St. 44-2, Moscow 119333, Russian)

Abstract

In this paper, we study a Markovian queuing system consisting of two subsystems of an arbitrary structure. Each subsystem generates a multi-class Markovian arrival process of customers arriving to the other subsystem. We derive the necessary and sufficient conditions for the stationary distribution to be of product form and consider some particular cases of the subsystem interaction for which these conditions can be easily verified.

Suggested Citation

  • Valeriy A. Naumov & Yuliya V. Gaidamaka & Konstantin E. Samouylov, 2019. "On Two Interacting Markovian Queueing Systems," Mathematics, MDPI, vol. 7(9), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:799-:d:262935
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    References listed on IDEAS

    as
    1. Xiuli Chao, 2011. "Networks with Customers, Signals, and Product Form Solution," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. Dijk (ed.), Queueing Networks, chapter 0, pages 217-267, Springer.
    2. William J. Gordon & Gordon F. Newell, 1967. "Closed Queuing Systems with Exponential Servers," Operations Research, INFORMS, vol. 15(2), pages 254-265, April.
    3. Gely Basharin & Valeriy Naumov & Konstantin Samouylov, 2018. "On Markovian modelling of arrival processes," Statistical Papers, Springer, vol. 59(4), pages 1533-1540, December.
    4. James R. Jackson, 1963. "Jobshop-Like Queueing Systems," Management Science, INFORMS, vol. 10(1), pages 131-142, October.
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