Bae, Jongho; Kim, Sunggon; Lee, Eui Yong Average cost under the \(P^M_{\lambda,\tau}\) policy in a finite dam with compound Poisson inputs. (English) Zbl 1030.60088 J. Appl. Probab. 40, No. 2, 519-526 (2003). 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. Cited in 9 Documents MSC: 60K25 Queueing theory (aspects of probability theory) Keywords:\(P^M_{\lambda,\tau}\) policy; finite dam; compound Poisson input; long-run average cost PDF BibTeX XML Cite \textit{J. Bae} et al., J. Appl. Probab. 40, No. 2, 519--526 (2003; Zbl 1030.60088) Full Text: DOI References: [1] Abdel-Hameed, M. S. (2000). Optimal control of a dam using \(P^M_{\l}ambda,\tau\) policies and penalty cost when the input process is a compound Poisson process with positive drift. J. Appl. Prob. 37 , 408–416. · Zbl 0970.60087 [2] Asmussen, S. (1987). Applied Probability and Queues . John Wiley, Chichester. · Zbl 0624.60098 [3] Bae, J., Kim, S. and Lee, E. Y. (2001). The virtual waiting time of the M/G/\(1\) queue with impatient customers. Queueing Systems 38 , 485–494. · Zbl 0982.60097 [4] Bae, J., Kim, S. and Lee, E. Y. (2002). A \(P^M_{\l}ambda\)-policy for an M/G/\(1\) queueing system. Appl. Math. Modelling 26 , 929–939. · Zbl 1175.90104 [5] Faddy, M. J. (1974). Optimal control of finite dams: discrete (2-stage) output procedure. J. Appl. Prob. 11 , 111—121. · Zbl 0277.60066 [6] Lee, E. Y. and Ahn, S. K. (1998). \(P_{\l}ambda^M\)-policy for a dam with input formed by a compound Poisson process. J. Appl. Prob. 35 , 482–488. · Zbl 0913.60081 [7] Ross, S. M. (1983). Stochastic Processes . John Wiley, New York. · Zbl 0555.60002 [8] Yeh, L. (1985). Optimal control of a finite dam: average-cost case. J. Appl. Prob. 22 , 480–484. · Zbl 0637.93076 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.