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A Comparison of the Multiple Dispatch and M/M/c Priority Queueing Models of Police Patrol

Author

Listed:
  • Linda Green

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • Peter Kolesar

    (Graduate School of Business, Columbia University, New York, New York 10027)

Abstract

In many cities, a substantial fraction of calls for police service require more than one patrol car. We compare Green's multiple dispatch queueing model to several M/M/c-based approximations for multiple car dispatching that are obtained by adjusting the parameters. We found that none of the approximate models yields consistently reliable results under a broad range of conditions. The best approximations are produced by reducing the actual number of servers. Increasing the call rate gives the worst results.

Suggested Citation

  • Linda Green & Peter Kolesar, 1984. "A Comparison of the Multiple Dispatch and M/M/c Priority Queueing Models of Police Patrol," Management Science, INFORMS, vol. 30(6), pages 665-670, June.
    • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:6:p:665-670
    DOI: 10.1287/mnsc.30.6.665
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    Citations

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    Cited by:

    1. Phillip R. Jenkins & Matthew J. Robbins & Brian J. Lunday, 2021. "Approximate Dynamic Programming for Military Medical Evacuation Dispatching Policies," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 2-26, January.
    2. Linda V. Green & Peter J. Kolesar, 2004. "ANNIVERSARY ARTICLE: Improving Emergency Responsiveness with Management Science," Management Science, INFORMS, vol. 50(8), pages 1001-1014, August.
    3. Sukanya Samanta & Goutam Sen & Soumya Kanti Ghosh, 2022. "A literature review on police patrolling problems," Annals of Operations Research, Springer, vol. 316(2), pages 1063-1106, September.
    4. Alfonso J. Pedraza-Martinez & Sameer Hasija & Luk N. Van Wassenhove, 2020. "Fleet Coordination in Decentralized Humanitarian Operations Funded by Earmarked Donations," Operations Research, INFORMS, vol. 68(4), pages 984-999, July.
    5. Rettke, Aaron J. & Robbins, Matthew J. & Lunday, Brian J., 2016. "Approximate dynamic programming for the dispatch of military medical evacuation assets," European Journal of Operational Research, Elsevier, vol. 254(3), pages 824-839.
    6. P. Daniel Wright & Matthew J. Liberatore & Robert L. Nydick, 2006. "A Survey of Operations Research Models and Applications in Homeland Security," Interfaces, INFORMS, vol. 36(6), pages 514-529, December.
    7. Nilay Tan{i}k Argon & Serhan Ziya, 2009. "Priority Assignment Under Imperfect Information on Customer Type Identities," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 674-693, June.
    8. Diwas S. Kc & Christian Terwiesch, 2009. "Impact of Workload on Service Time and Patient Safety: An Econometric Analysis of Hospital Operations," Management Science, INFORMS, vol. 55(9), pages 1486-1498, September.
    9. Hall, Randolph, 2000. "Incident Dispatching, Clearance and Delay," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt2pp689vn, Institute of Transportation Studies, UC Berkeley.
    10. Drent, Collin & Keizer, Minou Olde & Houtum, Geert-Jan van, 2020. "Dynamic dispatching and repositioning policies for fast-response service networks," European Journal of Operational Research, Elsevier, vol. 285(2), pages 583-598.
    11. Yoon, Soovin & Albert, Laura A., 2021. "Dynamic dispatch policies for emergency response with multiple types of vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    12. Hall, Randolph W., 2002. "Incident dispatching, clearance and delay," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(1), pages 1-16, January.
    13. Ansari, Sardar & Yoon, Soovin & Albert, Laura A., 2017. "An approximate hypercube model for public service systems with co-located servers and multiple response," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 143-157.
    14. Hall, Randolph W., 2001. "Incident Management: Process Analysis and Improvement," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt1jf6j37t, Institute of Transportation Studies, UC Berkeley.
    15. William P. Millhiser & Charu Sinha & Matthew J. Sobel, 2016. "Optimality of the fastest available server policy," Queueing Systems: Theory and Applications, Springer, vol. 84(3), pages 237-263, December.

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