Control of Dams Using Pλ,τM Policies When the Input Process Is a Nonnegative Lévy Process-Reference-Cited by-同舟云学术

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

Published:2011-09-15 Issue: Volume:2011 Page:1-17
ISSN:2090-3332
Container-title:International Journal of Stochastic Analysis
language:en
Short-container-title:International Journal of Stochastic Analysis

Author:

Abdel-Hameed Mohamed¹

Affiliation:

1. Department of Statistics, College of Business and Economics, United Arab Emirates University, Al-Ain 17555, UAE

Abstract

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.

Funder

College of Business and Economics, United Arab Emirates University

Publisher

Hindawi Limited

Subject

Applied Mathematics,Modeling and Simulation,Statistics and Probability,Analysis

Link

http://downloads.hindawi.com/archive/2011/916952.pdf

Reference12 articles.

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

5. A PλM-policy for an M/G/1 queueing system