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An optimal policy for an infinite dam with exponential inputs of water  

Kim, Myung-Hwa (Department of Statistics, Sookmyung Women's University)
Baek, Jee-Seon (Methodology Division, Statistical Research institute)
Choi, Seung-Kyoung (Department of Statistics, Sookmyung Women's University)
Lee, Eui-Yong (Department of Statistics, Sookmyung Women's University)
Publication Information
Journal of the Korean Data and Information Science Society / v.22, no.6, 2011 , pp. 1089-1096 More about this Journal
Abstract
We consider an infinite dam with inputs formed by a compound Poisson process and adopt a $P^M_{\lambda}$-policy to control the level of water, where the water is released at rate M when the level of water exceeds threshold ${\lambda}$. We obtain interesting stationary properties of the level of water, when the amount of each input independently follows an exponential distribution. After assigning several managing costs to the dam, we derive the long-run average cost per unit time and show that there exist unique values of releasing rate M and threshold ${\lambda}$ which minimize the long-run average cost per unit time. Numerical results are also illustrated by using MATLAB.
Keywords
Compound Poisson process; infinite dam; long-run average cost per unit time; $P^M_{\lambda}$-policy; stationary state;
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Times Cited By KSCI : 3  (Citation Analysis)
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