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Asymptotic Diffusion Analysis of Multi-Server Retrial Queue with Hyper-Exponential Service

Author

Listed:
  • Alexander Moiseev

    (Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk 634050, Russia)

  • Anatoly Nazarov

    (Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk 634050, Russia)

  • Svetlana Paul

    (Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk 634050, Russia)

Abstract

A multi-server retrial queue with a hyper-exponential service time is considered in this paper. The study is performed by the method of asymptotic diffusion analysis under the condition of long delay in orbit. On the basis of the constructed diffusion process, we obtain approximations of stationary probability distributions of the number of customers in orbit and the number of busy servers. Using simulations and numerical analysis, we estimate the accuracy and applicability area of the obtained approximations.

Suggested Citation

  • Alexander Moiseev & Anatoly Nazarov & Svetlana Paul, 2020. "Asymptotic Diffusion Analysis of Multi-Server Retrial Queue with Hyper-Exponential Service," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:531-:d:341275
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    References listed on IDEAS

    as
    1. Tuan Phung-Duc & Hiroyuki Masuyama & Shoji Kasahara & Yutaka Takahashi, 2013. "A matrix continued fraction approach to multiserver retrial queues," Annals of Operations Research, Springer, vol. 202(1), pages 161-183, January.
    2. Che Kim & Vilena Mushko & Alexander Dudin, 2012. "Computation of the steady state distribution for multi-server retrial queues with phase type service process," Annals of Operations Research, Springer, vol. 201(1), pages 307-323, December.
    3. J.R. Artalejo & M. Pozo, 2002. "Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue," Annals of Operations Research, Springer, vol. 116(1), pages 41-56, October.
    Full references (including those not matched with items on IDEAS)

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