Average cost under the \(P^M_{\lambda,\tau}\) policy in a finite dam with compound Poisson inputs. (English) Zbl 1030.60088

Summary: We consider the \(P^M_{\lambda,\tau}\) policy in a finite dam in which the input of water is formed by a compound Poisson process and the rate of water release is changed instantaneously from \(a\) to \(M\) and from \(M\) to \(a\) \((M > a)\) at the moments when the level of water exceeds \(\lambda\) and downcrosses \(\tau\) \((\lambda>\tau)\), respectively. After assigning costs to the changes of release rate, a reward to each unit of output, and a cost related to the level of water in the reservoir, we determine the long-run average cost per unit time.


60K25 Queueing theory (aspects of probability theory)
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