On the control of a truncated general immigration process through the introduction of a predator

This paper is concerned with the problem of controlling a truncated general immigration process, which represents a population of harmful individuals, by the introduction of a predator. If the parameters of the model satisfy some mild conditions, the existence of a control-limit policy that is average-cost optimal is proved. The proof is based on the uniformization technique and on the variation of a fictitious parameter over the entire real line. Furthermore, an efficientMarkov decision algorithm is developed that generates a sequence of improving control-limit policies converging to the optimal policy.