A simple physical model of the way fire engines travel leads to the hypothesis that T, the average fire engine travel time, depends on D, the distance travelled according to T(D) = 2(D/a)1/2 if D ≤ d and T(D) = vc/a + D/vc if D > d. The parameter a can be interpreted as an acceleration and vc as a cruising velocity. A field experiment was run, and the above model validated and the parameters estimated, for New York City. It was also found that regional traffic conditions and hour of day appear to have only minor effects on average response velocities.
Kolesar, Peter, Warren Walker, and John Hausner. "Determining the relation between fire engine travel times and travel distances in New York City." Operations Research 23, no. 4 (1975): 614-627.
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