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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
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    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.
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