International Journal of Stochastic Analysis
Volume 2011 (2011), Article ID 916952, 17 pages
http://dx.doi.org/10.1155/2011/916952
Research Article

Control of Dams Using 𝑃 𝐌 𝝀 , 𝝉 Policies When the Input Process Is a Nonnegative Lévy Process

Mohamed Abdel-Hameed

Department of Statistics, College of Business and Economics, United Arab Emirates University, Al-Ain 17555, UAE

Received 28 April 2011; Accepted 17 July 2011

Academic Editor: Ho Lee

Copyright © 2011 Mohamed Abdel-Hameed. 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

We consider 𝑃 𝑀 𝜆 , 𝜏 policy of a dam in which the water input is an increasing Lévy process. The release rate of the water is changed from 0 to 𝑀 and from 𝑀 to 0 ( 𝑀 > 0 ) at the moments when the water level upcrosses level 𝜆 and downcrosses level 𝜏 ( 𝜏 < 𝜆 ) , respectively. We determine the potential of the dam content and compute the total discounted as well as the long-run average cost. We also find the stationary distribution of the dam content. Our results extend the results in the literature when the water input is assumed to be a Poisson process.