Multiple vehicle routing and dispatching to an emergency scene

A model of the distribution of arrival time at the scene of an emergency for the first of many vehicles is developed for the case in which travel times on the links of the network are normally distributed and the path travel times of different vehicles are correlated. The model suggests that the probability that the first vehicle arrives at the scene within a given time may be increased by reducing the path time correlations, even if doing so necessitates increasing the mean path travel time for some vehicles. The model with normally distributed travel times is compared with a more complex model that assumes Erlang distributed travel times and the results are shown to be in close agreement.