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Police Patrol-Initiated Activities Within a Systems Queueing Model


  • Richard C. Larson

    (Massachusetts Institute of Technology)

  • Mark A. Mcknew

    (Clemson University)


Officers in police patrol cars operate in a complex stochastic environment. In addition to handling dispatcher-assigned calls for service from the public, they patrol to pose a threat of apprehension to would-be offenders and undertake certain on-site interventions to help improve general public safety. The on-site work, often highly discretionary, is called patrol-initiated activity. It includes issuing tickets for traffic violations, building checks, car checks, pedestrian checks and assisting motorists. In many cities patrol-initiated activities and calls for service consume comparable amounts of officers' time. In this paper we develop a spatially-oriented queueing-type model of a police patrol force that allows each of N patrol cars to be in one of three states: (1) busy, on a call for service; (2) busy, on a patrol-initiated activity; (3) free, on patrol. Designed for computer solution, the model yields N nonlinear equations whose unknowns are the workloads of the N patrol cars. Other performance measures of patrol can be computed easily in terms of the workloads. The incorporation of patrol-initiated activities represents an improvement over previous OR/MS models, and could result in more informed police management decisions regarding patrol beat design, workload smoothing among officers, and reduction of neighborhood-specific inequities in police accessibility. The methods of this paper are potentially applicable to other urban services, including taxi and maintenance operations.

Suggested Citation

  • Richard C. Larson & Mark A. Mcknew, 1982. "Police Patrol-Initiated Activities Within a Systems Queueing Model," Management Science, INFORMS, vol. 28(7), pages 759-774, July.
  • Handle: RePEc:inm:ormnsc:v:28:y:1982:i:7:p:759-774

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    Cited by:

    1. Iannoni, Ana Paula & Chiyoshi, Fernando & Morabito, Reinaldo, 2015. "A spatially distributed queuing model considering dispatching policies with server reservation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 75(C), pages 49-66.
    2. Boyacı, Burak & Geroliminis, Nikolas, 2015. "Approximation methods for large-scale spatial queueing systems," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 151-181.
    3. Hall, Randolph, 2000. "Incident Dispatching, Clearance and Delay," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt2pp689vn, Institute of Transportation Studies, UC Berkeley.
    4. Atkinson, J.B. & Kovalenko, I.N. & Kuznetsov, N. & Mykhalevych, K.V., 2008. "A hypercube queueing loss model with customer-dependent service rates," European Journal of Operational Research, Elsevier, vol. 191(1), pages 223-239, November.
    5. Hall, Randolph W., 2002. "Incident dispatching, clearance and delay," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(1), pages 1-16, January.
    6. repec:eee:transe:v:103:y:2017:i:c:p:143-157 is not listed on IDEAS
    7. repec:pal:jorsoc:v:60:y:2009:i:1:d:10.1057_jors.2009.3 is not listed on IDEAS
    8. de Souza, Regiane Máximo & Morabito, Reinaldo & Chiyoshi, Fernando Y. & Iannoni, Ana Paula, 2015. "Incorporating priorities for waiting customers in the hypercube queuing model with application to an emergency medical service system in Brazil," European Journal of Operational Research, Elsevier, vol. 242(1), pages 274-285.
    9. 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.


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