Extreme value theory applied to police performance analysis

Abstract

Extreme value theory is used to provide, according to one reviewer, a quantitative measure of the probability of a police dispatch operation going “haywire” under pressure. Convensional queuing theory that concentrates on measures of average performance is not readily adaptable to this application. In a major police department, average values of delay response were found to be acceptable, and preliminary analysis showed that sufficient resources were available to avoid excessive queuing at peak loads. Nevertheless, reports of occasional excessively delayed responses indicated the existence of serious problems. Extreme value theory concentrates on the statistically rare long delays that, because of the many repetitions of requests for service, can occur more frequently in time than is acceptable to police management. In the example discussed, the predicted magnitudes and frequencies of these long delays provided the justification for an immediate improvement program. In general, the straightforward methodology described would appear to have broad applications and great practical value. The subsequent analysis to identify causal factors is not a part of the discussion.