Square Root Laws for Fire Engine Response Distances

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.