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Optimal control of a finite dam using PMλΤ policies and penalty cost: total discounted and long run average cases

Published online by Cambridge University Press:  14 July 2016

M. Abdel-hameed  and
Y. Nakhi
M. Abdel-hameed*
Affiliation:
University of Kuwait
Y. Nakhi
Affiliation:
University of Kuwait
*
∗ Postal address for both authors: Department of Statistics and Operations Research, Kuwait University, College of Science, P.O. Box 5969, Kuwait.
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Abstract

Zuckermann [10] considers the problem of optimal control of a finite dam using policies, assuming that the input process is Wiener with drift term μ ≧ 0. Lam Yeh and Lou Jiann Hua [7] treat the case where the input is a Wiener process with a reflecting boundary at zero, with drift term μ ≧ 0, using the long-run average cost and total discounted cost criteria. Attia [1] obtains results similar to those of Lam Yeh and Lou Jiann Hua for the long-run average case and extends them to include μ < 0. In this paper we look further into the results of Zuckerman [10], simplify some of the work of Attia [1], [2], offering corrections to some of his formulae and extend the results of Lam Yeh and Lou Jiann Hua [7].

Keywords

WIENER INPUTDRIFTREFLECTING BOUNDARYGEOMETRIC WIENER INPUT
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 4 , December 1990 , pp. 888 - 898
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

∗

Research supported by Kuwait University Grant SM064. Research partly carried out while this author was at the University of North Carolina.

References

[1] Attia, F. A. (1987) The control of a finite dam with penalty cost function: Wiener process input. Stoch. Proc. Appl. 25, 289–299.Google Scholar
[2] Attia, F. A. (1989) Resolvent operators of Markov processes and their applications in the control of a finite dam. J. Appl. Prob. 26, 314–324.Google Scholar
[3] Blumenthal, R. M. and Getoor, R. K. (1968) Markov Process and Potential Theory. Academic Press, New York.Google Scholar
[4] Harrison, J. M. (1985) Brownian Motion and Stochastic Flow System. Wiley, New York.Google Scholar
[5] Karlin, S. and Taylor, H. W. (1975) A First Course In Stochastic Processes. Academic Press, New York.Google Scholar
[6] Karlin, S. and Taylor, H. W. (1981) A Second Course In Stochastic Processes. Academic Press, New York.Google Scholar
[7] Yeh, Lam and Hua, Lou Jiann (1987) Optimal control of a finite dam. J. Appl. Prob. 24, 186–199.Google Scholar
[8] Lamperti, J. (1977) Stochastic Processes: A Survey of the Mathematical Theory. Springer-Verlag, New York.Google Scholar
[9] Oberhettinger, F. (1977) Tables of Mellin Transforms. Springer-Verlag, Berlin.Google Scholar
[10] Zuckerman, D. (1977) Two-stage output procedure of a finite dam. J. Appl. Prob. 14, 421–425.Google Scholar