Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T06:05:28.905Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal control of an M/G/1 queue with imperfectly observed queue length when the input source is finite

Published online by Cambridge University Press:  14 July 2016

Kazuyoshi Wakuta
Kazuyoshi Wakuta*
Affiliation:
Nagaoka Technical College
*
∗Postal address: Nagaoka Technical College, Nagaoka, Niigata 940, Japan.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the optimal control of an M/G/1 queue with finite input source. The queue length, however, can be only imperfectly observed through the observations at the initial time and the times of successive departures. At these times, the service rate can be chosen, based on the observable histories. A service cost and a holding cost are incurred. We show that such a control problem can be formulated as a semi-Markov decision process with imperfect state information, and present sufficient conditions for the existence of an optimal stationary I-policy.

Keywords

FINITE INPUT SOURCEIMPERFECT OBSERVATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 210 - 220
Copyright
Copyright © Applied Probability Trust 1991 

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.)

References

[1] Ash, R. B. (1972) Real Analysis and Probability. Academic Press, New York.Google Scholar
[2] Bertsekas, D. P. and Shreve, S. E. (1978) Optimal Control: The Discrete Time Case. Academic Press, New York.Google Scholar
[3] Crabill, T. B. (1972) Optimal control of a maintenance system with variable service rates. Operat. Res. 22, 736–745.CrossRefGoogle Scholar
[4] Maitra, A. (1968) Discounted dynamic programming on compact metric spaces. Sankhya A 30, 211–216.Google Scholar
[5] Royden, H. L. (1968) Real Analysis. Macmillan, New York.Google Scholar
[6] Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
[7] Sawaragi, Y. and Yoshikawa, T. (1970) Discrete-time Markovian decision process with incomplete state observation. Ann. Math. Statist. 41, 78–86.CrossRefGoogle Scholar
[8] Schäl, M. (1987) Estimation and control in stochastic dynamic programmings. Stochastics 20, 51–71.Google Scholar
[9] Wakuta, K. (1987) Arbitrary state semi-Markov decision processes with unbounded rewards. Optimization 18, 447–454.CrossRefGoogle Scholar