Determining the relation between fire engine travel times and travel distances in New York City

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) = v_c/a + D/v_c if D > d. The parameter a can be interpreted as an acceleration and v_c 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.