On a theory of search

Abstract

SUMMARY Stochastic models are developed to study the success of a search by what is termed a predator for randomly or contagiously located points, called prey. The model is specified by giving the distribution of the searching time to locate a prey, school or cluster of prey and the joint distribution of handling time and numbers caught from each cluster sighted. If a stationary distribution of prey is assumed and their removal is ignored, then the process is analogous to a cumulative renewal process. The mean numbers of prey or clusters of prey and their variances are readily obtained by use of limit theorems of renewal theory.