IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v62y2015i3p171-189.html
   My bibliography  Save this article

An MX/G/1 queueing system with disasters and repairs under a multiple adapted vacation policy

Author

Listed:
  • George C. Mytalas
  • Michael A. Zazanis

Abstract

We consider a queueing system with batch Poisson arrivals subject to disasters which occur independently according to a Poisson process but affect the system only when the server is busy, in which case the system is cleared of all customers. Following a disaster that affects the system, the server initiates a repair period during which arriving customers accumulate without receiving service. The server operates under a Multiple Adapted Vacation policy. The stationary regime of this process is analyzed using the supplementary variables method. We obtain the probability generating function of the number of customers in the system, the fraction of customers who complete service, and the Laplace transform of the system time of a typical customer in stationarity. The stability condition for the system and the Laplace transform of the time between two consecutive disasters affecting the system is obtained by analyzing an embedded Markov renewal process. The statistical characteristics of the batches that complete service without being affected by disasters and those of the partially served batches are also derived. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 171–189, 2015

Suggested Citation

  • George C. Mytalas & Michael A. Zazanis, 2015. "An MX/G/1 queueing system with disasters and repairs under a multiple adapted vacation policy," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(3), pages 171-189, April.
    • Handle: RePEc:wly:navres:v:62:y:2015:i:3:p:171-189
    DOI: 10.1002/nav.21621
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21621
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21621?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
    ---><---

    References listed on IDEAS

    as
    1. 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, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2019. "Performance improvement of a service system via stocking perishable preliminary services," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1000-1011.
    2. Gabi Hanukov & Shoshana Anily & Uri Yechiali, 2020. "Ticket queues with regular and strategic customers," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 145-171, June.
    3. Jiang Tao, 2018. "Analysis of a Discrete-Time Geo/G/1 Queue in a Multi-Phase Service Environment with Disasters," Journal of Systems Science and Information, De Gruyter, vol. 6(4), pages 349-365, August.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Stefan Creemers & Marc Lambrecht, 2010. "Queueing models for appointment-driven systems," Annals of Operations Research, Springer, vol. 178(1), pages 155-172, July.
    13. F. P. Barbhuiya & U. C. Gupta, 2020. "A Discrete-Time GIX/Geo/1 Queue with Multiple Working Vacations Under Late and Early Arrival System," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 599-624, June.
    14. Alexander Dudin & Sergei Dudin & Valentina Klimenok & Yuliya Gaidamaka, 2021. "Vacation Queueing Model for Performance Evaluation of Multiple Access Information Transmission Systems without Transmission Interruption," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    15. Chakravarthy, Srinivas R. & Shruti, & Kulshrestha, Rakhee, 2020. "A queueing model with server breakdowns, repairs, vacations, and backup server," Operations Research Perspectives, Elsevier, vol. 7(C).
    16. Kumar, Anshul & Jain, Madhu, 2023. "Cost Optimization of an Unreliable server queue with two stage service process under hybrid vacation policy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 259-281.
    17. Igor Kleiner & Esther Frostig & David Perry, 2023. "Busy Periods for Queues Alternating Between Two Modes," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-16, June.
    18. Tuan Phung-Duc, 2017. "Exact solutions for M/M/c/Setup queues," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 64(2), pages 309-324, February.
    19. Dieter Claeys & Stijn De Vuyst, 2019. "Discrete-time modified number- and time-limited vacation queues," Queueing Systems: Theory and Applications, Springer, vol. 91(3), pages 297-318, April.
    20. Oz, Binyamin & Adan, Ivo & Haviv, Moshe, 2019. "The Mn/Gn/1 queue with vacations and exhaustive service," European Journal of Operational Research, Elsevier, vol. 277(3), pages 945-952.

    More about this item

    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:wly:navres:v:62:y:2015:i:3:p:171-189. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.