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Priority queue with customer upgrades

Author

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  • Qi‐Ming He
  • Jingui Xie
  • Xiaobo Zhao

Abstract

This article is concerned with a general multi‐class multi‐server priority queueing system with customer priority upgrades. The queueing system has various applications in inventory control, call centers operations, and health care management. Through a novel design of Lyapunov functions, and using matrix‐analytic methods, sufficient conditions for the queueing system to be stable or instable are obtained. Bounds on the queue length process are obtained by a sample path method, with the help of an auxiliary queueing system. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Suggested Citation

  • Qi‐Ming He & Jingui Xie & Xiaobo Zhao, 2012. "Priority queue with customer upgrades," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 362-375, August.
    • Handle: RePEc:wly:navres:v:59:y:2012:i:5:p:362-375
    DOI: 10.1002/nav.21494
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    1. Borga Deniz & Itir Karaesmen & Alan Scheller-Wolf, 2010. "Managing Perishables with Substitution: Inventory Issuance and Replenishment Heuristics," Manufacturing & Service Operations Management, INFORMS, vol. 12(2), pages 319-329, July.
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    4. Ward Whitt, 1986. "Deciding Which Queue to Join: Some Counterexamples," Operations Research, INFORMS, vol. 34(1), pages 55-62, February.
    5. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
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    Cited by:

    1. Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Single-Server Multi-Class Queue with Unreliable Service, Batch Correlated Arrivals, Customers Impatience, and Dynamical Change of Priorities," Mathematics, MDPI, vol. 9(11), pages 1-17, May.
    2. Vladimir Vishnevsky & Valentina Klimenok & Alexander Sokolov & Andrey Larionov, 2021. "Performance Evaluation of the Priority Multi-Server System MMAP/PH/M/N Using Machine Learning Methods," Mathematics, MDPI, vol. 9(24), pages 1-27, December.
    3. Valentina Klimenok & Alexander Dudin & Vladimir Vishnevsky, 2020. "Priority Multi-Server Queueing System with Heterogeneous Customers," Mathematics, MDPI, vol. 8(9), pages 1-16, September.
    4. Jiang, Yangzi & Abouee-Mehrizi, Hossein & Diao, Yuhe, 2020. "Data-driven analytics to support scheduling of multi-priority multi-class patients with wait time targets," European Journal of Operational Research, Elsevier, vol. 281(3), pages 597-611.
    5. Seokjun Lee & Sergei Dudin & Olga Dudina & Chesoong Kim & Valentina Klimenok, 2020. "A Priority Queue with Many Customer Types, Correlated Arrivals and Changing Priorities," Mathematics, MDPI, vol. 8(8), pages 1-20, August.
    6. Valentina Klimenok & Alexander Dudin & Olga Dudina & Irina Kochetkova, 2020. "Queuing System with Two Types of Customers and Dynamic Change of a Priority," Mathematics, MDPI, vol. 8(5), pages 1-25, May.

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