arXiv subjects
Publications and source records attributed to Mohamed Abdel-Hameed.
We consider the P(M,lambda,tau) maintenance policy of a dam using the total discounted and long-run average costs, when the input process is inverse Gaussian.
We consider the control of a finite dam when the input process is either spectrally positive Levy or spectrally positive Levy reflected at its infimum, using P(M,Lambda,tau) control policies. Our results extend and unify the results Bea et al (2003), Lam and Lou (1987), and Attia (1987). The techniques used by the above authors involve solving systems of differential or integral equations. Our methods of proof are based on the theory and methods of scale functions of Levy processes.
Zuckermann [10] considers the problem of optimal control of a finite dam assuming that the input process is Wiener with positive drift term μ\geq 0. Lam and Lou [7] treat the case where the input is a Wiener process with a reflecting boundary at its infimum, with a positive drift term, using the long-run Average and total discounted cost criteria. Attia [3] obtains results similar to those of Lam and Lou, through simpler and more direct methods. Bae et al. [5] treat the long-run average cost case when the input process is a compound Poisson process with a negative drift. In this paper we unify and extend the results of these authors