IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i10p1500-d1392540.html
   My bibliography  Save this article

Analysis of a Two-Stage Tandem Queuing System with Priority and Clearing Service in the Second Stage

Author

Listed:
  • Jia Xu

    (School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China)

  • Liwei Liu

    (School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China)

Abstract

This paper considers a two-stage tandem queuing system with ordinary customers and priority customers. Upon arrival, ordinary customers are individually served in the first stage, then move to the second stage and receive clearing service. Priority customers can bypass the first stage and proceed directly to the second stage for clearing service. The second stage has N service seats. All customers currently in the second stage are served simultaneously (i.e., clearing service). Once there are N customers in the second stage, the first stage will be blocked, and newly arriving priority customers will balk and leave without joining. We first formulate a two-dimensional Markov chain to analyze this queuing system and derive the stability condition. Subsequently, the stationary distribution of the system is derived using the matrix-analytic method and spectral expansion technique. Furthermore, analytical expressions for the mean queue length, mean sojourn time, and other performance measures are presented. Finally, some numerical examples are provided to illustrate the effects of various parameters, offering valuable insights for designing such two-stage tandem queuing systems.

Suggested Citation

  • Jia Xu & Liwei Liu, 2024. "Analysis of a Two-Stage Tandem Queuing System with Priority and Clearing Service in the Second Stage," Mathematics, MDPI, vol. 12(10), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1500-:d:1392540
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/10/1500/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/10/1500/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jia Xu & Liwei Liu & Kan Wu, 2023. "Analysis of a retrial queueing system with priority service and modified multiple vacations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(17), pages 6207-6231, September.
    2. Joris Walraevens & Bart Steyaert & Herwig Bruneel, 2006. "A preemptive repeat priority queue with resampling: Performance analysis," Annals of Operations Research, Springer, vol. 146(1), pages 189-202, September.
    3. Anatoly Nazarov & Tuan Phung-Duc & Svetlana Paul & Mariya Morozova, 2023. "Scaling Limits of a Tandem Queue with Two Infinite Orbits," Mathematics, MDPI, vol. 11(11), pages 1-14, 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. Herwig Bruneel & Arnaud Devos, 2024. "Explicit Solutions for Coupled Parallel Queues," Mathematics, MDPI, vol. 12(15), pages 1-31, July.
    2. Atencia, I., 2017. "A Geo/G/1 retrial queueing system with priority services," European Journal of Operational Research, Elsevier, vol. 256(1), pages 178-186.
    3. Atencia-Mc.Killop, Ivan & Galán-García, José L. & Aguilera-Venegas, Gabriel & Rodríguez-Cielos, Pedro & Galán-García, MÁngeles, 2018. "A Geo[X]/G[X]/1 retrial queueing system with removal work and total renewal discipline," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 245-253.
    4. Sofian De Clercq & Koenraad Laevens & Bart Steyaert & Herwig Bruneel, 2013. "A multi-class discrete-time queueing system under the FCFS service discipline," Annals of Operations Research, Springer, vol. 202(1), pages 59-73, January.
    5. I. Atencia, 2015. "A discrete-time queueing system with server breakdowns and changes in the repair times," Annals of Operations Research, Springer, vol. 235(1), pages 37-49, December.
    6. Kim, Kilhwan & Chae, Kyung C., 2010. "Discrete-time queues with discretionary priorities," European Journal of Operational Research, Elsevier, vol. 200(2), pages 473-485, January.
    7. Herwig Bruneel & Dieter Fiems & Joris Walraevens & Sabine Wittevrongel, 2014. "Queueing models for the analysis of communication systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 421-448, July.
    8. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    9. Przemysław Korytkowski & Tomasz Wiśniewski, 2011. "Performance analysis of commercial offset printing under dynamic priority rules," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(1), pages 53-64.

    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:12:y:2024:i:10:p:1500-:d:1392540. 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.