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A Network of Time-Varying Many-Server Fluid Queues with Customer Abandonment

Author

Listed:
  • Yunan Liu

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Ward Whitt

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

To describe the congestion in large-scale service systems, we introduce and analyze a non-Markovian open network of many-server fluid queues with customer abandonment, proportional routing, and time-varying model elements. Proportions of the fluid completing service from each queue are immediately routed to the other queues, with the fluid not routed to one of the queues being immediately routed out of the network. The fluid queue network serves as an approximation for the corresponding non-Markovian open network of many-server queues with Markovian routing, where all model elements may be time varying. We establish the existence of a unique vector of (net) arrival rate functions at each queue and the associated time-varying performance. In doing so, we provide the basis for an efficient algorithm, even for networks with many queues.

Suggested Citation

  • Yunan Liu & Ward Whitt, 2011. "A Network of Time-Varying Many-Server Fluid Queues with Customer Abandonment," Operations Research, INFORMS, vol. 59(4), pages 835-846, August.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:4:p:835-846
    DOI: 10.1287/opre.1110.0942
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    References listed on IDEAS

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    1. Hong Chen & Avi Mandelbaum, 1991. "Discrete Flow Networks: Bottleneck Analysis and Fluid Approximations," Mathematics of Operations Research, INFORMS, vol. 16(2), pages 408-446, May.
    2. Zohar Feldman & Avishai Mandelbaum & William A. Massey & Ward Whitt, 2008. "Staffing of Time-Varying Queues to Achieve Time-Stable Performance," Management Science, INFORMS, vol. 54(2), pages 324-338, February.
    3. Ward Whitt, 2006. "Fluid Models for Multiserver Queues with Abandonments," Operations Research, INFORMS, vol. 54(1), pages 37-54, February.
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    Citations

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    Cited by:

    1. Andrew Daw & Brian Fralix & Jamol Pender, 2025. "Establishing Convergence of Infinite-Server Queues with Batch Arrivals to Shot-Noise Processes," Operations Research, INFORMS, vol. 73(4), pages 2002-2009, July.
    2. Avishai Mandelbaum & Petar Momčilović, 2017. "Personalized queues: the customer view, via a fluid model of serving least-patient first," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 23-53, October.
    3. Kawai, Yosuke & Takagi, Hideaki, 2015. "Fluid approximation analysis of a call center model with time-varying arrivals and after-call work," Operations Research Perspectives, Elsevier, vol. 2(C), pages 81-96.
    4. Angelos Aveklouris & Amber L. Puha & Amy R. Ward, 2024. "A fluid approximation for a matching model with general reneging distributions," Queueing Systems: Theory and Applications, Springer, vol. 106(3), pages 199-238, April.
    5. Barbara Margolius & Małgorzata M. O’Reilly, 2016. "The analysis of cyclic stochastic fluid flows with time-varying transition rates," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 43-73, February.
    6. Ryan Palmer & Martin Utley, 2020. "On the modelling and performance measurement of service networks with heterogeneous customers," Annals of Operations Research, Springer, vol. 293(1), pages 237-268, October.
    7. Jinsheng Chen & Jing Dong & Pengyi Shi, 2025. "Optimal Routing Under Demand Surges: The Value of Future Arrival Rates," Operations Research, INFORMS, vol. 73(1), pages 510-542, January.
    8. Hu, Lu & Zhao, Bin & Zhu, Juanxiu & Jiang, Yangsheng, 2019. "Two time-varying and state-dependent fluid queuing models for traffic circulation systems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 997-1019.
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    10. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.
    11. Noa Zychlinski & Avishai Mandelbaum & Petar Momčilović, 2018. "Time-varying tandem queues with blocking: modeling, analysis, and operational insights via fluid models with reflection," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 15-47, June.
    12. Max Tschaikowski & Mirco Tribastone, 2017. "A computational approach to steady-state convergence of fluid limits for Coxian queuing networks with abandonment," Annals of Operations Research, Springer, vol. 252(1), pages 101-120, May.
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    14. Mozhu Wang & Jianming Yao, 2023. "Replenishment and delivery optimization for unmanned vending machines service system based on fuzzy clustering," Electronic Commerce Research, Springer, vol. 23(4), pages 2419-2461, December.
    15. A. Korhan Aras & Xinyun Chen & Yunan Liu, 2018. "Many-server Gaussian limits for overloaded non-Markovian queues with customer abandonment," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 81-125, June.
    16. Avishai Mandelbaum & Petar Momčilović & Nikolaos Trichakis & Sarah Kadish & Ryan Leib & Craig A. Bunnell, 2020. "Data-Driven Appointment-Scheduling Under Uncertainty: The Case of an Infusion Unit in a Cancer Center," Management Science, INFORMS, vol. 66(1), pages 243-270, January.
    17. Mozhu Wang & Jianming Yao, 2023. "A reliable location design of unmanned vending machines based on customer satisfaction," Electronic Commerce Research, Springer, vol. 23(1), pages 541-575, March.

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