IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i24p4771-d1004452.html
   My bibliography  Save this article

Evaluation of the Waiting Time in a Finite Capacity Queue with Bursty Input and a Generalized Push-Out Strategy

Author

Listed:
  • Chris Blondia

    (IDLab-Department of Computer Science, University of Antwerp-imec, 2000 Antwerp, Belgium)

Abstract

In this paper, we study a finite capacity queue where the arrival process is a special case of the discrete time Markov modulated Poisson process, the service times are generally distributed, and the server takes repeated vacations when the system is empty. The buffer acceptance strategy is based on a generalized push-out scheme: when the buffer is full, an arriving customer pushes out the N t h customer in the queue, where N takes values between 2 and the capacity of the system, and the arriving customer joins the end of the queue. Such a strategy is important when, as well as short waiting times for served customers, the time a pushed-out customer occupies a buffer space is also an important performance measure. The Laplace transform of the waiting time of a served customer is determined. Numerical examples show the influence of the bustiness of the input process and also the trade-off between the average waiting time of served customers and the occupancy of the buffer space of pushed-out customers.

Suggested Citation

  • Chris Blondia, 2022. "Evaluation of the Waiting Time in a Finite Capacity Queue with Bursty Input and a Generalized Push-Out Strategy," Mathematics, MDPI, vol. 10(24), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4771-:d:1004452
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/24/4771/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/24/4771/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tony T. Lee, 1984. "M / G /1/ N Queue with Vacation Time and Exhaustive Service Discipline," Operations Research, INFORMS, vol. 32(4), pages 774-784, August.
    2. Rostislav V. Razumchik, 2014. "Analysis Of Finite Capacity Queue With Negative Customers And Bunker For Ousted Customers Using Chebyshev And Gegenbauer Polynomials," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-21.
    3. Chris Blondia, 2021. "A queueing model for a wireless sensor node using energy harvesting," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 77(2), pages 335-349, June.
    4. Shoji Kasahara & Hideaki Takagi & Yutaka Takahashi & Toshiharu Hasegawa, 1996. "M / G / 1 / K system with push-out scheme under vacation policy," International Journal of Stochastic Analysis, Hindawi, vol. 9, pages 1-15, January.
    5. Yutae Lee & Bong Dae Choi & Bara Kim & Dan Keun Sung, 2007. "Delay Analysis of an M / G / 1 / K Priority Queueing System with Push-out Scheme," Mathematical Problems in Engineering, Hindawi, vol. 2007, pages 1-12, December.
    6. Kilhwan Kim & Xindong Peng, 2022. "Finite-Buffer M/G/1 Queues with Time and Space Priorities," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-30, May.
    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. V. Deepa & M. Haridass, 2023. "Simulation Analysis of a Base Station Using Finite Buffer M/G/1 Queueing System with Variant Sleeps," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-18, December.
    2. Doo Il Choi & Dae-Eun Lim, 2020. "Analysis of the State-Dependent Queueing Model and Its Application to Battery Swapping and Charging Stations," Sustainability, MDPI, vol. 12(6), pages 1-15, March.
    3. Chris Blondia, 2021. "A queueing model for a wireless sensor node using energy harvesting," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 77(2), pages 335-349, June.
    4. 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.
    5. Luis Zabala & Josu Doncel & Armando Ferro, 2023. "Modeling a Linux Packet-Capturing System with a Queueing System with Vacations," Mathematics, MDPI, vol. 11(7), pages 1-27, March.
    6. S. P. Niranjan & S. Devi Latha & Miroslav Mahdal & Krishnasamy Karthik, 2023. "Multiple Control Policy in Unreliable Two-Phase Bulk Queueing System with Active Bernoulli Feedback and Vacation," Mathematics, MDPI, vol. 12(1), pages 1-20, December.
    7. Grasman, Scott E. & Olsen, Tava Lennon & Birge, John R., 2005. "Finite buffer polling models with routing," European Journal of Operational Research, Elsevier, vol. 165(3), pages 794-809, September.
    8. 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.
    9. V. Deepa & M. Haridass & Dharmaraja Selvamuthu & Priyanka Kalita, 2023. "Analysis of energy efficiency of small cell base station in 4G/5G networks," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 82(3), pages 381-401, March.
    10. Mu-Song Chen & Hao-Wei Yen, 2016. "A two-stage approach in solving the state probabilities of the multi-queue //1 model," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(5), pages 1230-1244, April.

    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:gam:jmathe:v:10:y:2022:i:24:p:4771-:d:1004452. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.