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.

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 &gt; a) at the moments when the level of water exceeds λ and downcrosses τ (λ &gt; 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.

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.

Emptiness times of a dam with stable input and general release function

1975 ◽  
Vol 12 (01) ◽  
pp. 212-217 ◽  
Author(s):  
P. J. Brockwell ◽  
K. L. Chung
Keyword(s):  
Release Rate ◽  
Lévy Process ◽  
Levy Process ◽  
Input Process

We investigate the nature of the set of emptiness times of a dam whose release rate depends on the content and whose cumulative input process is a pure-jump Lévy process. Detailed results are obtained for stable input processes and release functions of the form r(x) = xβ I (o,∞)(x).

Emptiness times of a dam with stable input and general release function

1975 ◽  
Vol 12 (1) ◽  
pp. 212-217 ◽  
Author(s):  
P. J. Brockwell ◽  
K. L. Chung
Keyword(s):  
Release Rate ◽  
Lévy Process ◽  
Levy Process ◽  
Input Process

We investigate the nature of the set of emptiness times of a dam whose release rate depends on the content and whose cumulative input process is a pure-jump Lévy process. Detailed results are obtained for stable input processes and release functions of the form r(x) = xβ I(o,∞)(x).

scholarly journals The Class of Distributions Associated with the Generalized Pollaczek-Khinchine Formula

2012 ◽  
Vol 49 (3) ◽  
pp. 883-887 ◽  
Author(s):  
Offer Kella
Keyword(s):  
Brownian Motion ◽  
Stationary Distribution ◽  
Lévy Process ◽  
Random Variables ◽  
Levy Process ◽  
Independent Random Variables ◽  
Reflected Brownian Motion ◽  
Distribution Of The Maximum ◽  
Workload Distribution ◽  
Stationary Workload

The goal is to identify the class of distributions to which the distribution of the maximum of a Lévy process with no negative jumps and negative mean (equivalently, the stationary distribution of the reflected process) belongs. An explicit new distributional identity is obtained for the case where the Lévy process is an independent sum of a Brownian motion and a general subordinator (nondecreasing Lévy process) in terms of a geometrically distributed sum of independent random variables. This generalizes both the distributional form of the standard Pollaczek-Khinchine formula for the stationary workload distribution in the M/G/1 queue and the exponential stationary distribution of a reflected Brownian motion.

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.

The control of a finite dam

1982 ◽  
Vol 19 (4) ◽  
pp. 815-825 ◽  
Author(s):  
F. A. Attia ◽  
P. J. Brockwell
Keyword(s):  
Markov Chain ◽  
Wiener Process ◽  
Average Cost ◽  
Type B ◽  
Input Process ◽  
Long Run ◽  
The Cost ◽  
Finite Dam

The long-run average cost per unit time of operating a finite dam controlled by a PlM policy (Faddy (1974), Zuckerman (1977)) is determined when the cumulative input process is (a) a Wiener process with drift and (b) the integral of a Markov chain. It is shown how the cost for (a) can be obtained as the limit of the costs associated with a sequence of input processes of the type (b).

scholarly journals Property Claim Services by Compound Poisson Process And Inhomogeneous Levy Process

2018 ◽  
Vol 6 (1) ◽  
pp. 32
Author(s):  
Muhammed A. S. Murad
Keyword(s):  
Poisson Process ◽  
Lévy Process ◽  
Compound Poisson Process ◽  
Levy Process ◽  
Arrival Process ◽  
Compound Poisson ◽  
Process Factor ◽  
Before And After ◽  
Exponential Lévy Process ◽  
Loss Index

In this paper, stochastic compound Poisson process is employed to value the catastrophic insurance options and model the claim arrival process for catastrophic events, which were written in the loss period , during which the catastrophe took place. Here, a time compound process gives the underlying loss index before and after  whose losses are revaluated by inhomogeneous exponential Levy process factor. For this paper, an exponential Levy process is used to evaluate the well-known European call option in order to price Property Claim Services catastrophe insurance based on catastrophe index.

Sign in / Sign up

Export Citation Format

Share Document