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Queueing system with control by admission of retrial requests depending on the number of busy servers and state of the underlying process of Markov arrival process of primary requests

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Listed:
  • Alexander Dudin

    (Belarusian State University)

  • Achyutha Krishnamoorthy

    (CMS College)

  • Sergei Dudin

    (Belarusian State University)

  • Olga Dudina

    (Belarusian State University)

Abstract

A multi-server retrial queuing model is under study. Arrivals occur according to the Markov arrival process (MAP). Aiming to increase the probability of immediate access of arriving requests to service, control by the admission of retrying requests, which did not succeed to start service immediately after arrival, is supposed. A control strategy is determined by the set of the integer thresholds defined for each value of the underlying Markov chain of the MAP. Any retrying request is accepted for service if the number of busy servers is less than the threshold corresponding to the current state of the underlying Markov chain. Retrying requests are impatient and can depart from the system without receiving service. Dynamics of the system is described by the three-dimensional Markov chain. Its generator is obtained, steady-state probabilities are computed and formulas for computation of certain performance measures are given. Numerical examples are presented including illustration of a possibility to use the obtained results for managerial goals.

Suggested Citation

  • Alexander Dudin & Achyutha Krishnamoorthy & Sergei Dudin & Olga Dudina, 2024. "Queueing system with control by admission of retrial requests depending on the number of busy servers and state of the underlying process of Markov arrival process of primary requests," Annals of Operations Research, Springer, vol. 335(1), pages 135-150, April.
  • Handle: RePEc:spr:annopr:v:335:y:2024:i:1:d:10.1007_s10479-023-05728-1
    DOI: 10.1007/s10479-023-05728-1
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    References listed on IDEAS

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    1. Sergey Stepanov & Mikhail Stepanov, 2021. "Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation," Mathematics, MDPI, vol. 9(21), pages 1-24, November.
    2. Ger Koole & Avishai Mandelbaum, 2002. "Queueing Models of Call Centers: An Introduction," Annals of Operations Research, Springer, vol. 113(1), pages 41-59, July.
    3. Aguir, M. Salah & Aksin, O. Zeynep & Karaesmen, Fikri & Dallery, Yves, 2008. "On the interaction between retrials and sizing of call centers," European Journal of Operational Research, Elsevier, vol. 191(2), pages 398-408, December.
    4. Oualid Jouini & Ger Koole & Alex Roubos, 2013. "Performance indicators for call centers with impatient customers," IISE Transactions, Taylor & Francis Journals, vol. 45(3), pages 341-354.
    5. A. Gómez-Corral, 2006. "A bibliographical guide to the analysis of retrial queues through matrix analytic techniques," Annals of Operations Research, Springer, vol. 141(1), pages 163-191, January.
    6. Kejia Hu & Gad Allon & Achal Bassamboo, 2022. "Understanding Customer Retrials in Call Centers: Preferences for Service Quality and Service Speed," Manufacturing & Service Operations Management, INFORMS, vol. 24(2), pages 1002-1020, March.
    7. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
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