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Performance Analysis of a Queue with Congestion-Based Staffing Policy

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  • Zhe George Zhang

    (Department of Decision Sciences, Western Washington University, Bellingham, Washington 98225; and Faculty of Business Administration, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada)

Abstract

This paper analyzes a waiting line system that is motivated by the operations of border-crossing stations between the United States and Canada. There are two main conflicting goals in such a system: high security level, which often leads to a longer line; and good customer service, which requires a shorter line. Thus, unlike other queueing systems, maintaining the average queue length within a certain range is the primary objective. This is achieved using a staffing policy, called "congestion-based staffing," or CBS, where the number of servers (inspection booths) is adjusted according to the queue length during a planning period. We first present an exact benchmark model of Markovian type based on the matrix-geometric solution. For practical CBS policies, we develop a set of closed-form formulas for the major performance measures based on regenerative cycle analysis and fluid limit approximation. Numerical examples show that these approximation formulas are simple, accurate, and robust for practitioners to use in designing CBS policies.

Suggested Citation

  • Zhe George Zhang, 2009. "Performance Analysis of a Queue with Congestion-Based Staffing Policy," Management Science, INFORMS, vol. 55(2), pages 240-251, February.
    • Handle: RePEc:inm:ormnsc:v:55:y:2009:i:2:p:240-251
    DOI: 10.1287/mnsc.1080.0914
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    References listed on IDEAS

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    1. Colin E. Bell, 1975. "Technical Note—Turning Off a Server with Customers Present: Is This Any Way to Run an M / M / c Queue with Removable Servers?," Operations Research, INFORMS, vol. 23(3), pages 571-574, June.
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    Cited by:

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    4. Tirdad, Ali & Grassmann, Winfried K. & Tavakoli, Javad, 2016. "Optimal policies of M(t)/M/c/c queues with two different levels of servers," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1124-1130.
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    7. Song, Cen & Zhuang, Jun, 2017. "N-stage security screening strategies in the face of strategic applicants," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 292-301.
    8. Liu, Zhongyi & Liu, Jingchen & Zhai, Xin & Wang, Guanying, 2019. "Police staffing and workload assignment in law enforcement using multi-server queueing models," European Journal of Operational Research, Elsevier, vol. 276(2), pages 614-625.
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    10. Li Xia & Zhe George Zhang & Quan‐Lin Li, 2022. "A c/μ‐Rule for Job Assignment in Heterogeneous Group‐Server Queues," Production and Operations Management, Production and Operations Management Society, vol. 31(3), pages 1191-1215, March.
    11. Lingjiao Zhang & Jinting Wang & Yilin Wang, 2023. "Strategic Behavior and Optimization of an M/M/1 Queue with N-Policy and Hysteretic Control," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-29, December.
    12. Zhe George Zhang & Hsing Paul Luh & Chia-Hung Wang, 2011. "Modeling Security-Check Queues," Management Science, INFORMS, vol. 57(11), pages 1979-1995, November.
    13. James J. Kim & Douglas G. Down & Mohan Chaudhry & Abhijit Datta Banik, 2022. "Difference Equations Approach for Multi-Server Queueing Models with Removable Servers," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1297-1321, September.
    14. Pengfei Guo & Zhe George Zhang, 2013. "Strategic Queueing Behavior and Its Impact on System Performance in Service Systems with the Congestion-Based Staffing Policy," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 118-131, September.
    15. Pengfei Guo & Refael Hassin, 2011. "Strategic Behavior and Social Optimization in Markovian Vacation Queues," Operations Research, INFORMS, vol. 59(4), pages 986-997, August.
    16. Yu, Mengqiao & Ding, Yichuan & Lindsey, Robin & Shi, Cong, 2016. "A data-driven approach to manpower planning at U.S.–Canada border crossings," Transportation Research Part A: Policy and Practice, Elsevier, vol. 91(C), pages 34-47.
    17. Cen Song & Jun Zhuang, 2017. "Two-stage security screening strategies in the face of strategic applicants, congestions and screening errors," Annals of Operations Research, Springer, vol. 258(2), pages 237-262, November.

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