Average cost under the PMλ, τ policy in a finite dam with compound Poisson inputs

2003 ◽  
Vol 40 (2) ◽  
pp. 519-526 ◽  
Author(s):  
Jongho Bae ◽  
Sunggon Kim ◽  
Eui Yong Lee
Keyword(s):  
Poisson Process ◽  
Release Rate ◽  
Average Cost ◽  
Compound Poisson Process ◽  
Water Release ◽  
Compound Poisson ◽  
Long Run ◽  
Finite Dam

We consider the 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 λ and downcrosses τ (λ > τ) 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.

Average cost under the P M λ, τ policy in a finite dam with compound Poisson inputs

2003 ◽  
Vol 40 (02) ◽  
pp. 519-526
Author(s):  
Jongho Bae ◽  
Sunggon Kim ◽  
Eui Yong Lee
Keyword(s):  
Poisson Process ◽  
Release Rate ◽  
Average Cost ◽  
Compound Poisson Process ◽  
Water Release ◽  
Compound Poisson ◽  
Long Run ◽  
Finite Dam

We consider the 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 λ and downcrosses τ (λ > τ) 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.

scholarly journals Optimization under the PMλ,τ policy of a finite dam with both continuous and jumpwise inputs

2005 ◽  
Vol 42 (2) ◽  
pp. 587-594
Author(s):  
Kyung Eun Lim ◽  
Jee Seon Baek ◽  
Eui Yong Lee
Keyword(s):  
Poisson Process ◽  
Wiener Process ◽  
Release Rate ◽  
Average Cost ◽  
Long Run ◽  
Random Jumps ◽  
Finite Dam

We consider a finite dam under the policy, where the input of water is formed by a Wiener process subject to random jumps arriving according to a Poisson process. The long-run average cost per unit time is obtained after assigning costs to the changes of release rate, a reward to each unit of output, and a penalty that is a function of the level of water in the reservoir.

scholarly journals Optimization under the P M λ,τ policy of a finite dam with both continuous and jumpwise inputs

2005 ◽  
Vol 42 (02) ◽  
pp. 587-594
Author(s):  
Kyung Eun Lim ◽  
Jee Seon Baek ◽  
Eui Yong Lee
Keyword(s):  
Poisson Process ◽  
Wiener Process ◽  
Release Rate ◽  
Average Cost ◽  
Long Run ◽  
Random Jumps ◽  
Finite Dam

We consider a finite dam under the policy, where the input of water is formed by a Wiener process subject to random jumps arriving according to a Poisson process. The long-run average cost per unit time is obtained after assigning costs to the changes of release rate, a reward to each unit of output, and a penalty that is a function of the level of water in the reservoir.

Optimal control of a finite dam: average-cost case

1985 ◽  
Vol 22 (02) ◽  
pp. 480-484 ◽  
Author(s):  
Lam Yeh
Keyword(s):  
Optimal Control ◽  
Wiener Process ◽  
Release Rate ◽  
Optimal Policy ◽  
Average Cost ◽  
Output Rate ◽  
Penalty Cost ◽  
Long Run ◽  
Negative Drift ◽  
Finite Dam

We consider the problem of minimizing the long-run average cost per unit time of operating a finite dam in the class of the policies of the following type. Assume that the dam is initially empty, the release rate is kept at 0 until the dam storage increases to λ, and as soon as this occurs, water is released at rate M, then the output rate is kept at M as long as the dam storage is more than τ and it must be decreased to 0 if the dam storage becomes τ. We assume that the input of water into the finite dam is a Wiener process with non-negative drift μ and variance parameter σ 2. There is a cost in increasing the output rate from 0 to M as well as in decreasing the rate from M to 0 and whenever the dam storage is below level a, there is a penalty cost per unit time depending on the level. A reward is given for each unit of water released. In this paper, the long-run average cost per unit time is determined, and therefore the optimal policy can be found numerically.

Optimal control of a finite dam: average-cost case

1985 ◽  
Vol 22 (2) ◽  
pp. 480-484 ◽  
Author(s):  
Lam Yeh
Keyword(s):  
Optimal Control ◽  
Wiener Process ◽  
Release Rate ◽  
Optimal Policy ◽  
Average Cost ◽  
Output Rate ◽  
Penalty Cost ◽  
Long Run ◽  
Negative Drift ◽  
Finite Dam

We consider the problem of minimizing the long-run average cost per unit time of operating a finite dam in the class of the policies of the following type. Assume that the dam is initially empty, the release rate is kept at 0 until the dam storage increases to λ, and as soon as this occurs, water is released at rate M, then the output rate is kept at M as long as the dam storage is more than τ and it must be decreased to 0 if the dam storage becomes τ. We assume that the input of water into the finite dam is a Wiener process with non-negative drift μ and variance parameter σ2. There is a cost in increasing the output rate from 0 to M as well as in decreasing the rate from M to 0 and whenever the dam storage is below level a, there is a penalty cost per unit time depending on the level. A reward is given for each unit of water released. In this paper, the long-run average cost per unit time is determined, and therefore the optimal policy can be found numerically.

Optimal control of a dam using Pλ,τM policies and penalty cost when the input process is a compound Poisson process with positive drift

2000 ◽  
Vol 37 (2) ◽  
pp. 408-416 ◽  
Author(s):  
Mohamed Abdel-Hameed
Keyword(s):  
Optimal Control ◽  
Poisson Process ◽  
Compound Poisson Process ◽  
Input Process ◽  
Compound Poisson ◽  
Discounted Cost ◽  
Penalty Cost ◽  
Drift Term ◽  
Long Run ◽  
Negative Drift

In this paper we consider the optimal control of an infinite dam using policies assuming that the input process is a compound Poisson process with a non-negative drift term, and using the total discounted cost and long-run average cost criteria. The results of Lee and Ahn (1998) as well as other well-known results are shown to follow from our results.

Optimal control of a dam using P λ,τ M policies and penalty cost when the input process is a compound Poisson process with positive drift

2000 ◽  
Vol 37 (02) ◽  
pp. 408-416
Author(s):  
Mohamed Abdel-Hameed
Keyword(s):  
Optimal Control ◽  
Poisson Process ◽  
Compound Poisson Process ◽  
Input Process ◽  
Compound Poisson ◽  
Discounted Cost ◽  
Penalty Cost ◽  
Drift Term ◽  
Long Run ◽  
Negative Drift

In this paper we consider the optimal control of an infinite dam using policies assuming that the input process is a compound Poisson process with a non-negative drift term, and using the total discounted cost and long-run average cost criteria. The results of Lee and Ahn (1998) as well as other well-known results are shown to follow from our results.

scholarly journals Control of Dams Using Pλ,τM Policies When the Input Process Is a Nonnegative Lévy Process

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Mohamed Abdel-Hameed
Keyword(s):  
Poisson Process ◽  
Water Level ◽  
Stationary Distribution ◽  
Release Rate ◽  
Average Cost ◽  
Lévy Process ◽  
Levy Process ◽  
Input Process ◽  
Long Run

We consider Pλ,τM policy of a dam in which the water input is an increasing Lévy process. The release rate of the water is changed from 0 to M and from M to 0 (M>0) at the moments when the water level upcrosses level λ and downcrosses level τ   (τ<λ), respectively. We determine the potential of the dam content and compute the total discounted as well as the long-run average cost. We also find the stationary distribution of the dam content. Our results extend the results in the literature when the water input is assumed to be a Poisson process.

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