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Retrial Queues with Unreliable Servers and Delayed Feedback

Author

Listed:
  • Agassi Melikov

    (Institute of Control Systems, National Academy of Science, Baku AZ 1141, Azerbaijan)

  • Sevinj Aliyeva

    (Faculty of Applied Mathematics and Cybernetics, Baku State University, Baku AZ 1148, Azerbaijan)

  • Janos Sztrik

    (Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary)

Abstract

In this paper, models of unreliable multi-server retrial queues with delayed feedback are examined. The Bernoulli retrial is allowed upon the arrival of both primary (from outside) and feedback customers (from orbit), as well as the Bernoulli feedback that may occur after each service in this system. Servers can break down both during the service of customers and when they are idle. If a server breaks down during the service of a customer, then the interrupted customer, in accordance with the Bernoulli scheme, decides either to leave the system or join a common orbit of retrial and feedback customers. An approximate method, based on the space merging approach of three-dimensional Markov chains, is proposed for the calculation of the steady-state probabilities, as well as performance measures of the system. The results of the numerical experiments are demonstrated.

Suggested Citation

  • Agassi Melikov & Sevinj Aliyeva & Janos Sztrik, 2021. "Retrial Queues with Unreliable Servers and Delayed Feedback," Mathematics, MDPI, vol. 9(19), pages 1-23, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2415-:d:645306
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    References listed on IDEAS

    as
    1. Chia-Jung Chang & Jau-Chuan Ke & Fu-Min Chang, 2018. "Unreliable retrial queue with loss and feedback under threshold-based policy," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 30(1), pages 1-20.
    2. Anatoly Nazarov & János Sztrik & Anna Kvach & Ádám Tóth, 2020. "Asymptotic sojourn time analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs," Annals of Operations Research, Springer, vol. 288(1), pages 417-434, May.
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