Control of Dams When the Input Is a Levy Type Process

TL;DR

This paper extends and unifies existing dam control models by considering Levy process inputs, broadening the scope beyond Wiener and compound Poisson processes, and providing a comprehensive framework for optimal dam management.

Contribution

It introduces a unified approach to dam control when the input process is a Levy process, generalizing previous models based on Wiener and Poisson processes.

Findings

Extended control results to Levy process inputs

Unified framework for various input process models

Provided explicit control strategies for new process types

Abstract

Zuckermann [10] considers the problem of optimal control of a finite dam assuming that the input process is Wiener with positive drift term \mu \geq 0. Lam and Lou [7] treat the case where the input is a Wiener process with a reflecting boundary at its infimum, with a positive drift term, using the long-run Average and total discounted cost criteria. Attia [3] obtains results similar to those of Lam and Lou, through simpler and more direct methods. Bae et al. [5] treat the long-run average cost case when the input process is a compound Poisson process with a negative drift. In this paper we unify and extend the results of these authors