IDEAS home Printed from https://ideas.repec.org/a/spr/snopef/v5y2024i1d10.1007_s43069-024-00295-y.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s43069-024-00295-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s43069-024-00295-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Nakdimon, Oren & Yechiali, Uri, 2003. "Polling systems with breakdowns and repairs," European Journal of Operational Research, Elsevier, vol. 149(3), pages 588-613, September.
    3. 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.
    4. 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, December.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nada Riheb Yatim & Amina Angelika Bouchentouf & Pikkala Vijaya Laxmi, 2024. "A queueing model for an automatic manufacturing system with disasters, breakdowns and vacations. Optimal design and analysis," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(4), pages 231-250.
    2. Amina Angelika Bouchentouf & Abdelhak Guendouzi, 2021. "Single Server Batch Arrival Bernoulli Feedback Queueing System with Waiting Server, K-Variant Vacations and Impatient Customers," SN Operations Research Forum, Springer, vol. 2(1), pages 1-23, March.
    3. Alka Choudhary & Srinivas R. Chakravarthy & Dinesh C. Sharma, 2023. "Impact of the degradation in service rate in MAP/PH/1 queueing system with phase type vacations, breakdowns, and repairs," Annals of Operations Research, Springer, vol. 331(2), pages 1207-1248, December.
    4. Ramachandran Remya & Amina Angelika Bouchentouf & Kaliappan Kalidass, 2024. "Cost optimization of a M/M/1/WV&MAV queueing system using Newton–Raphson and particle swarm optimization techniques," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(3), pages 205-220.
    5. Gabi Hanukov & Uri Yechiali, 2024. "Orbit while in service," Operational Research, Springer, vol. 24(2), pages 1-32, June.
    6. Yang, Dong-Yuh & Wu, Chia-Huang, 2021. "Evaluation of the availability and reliability of a standby repairable system incorporating imperfect switchovers and working breakdowns," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    7. Amina Angelika Bouchentouf & Lahcene Yahiaoui & Mokhtar Kadi & Shakir Majid, 2020. "Impatient customers in Markovian queue with Bernoulli feedback and waiting server under variant working vacation policy," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 30(4), pages 5-28.
    8. Priyanka Kalita & Gautam Choudhury & Dharmaraja Selvamuthu, 2020. "Analysis of Single Server Queue with Modified Vacation Policy," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 511-553, June.
    9. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 123-146.
    10. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    11. Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    12. Yi Peng & Jinbiao Wu, 2020. "A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations," Mathematics, MDPI, vol. 8(8), pages 1-12, July.
    13. Jianjun Li & Liwei Liu & Tao Jiang, 2018. "Analysis of an M/G/1 queue with vacations and multiple phases of operation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 51-72, February.
    14. Ambika, K. & Vijayashree, K.V. & Janani, B., 2024. "Modelling and analysis of production management system using vacation queueing theoretic approach," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    15. Srinivas R. Chakravarthy & Serife Ozkar, 2016. "Crowdsourcing and Stochastic Modeling," Business and Management Research, Business and Management Research, Sciedu Press, vol. 5(2), pages 19-30, June.
    16. Zsolt Saffer & Sergey Andreev & Yevgeni Koucheryavy, 2016. "$$M/D^{[y]}/1$$ M / D [ y ] / 1 Periodically gated vacation model and its application to IEEE 802.16 network," Annals of Operations Research, Springer, vol. 239(2), pages 497-520, April.
    17. Amina Angelika Bouchentouf & Lahcene Yahiaoui & Mokhtar Kadi & Shakir Majid, 2020. "Impatient customers in Markovian queue with Bernoulli feedback and waiting server under variant working vacation policy," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(4), pages 5-28.
    18. Shunfu Jin & Xiuchen Qie & Wenjuan Zhao & Wuyi Yue & Yutaka Takahashi, 2020. "A clustered virtual machine allocation strategy based on a sleep-mode with wake-up threshold in a cloud environment," Annals of Operations Research, Springer, vol. 293(1), pages 193-212, October.
    19. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 31, pages 123-146.
    20. Stefan Creemers & Marc Lambrecht, 2010. "Queueing models for appointment-driven systems," Annals of Operations Research, Springer, vol. 178(1), pages 155-172, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:snopef:v:5:y:2024:i:1:d:10.1007_s43069-024-00295-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.