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A Markovian Queueing Model for Telecommunications Support Center with Breakdowns and Vacation Periods

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  • Anis Chettouf

    (University of Bejaia)

  • Amina Angelika Bouchentouf

    (Djillali Liabes University of Sidi Bel Abbes)

  • Mohamed Boualem

    (University of Bejaia)

Abstract

This paper presents an in-depth analysis of an infinite-space single-server Markovian queueing model for a customer support center that incorporates working breakdowns, repairs, balking, and reneging, along with both single and multiple vacation policies. Additionally, we consider the scenario where the server must wait for a random period before going on vacation. By employing the matrix-geometric method, we determine the steady-state probabilities of the system and derive essential performance measures. We construct an expected cost function and formulate an optimization problem to minimize the cost, using the direct search method to find the optimal service rates during working breakdown and busy periods. To demonstrate the model’s usefulness, the results are complemented with numerical illustrations and sensitivity analysis. This work thus enables improved decision-making and resource management in customer support centers by deepening our understanding of their dynamics.

Suggested Citation

  • Anis Chettouf & Amina Angelika Bouchentouf & Mohamed Boualem, 2024. "A Markovian Queueing Model for Telecommunications Support Center with Breakdowns and Vacation Periods," SN Operations Research Forum, Springer, vol. 5(1), pages 1-26, March.
    • Handle: RePEc:spr:snopef:v:5:y:2024:i:1:d:10.1007_s43069-024-00295-y
    DOI: 10.1007/s43069-024-00295-y
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    References listed on IDEAS

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    1. Nakdimon, Oren & Yechiali, Uri, 2003. "Polling systems with breakdowns and repairs," European Journal of Operational Research, Elsevier, vol. 149(3), pages 588-613, September.
    2. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, February.
    3. Cheng-Dar Liou, 2015. "Markovian queue optimisation analysis with an unreliable server subject to working breakdowns and impatient customers," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(12), pages 2165-2182, September.
    4. Mouloud Cherfaoui & Amina Angelika Bouchentouf & Mohamed Boualem, 2023. "Modelling and simulation of Bernoulli feedback queue with general customers' impatience under variant vacation policy," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 46(4), pages 451-480.
    5. Amina Angelika Bouchentouf & Mouloud Cherfaoui & Mohamed Boualem, 2019. "Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 300-323, March.
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