Optimal control of a dam using \(P_{\lambda,\tau}\) policies and penalty cost when the input process is a compound Poisson process with positive drift. (English) Zbl 0970.60087

Abdel-Hameed, Mohamed

J. Appl. Probab. 37, No. 2, 408-416 (2000).

Techniques in the previous paper of the author and Y. Nakhi [ibid. 27, No. 4, 888-898 (1990; Zbl 0726.60099)] for the case when the water input is a Wiener process, are similarly used in the present paper for the case when the input process is a compound Poisson one with non-negative jumps, a non-negative drift term and the magnitude of the successive jumps having a common distribution function. The bivariate content process consisting of the dam content and the release rate is described in Section 2 together with the evaluation of parameters of the process during the first part of a cycle. The release rate is zero until the water reaches level \(\lambda\), then it is released at rate \(M\), until it reaches level \(\tau\) \((<\lambda\)); once the water reaches level \(\tau\) the release rate remains zero until level \(\lambda\) is reached again and the cycle is repeated. Computing the total discounted cost as well as the long run average cost under selected policies is realized in Section 3. The final section is devoted to applications for computing some distributions as generations of ones in the paper of E. Y. Lee and S. K. Ahn [ibid. 35, No. 2, 482-488 (1998; Zbl 0913.60081)].

Reviewer: T.N.Pham (Hanoi)

MSC:

60J25	Continuous-time Markov processes on general state spaces
60K25	Queueing theory (aspects of probability theory)

Keywords:

dam content; total discounted cost; long run average cost; compound Poisson process

Citations:

Zbl 0913.60081; Zbl 0726.60099