Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-09T22:06:05.534Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal control of batch service queues with switching costs

Published online by Cambridge University Press:  01 July 2016

Rajat K. Deb
Rajat K. Deb*
Affiliation:
State University of New York at Oswego
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a batch service queue which is controlled by switching the server on and off, and by controlling the batch size and timing of services. These batch sizes cannot exceed a fixed number Q, which we call the service capacity. Costs are charged for switching the server on and off, for serving customers and for holding them in the system. Viewing the system as a semi-Markov decision process, we show that the policies which minimize the expected continuously discounted cost and the expected cost per unit time over an infinite time horizon are of the following form: at a review point if the server is off, leave the server off until the number of customers x reaches an optimal level M, then turn the server on and serve min (x, Q) customers; and when the server is on, serve customers in batches of size min(x, Q) until the number of customers falls below an optimal level m(m ≦ M) and then turn the server off. An example for computing these optimal levels is also presented.

Keywords

BATCH SERVICE QUEUESBULK QUEUEMARKOV DECISION PROCESSDYNAMIC PROGRAMMINGSTOCHASTIC CONTROL
Type
Research Article
Information
Advances in Applied Probability , Volume 8 , Issue 1 , March 1976 , pp. 177 - 194
Copyright
Copyright © Applied Probability Trust 1976 

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] Bell, C. E. (1971) Characterization and computation of optimal policies for operating an M/G/1 queueing system with removable server. Operat. Res. 19, 208–218.CrossRefGoogle Scholar
[2] Blackburn, J. D. (1972) Optimal control of a single server queue with balking and reneging. Management Sci. 19, 297–313.Google Scholar
[3] Crabill, T. (1972) Optimal control of a service facility with variable exponential service times and constant arrival rate. Management Sci. 18, 560–566.Google Scholar
[4] Deb, R. (1971) Optimal control of bulk queues. Ph.D. Dissertation, Syracuse University.Google Scholar
[5] Deb, R. and Serfozo, R. (1972) Optimal control of batch service queues. Adv. Appl. Prob. 5, 340–361.Google Scholar
[6] Deb, R. (1973) Optimal control of batch service queues, with start-up and shut-down costs. Technical Report No CS/OR/1–73 (Revised), Department of Computer Science, SUNY-Oswego.Google Scholar
[7] Heyman, D. P. (1968) Optimal operating policies for M/G/1 queueing systems. Operat. Res. 16, 362–382.Google Scholar
[8] Jaiswal, N. K. and Sinha, P. (1972) Optimal operating policies for the finite source queueing process. Operat. Res. 20, 698–707.Google Scholar
[9] Kaplan, R. S. (1972) Stochastic growth model. Management Sci. 18, 249–264.Google Scholar
[10] Lippman, S. A. (1973) Semi-Markov decision processes with unbounded rewards. Management Sci. 19, 717–731.Google Scholar
[11] McGill, J. T. (1969) Optimal control of queueing systems with variable number of exponential servers. Technical Report. Department of Operations Research, Stanford University.Google Scholar
[12] Prabhu, N. U. and Stidham, S. (1973) Optimal control of queuing systems, Research Report # 186, Department of Operations Research, Cornell University.Google Scholar
[13] Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
[14] Saaty, T. L. (1961) Elements of Queuing Theory with Applications. McGraw-Hill, New York.Google Scholar
[15] Sobel, M. J. (1969) Optimal average cost policies for a queue with start-up and shut-down costs. Operat. Res. 17, 145–162.Google Scholar
[16] Sobel, M. J. (1969) Smoothing start-up and shut-down costs in sequential production. Operat. Res. 17, 133–144.Google Scholar
[17] Stidham, S. (1972) L = λW: A discounted analogue and a new proof. Operat. Res. 20, 1115–1126.Google Scholar
[18] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
[19] Yadin, J. and Zacks, S. (1969) The optimal control of a queuing process. Technical Report No. 54, Industrial and Management Engineering, Haifa, Israel.Google Scholar