Square-Root Laws for Fire Company Travel Distances

by Peter Kolesar, Edward H. Blum


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An inverse square-root function is developed for the relation between average response distance and the number of locations at which fire companies 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 can be combined with relations between response distance and travel time to yield simple functions for predicting average travel times. Such models may then be employed as aids in the resolution of planning problems important to the management of urban fire departments. Our results can be used to find optimal allocations of fire companies given resource constraints and response time standards, or to describe the response time consequences of proposed allocation plans.

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