IDEAS home Printed from https://ideas.repec.org/a/spr/opsear/v62y2025i2d10.1007_s12597-024-00808-7.html
   My bibliography  Save this article

Steady state behavior of multiple variant hiatus queues with a waiting server at each stage

Author

Listed:
  • R. Remya

    (Karpagam Academy of Higher Education)

  • K. Kalidass

    (Karpagam Academy of Higher Education
    Chikkanna Government Arts College)

  • M. Vadivukarasi

    (Government College of Arts and Science College)

Abstract

This paper considers an infinite buffer single server Markovian queueing system with multiple variant hiatus (vacation) policy. After every busy period ends, the server remains wait in the system to new arrival customers for a random period of time. If no arrival occurs in this waiting time, the server takes a vacation. After completion of the vacation, if any customers waiting in the system the server immediately starts the service process. Otherwise, the server remains wait in the system to new arrival customers for a random period of time. If no arrival occurs in this waiting time, the server proceeds to another vacation. The server continues this policy till the server takes the maximum number of J (a pre-determined threshold value) vacations. After completing maximum number of random vacations, the server stays dormant in the system and waits for the new customers. Steady state analysis of the model is carried out by using a probability generating function approach. The stability condition of the model and stochastic decomposition results are discussed. Moreover, the optimality of the cost model is numerically derived by using particle swarm optimization and Newton–Raphson method. A comparative analysis is also done between these two techniques. Numerical illustrations are included to study the influence of system parameters on some important performance measures of the queueing model. Finally, we present some managerial insights.

Suggested Citation

  • R. Remya & K. Kalidass & M. Vadivukarasi, 2025. "Steady state behavior of multiple variant hiatus queues with a waiting server at each stage," OPSEARCH, Springer;Operational Research Society of India, vol. 62(2), pages 850-876, June.
    • Handle: RePEc:spr:opsear:v:62:y:2025:i:2:d:10.1007_s12597-024-00808-7
    DOI: 10.1007/s12597-024-00808-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12597-024-00808-7
    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/s12597-024-00808-7?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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. P. Vijaya Laxmi & P. Rajesh, 2016. "Analysis of variant working vacations on batch arrival queues," OPSEARCH, Springer;Operational Research Society of India, vol. 53(2), pages 303-316, June.
    3. M. Vadivukarasi & K. Kalidass, 2022. "Discussion on the transient solution of single server Markovian multiple variant vacation queues with disasters," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1352-1376, December.
    4. M. I. G. Suranga Sampath & K. Kalidass & Jicheng Liu, 2020. "Transient Analysis of an M/M/1 Queueing System Subjected to Multiple Differentiated Vacations, Impatient Customers and a Waiting Server with Application to IEEE 802.16E Power Saving Mechanism," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 297-320, March.
    5. 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.
    6. 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.
    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. Lidiya P & K Julia Rose Mary, 2024. "A study on the performance of a queuing system with heterogeneous arrivals and various types of breakdowns under multiple working vacations," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(4), pages 125-140.
    2. M. Vadivukarasi & K. Kalidass, 2022. "Discussion on the transient solution of single server Markovian multiple variant vacation queues with disasters," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1352-1376, December.
    3. Qi Shao & Linmin Hu & Fan Xu, 2024. "Reliability and Optimization for k-out-of-n: G Mixed Standby Retrial System with Dependency and J-Vacation," Methodology and Computing in Applied Probability, Springer, vol. 26(1), pages 1-27, March.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. R. Sudhesh & A. Mohammed Shapique, 2022. "Transient analysis of power management in wireless sensor network with start-up times and threshold policy," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 80(1), pages 1-16, May.
    9. Abdoun Sylia & Taleb Samira, 2024. "Strategic Joining in an Unobservable Markovian Queue with Differentiated Vacations," SN Operations Research Forum, Springer, vol. 5(3), pages 1-27, September.
    10. Gabi Hanukov & Michael Hassoun & Oren Musicant, 2021. "On the Benefits of Providing Timely Information in Ticket Queues with Balking and Calling Times," Mathematics, MDPI, vol. 9(21), pages 1-16, October.
    11. G. K. Tamrakar & A. Banerjee, 2020. "On steady-state joint distribution of an infinite buffer batch service Poisson queue with single and multiple vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1337-1373, December.
    12. Sylia Abdoun & Samira Taleb, 2025. "Efficiency of a markovian queue with non homogeneous vacations and strategic customers under partial vacation interruption," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 88(2), pages 1-18, June.
    13. Hossein Foroutan & Mohammad Reza Salehi Rad, 2024. "Two phases queue systems with dependent phases service times via copula," OPSEARCH, Springer;Operational Research Society of India, vol. 61(1), pages 189-204, March.
    14. Abdoun Sylia & Taleb Samira, 2025. "On a Balking M/G/1 Queue with General Differentiated Vacations," Methodology and Computing in Applied Probability, Springer, vol. 27(1), pages 1-32, March.
    15. Amita Bhagat & Madhu Jain, 2020. "Retrial queue with multiple repairs, multiple services and non preemptive priority," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 787-814, September.
    16. A. Mohammed Shapique & R. Sudhesh & S. Dharmaraja, 2024. "Transient Analysis of a Modified Differentiated Vacation Queueing System for Energy-Saving in WiMAX," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-33, September.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:opsear:v:62:y:2025:i:2:d:10.1007_s12597-024-00808-7. 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.