IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v104y2023i1d10.1007_s11134-022-09870-8.html
   My bibliography  Save this article

Further results of Markovian bulk-arrival and bulk-service queues with general-state-dependent control

Author

Listed:
  • Xiaohan Wu

    (Harbin Institute of Technology
    Southern University of Science and Technology)

  • Anyue Chen

    (Southern University of Science and Technology
    University of Liverpool)

Abstract

This paper aims to provide several further results for a queueing model recently discussed by Chen et al. (Queueing Syst 95:331–378, 2020), i.e. the Markovian bulk-arrival and bulk-service queue incorporating the general state-dependent control. We use an alternative method which is based on the resolvent decomposition theorem to obtain the important results for this model in this paper, including the important questions regarding equilibrium behaviour, queue length behaviour, hitting time and busy period distributions. Furthermore, a set of interesting examples are also provided in the last section.

Suggested Citation

  • Xiaohan Wu & Anyue Chen, 2023. "Further results of Markovian bulk-arrival and bulk-service queues with general-state-dependent control," Queueing Systems: Theory and Applications, Springer, vol. 104(1), pages 19-52, June.
    • Handle: RePEc:spr:queues:v:104:y:2023:i:1:d:10.1007_s11134-022-09870-8
    DOI: 10.1007/s11134-022-09870-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-022-09870-8
    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/s11134-022-09870-8?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. Anyue Chen & Xiaohan Wu & Jing Zhang, 2020. "Markovian bulk-arrival and bulk-service queues with general state-dependent control," Queueing Systems: Theory and Applications, Springer, vol. 95(3), pages 331-378, August.
    2. Kahraman, Aykut & Gosavi, Abhijit, 2011. "On the distribution of the number stranded in bulk-arrival, bulk-service queues of the M/G/1 form," European Journal of Operational Research, Elsevier, vol. 212(2), pages 352-360, July.
    3. M. Balasubramanian & R. Arumuganathan, 2011. "Steady state analysis of a bulk arrival general bulk service queueing system with modified M-vacation policy and variant arrival rate," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 11(4), pages 383-407.
    4. S. Jeyakumar & B. Senthilnathan, 2016. "Steady state analysis of bulk arrival and bulk service queueing model with multiple working vacations," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 9(3), pages 375-394.
    5. M. Haridass & R. Arumuganathan, 2011. "Analysis of a batch arrival general bulk service queueing system with variant threshold policy for secondary jobs," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 3(1), pages 56-77.
    6. Fakinos, D., 1991. "The relation between limiting queue size distributions at arrival and departure epochs in a bulk queue," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 327-329, April.
    7. Rajesh Kumar & Souvik Ghosh & Abhijit Datta Banik, 2021. "Numerical study on transient behaviour of finite bulk arrival or service queues with multiple working vacations," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 18(3), pages 384-403.
    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. Srinivas R. Chakravarthy & Serife Ozkar, 2024. "A Queueing Model with BMAP Arrivals and Heterogeneous Phase Type Group Services," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-30, December.
    2. 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.
    3. P. Rajasekhara Reddy & K. Srinivasa Rao & M. Venkateswaran, 2016. "Stochastic control of K-parallel and series queuing model and its applications," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 7(1), pages 178-197, December.
    4. G. Ayyappan & S. Karpagam, 2018. "An M [ X ] / G ( a , b )/1 Queueing System with Breakdown and Repair, Stand-By Server, Multiple Vacation and Control Policy on Request for Re-Service," Mathematics, MDPI, vol. 6(6), pages 1-18, June.
    5. Gérard Hébuterne & Catherine Rosenberg, 1999. "Arrival and departure state distributions in the general bulk‐service queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(1), pages 107-118, February.
    6. Anyue Chen & Xiaohan Wu & Jing Zhang, 2020. "Markovian bulk-arrival and bulk-service queues with general state-dependent control," Queueing Systems: Theory and Applications, Springer, vol. 95(3), pages 331-378, August.
    7. Xu, Jianjun & Serrano, Alejandro & Lin, Bing, 2017. "Optimal production and rationing policy of two-stage tandem production system," International Journal of Production Economics, Elsevier, vol. 185(C), pages 100-112.
    8. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.
    9. 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.
    10. Alexander Zeifman & Yacov Satin & Ivan Kovalev & Rostislav Razumchik & Victor Korolev, 2020. "Facilitating Numerical Solutions of Inhomogeneous Continuous Time Markov Chains Using Ergodicity Bounds Obtained with Logarithmic Norm Method," Mathematics, MDPI, vol. 9(1), pages 1-20, December.
    11. Marko A. A. Boon & Onno J. Boxma & Offer Kella & Masakiyo Miyazawa, 2017. "Queue-length balance equations in multiclass multiserver queues and their generalizations," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 277-299, August.
    12. Justus Arne Schwarz & Martin Epp, 2016. "Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6251-6264, October.
    13. Seok Ho Chang & Dae Won Choi, 2006. "Modeling and Performance Analysis of a Finite-Buffer Queue with Batch Arrivals, Batch Services, and Setup Times: The M X /G Y /1/K + B Queue with Setup Times," INFORMS Journal on Computing, INFORMS, vol. 18(2), pages 218-228, May.
    14. Yuan, Xuchuan & Brian Hwarng, H., 2023. "Examining the dynamics of reactive capacity allocation through a chaos lens," European Journal of Operational Research, Elsevier, vol. 308(2), pages 912-928.
    15. Anyue Chen & Junping Li & Xiaohan Wu & Jing Zhang, 2021. "Decay parameter for general stopped Markovian bulk-arrival and bulk-service queues," Queueing Systems: Theory and Applications, Springer, vol. 99(3), pages 305-344, December.

    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:queues:v:104:y:2023:i:1:d:10.1007_s11134-022-09870-8. 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.