IDEAS home Printed from
   My bibliography  Save this article

Square Root Laws for Fire Engine Response Distances


  • Peter Kolesar

    (The New York City-RAND Institute)

  • Edward H. Blum

    (The New York City-RAND Institute)


An inverse square-root function is developed for the relation between average response distance and the number of locations at which response units are stationed in a region. Analysis of theoretical models, simulation data, and empirical measurements are used to confirm the square-root model. The square-root response distance model is combined with response distance--response time relations to resolve decision problems important to the management of urban fire departments. The results can be used to find optimal resource allocations given resource constraints and response time standards, or to describe the response time consequences of proposed allocation plans.

Suggested Citation

  • Peter Kolesar & Edward H. Blum, 1973. "Square Root Laws for Fire Engine Response Distances," Management Science, INFORMS, vol. 19(12), pages 1368-1378, August.
  • Handle: RePEc:inm:ormnsc:v:19:y:1973:i:12:p:1368-1378

    Download full text from publisher

    File URL:
    Download Restriction: no


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. repec:bla:jorssa:v:180:y:2017:i:2:p:433-453 is not listed on IDEAS
    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. Patrick Sun, 2014. "Quality Competition in Mobile Telecommunications: Evidence from Connecticut," Working Papers 14-05, NET Institute.
    4. 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.
    5. Pavan, Giulia, 2017. "Green Car Adoption and the Supply of Alternative Fuels," TSE Working Papers 17-875, Toulouse School of Economics (TSE).
    6. repec:pal:jorsoc:v:56:y:2005:i:6:d:10.1057_palgrave.jors.2601950 is not listed on IDEAS
    7. Peter J. Kolesar, 2012. "OM Forum --Some Lessons on Operations Management Model Implementation Drawn from the RAND Fire Project," Manufacturing & Service Operations Management, INFORMS, vol. 14(1), pages 1-6, January.
    8. repec:pal:jorsoc:v:60:y:2009:i:1:d:10.1057_jors.2009.3 is not listed on IDEAS
    9. Nurski, Laura & Verboven, Frank, 2014. "Incumbency advantages, distribution networks and exclusivity — Evidence from the European car markets," International Journal of Industrial Organization, Elsevier, vol. 34(C), pages 75-79.
    10. Langevin, André & Mbaraga, Pontien & Campbell, James F., 1996. "Continuous approximation models in freight distribution: An overview," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 163-188, June.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:19:y:1973:i:12:p:1368-1378. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.