Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-24T14:27:14.584Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-stage output procedure of a finite dam

Published online by Cambridge University Press:  14 July 2016

Dror Zuckerman
Dror Zuckerman*
Affiliation:
Cornell University
*
*Now at The Hebrew University of Jerusalem.
Get access Rights & Permissions [Opens in a new window]

Abstract

The input of water into a finite dam is a Wiener process with positive drift. Water may be released at either of two possible rates 0 or M. At any time the output rate can be increased from 0 to M with cost KM, (K ≧ 0), or decreased from M to 0 with zero cost. There is a reward of A monetary units for each unit of output, (A > 0). We will consider the problem of specifying an optimal control output policy under the following optimal criteria:

  1. (a) Minimum total long-run average cost per unit time.

  2. (b) Minimum expected total discounted cost.

Keywords

WIENER PROCESSCONTROLLAPLACE TRANSFORMHITTING TIMESTRONG MARKOV PROPERTY
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 421 - 425
Copyright
Copyright © Applied Probability Trust 1977 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This research was supported in part by the National Science Foundation under Grant MBS 73–04437.

References

[1] Faddy, M. J. (1974) Optimal control of finite dams: discrete (2-stage) output procedure. J. Appl. Prob. 11, 111–121.Google Scholar
[2] Feller, W. (1971) An Introduction to Probability Theory and its Applications II. Wiley, New York.Google Scholar
[3] Haslett, J. (1976) The control of a multipurpose reservoir. Adv. Appl. Prob. 8, 592–609.CrossRefGoogle Scholar
[4] Karlin, S. and Taylor, H. M. (1975) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar
[5] Taylor, H. M. (1975) A stopped Brownian motion formula. Ann. Prob. 3, 234–246.Google Scholar