Minimizing the cost of dispatch delays by holding patrol cars in reserve

At many police departments high-priority callers sometimes incur undue delays that could be avoided by the use of a differential response strategy that takes full account of the different costs of delay for different priority calls. In this article we examine such a strategy, in which lower-priority callers may not be served immediately, even though some response units are available. Arriving priorityi callers are queued whenever the number of busy patrol units equals or exceeds the cutoff number for that priority. Our purpose is (1) to find a practical way of choosing the set of cutoff numbers that will minimize the expected total cost of delays for the entire system and (2) to use that method to investigate how the optimal set of cutoffs changes in response to changes in several important variables, including the relative costs of delay for different priorities, the overall workload, and the relative frequencies of different priority calls.