IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v24y2022i4d10.1007_s11009-022-09926-5.html
   My bibliography  Save this article

Analysis of a Multiple Dual-Stage Vacation Queueing System with Disaster and Repairable Server

Author

Listed:
  • Sudhesh R.

    (Anna University)

  • Mohammed Shapique A.

    (IFET College of Engineering)

  • Dharmaraja S.

    (Indian Institute of Technology Delhi)

Abstract

An M/M/1 dual-stage vacation queueing system with a system disaster is analysed in this paper. This work is motivated by the dual-stage sleep mode mechanism in the MAC (Media Access Control) and the physical layer of a WiMAX system with Denial of Service. In this model, the server switches to two types of vacation called stage-I and stage-II vacation. Disaster can occur at any stage of the system and subsequent repair is considered. For this system, explicit expressions for transient and steady-state probabilities are computed. Further, performance indices like the mean, variance of the system size, the probability that the server is on vacation mode and busy mode, and system throughput have been computed. Finally, numerical illustrations are presented to understand the effect of the parameters on the system performance.

Suggested Citation

  • Sudhesh R. & Mohammed Shapique A. & Dharmaraja S., 2022. "Analysis of a Multiple Dual-Stage Vacation Queueing System with Disaster and Repairable Server," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2485-2508, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09926-5
    DOI: 10.1007/s11009-022-09926-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-022-09926-5
    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/s11009-022-09926-5?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. R. Sudhesh & P. Savitha & S. Dharmaraja, 2017. "Transient analysis of a two-heterogeneous servers queue with system disaster, server repair and customers’ impatience," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 179-205, April.
    2. Ammar, Sherif I., 2015. "Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 97-105.
    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. 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.
    2. R. Sudhesh & P. Savitha & S. Dharmaraja, 2017. "Transient analysis of a two-heterogeneous servers queue with system disaster, server repair and customers’ impatience," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 179-205, April.
    3. 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.
    4. Xu Jia & Liu Liwei & Zhu Taozeng, 2018. "Transient Analysis of a Two-Heterogeneous Severs Queue with Impatient Behaviour and Multiple Vacations," Journal of Systems Science and Information, De Gruyter, vol. 6(1), pages 69-84, February.
    5. 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.
    6. R. Sudhesh & A. Azhagappan, 2018. "RETRACTED ARTICLE: Transient analysis of an M/M/1 queue with variant impatient behavior and working vacations," OPSEARCH, Springer;Operational Research Society of India, vol. 55(3), pages 787-806, November.
    7. Shekhar, Chandra & Kumar, Neeraj & Gupta, Amit & Kumar, Amit & Varshney, Shreekant, 2020. "Warm-spare provisioning computing network with switching failure, common cause failure, vacation interruption, and synchronized reneging," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    8. 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.
    9. 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.
    10. Ahuja, Anjali & Jain, Anamika & Jain, Madhu, 2022. "Transient analysis and ANFIS computing of unreliable single server queueing model with multiple stage service and functioning vacation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 464-490.

    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:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09926-5. 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.