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Fluid Models for Overloaded Multiclass Many-Server Queueing Systems with First-Come, First-Served Routing

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  • Rishi Talreja

    (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

Motivated by models of tenant assignment in public housing, we study approximating deterministic fluid models for overloaded queueing systems having multiple customer classes (classes of tenants) and multiple service pools (housing authorities), each with many servers (housing units). Customer abandonment acts to keep the system stable, yielding a proper steady-state description. Motivated by fairness considerations, we assume that customers are selected for service by newly available servers on a first-come, first-served (FCFS) basis from all classes the corresponding service pools are allowed to serve. In this context, it is challenging to determine stationary routing flow rates between customer classes and service pools. Given those routing flow rates, each single fluid queue can be analyzed separately using previously established methods. Our ability to determine the routing flow rates depends on the structure of the network routing graph. We obtain the desired routing flow rates in three cases: when the routing graph is (i) a tree (sparsely connected), (ii) complete bipartite (fully connected), and (iii) an appropriate combination of the previous two cases. Other cases remain unsolved. In the last two solved cases, the routing flow rates are actually not uniquely determined by the fluid model, but become so once we make stochastic assumptions about the queueing models that the fluid model approximates.

Suggested Citation

  • Rishi Talreja & Ward Whitt, 2008. "Fluid Models for Overloaded Multiclass Many-Server Queueing Systems with First-Come, First-Served Routing," Management Science, INFORMS, vol. 54(8), pages 1513-1527, August.
    • Handle: RePEc:inm:ormnsc:v:54:y:2008:i:8:p:1513-1527
    DOI: 10.1287/mnsc.1080.0868
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    References listed on IDEAS

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    1. Ward Whitt, 2004. "Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments," Management Science, INFORMS, vol. 50(10), pages 1449-1461, October.
    2. Johnson, Michael P., 2001. "Tenant-based subsidized housing location planning under uncertainty," Socio-Economic Planning Sciences, Elsevier, vol. 35(3), pages 149-173, September.
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    4. Michael Johnson, 2003. "Single-Period Location Models for Subsidized Housing: Tenant-Based Subsidies," Annals of Operations Research, Springer, vol. 123(1), pages 105-124, October.
    5. Edward H. Kaplan, 1986. "Tenant Assignment Models," Operations Research, INFORMS, vol. 34(6), pages 832-843, December.
    6. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    7. Ward Whitt, 1984. "Departures from a Queue with Many Busy Servers," Mathematics of Operations Research, INFORMS, vol. 9(4), pages 534-544, November.
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    Citations

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    Cited by:

    1. Otis B. Jennings & Josh E. Reed, 2012. "An Overloaded Multiclass FIFO Queue with Abandonments," Operations Research, INFORMS, vol. 60(5), pages 1282-1295, October.
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    3. John N. Tsitsiklis & Kuang Xu, 2017. "Flexible Queueing Architectures," Operations Research, INFORMS, vol. 65(5), pages 1398-1413, October.
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    5. Yongjiang Guo & Xiyang Hou & Yunan Liu, 2021. "A functional law of the iterated logarithm for multi-class queues with batch arrivals," Annals of Operations Research, Springer, vol. 300(1), pages 51-77, May.
    6. Francisco Castro & Hamid Nazerzadeh & Chiwei Yan, 2020. "Matching queues with reneging: a product form solution," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 359-385, December.
    7. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    8. Ivo Adan & Brett Hathaway & Vidyadhar G. Kulkarni, 2019. "On first-come, first-served queues with two classes of impatient customers," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 113-142, February.

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