Optimal control of a simple immigration process through the introduction of a predator

This article is concerned with the problem of controlling a simple immigration process, which represents a pest population, by the introduction of a predator. It is assumed that the cost rate caused by the pests is an increasing function of their population size and that the cost rate of the controlling action is constant. The existence of a control-limit policy that minimizes the expected long-run average cost per unit is established. The proof is based on the variation of a fictitious parameter over the entire real line.