Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 76398, 12 pages
doi:10.1155/JAMDS/2006/76398
On the control of a truncated general immigration process through the introduction of a predator
Department of Financial and Management Engineering, University of the Aegean, 31 Fostini Str., Chios 82100, Greece
Received 17 December 2003; Accepted 15 February 2005
Copyright © 2006 E. G. Kyriakidis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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 efficient
Markov decision algorithm is developed that generates a sequence
of improving control-limit policies converging to the optimal
policy.