Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-11T07:21:19.836Z Has data issue: false hasContentIssue false
  • English
  • Français

Constrained admission control to a queueing system

Published online by Cambridge University Press:  01 July 2016

Arie Hordijk  and
Flos Spieksma
Arie Hordijk*
Affiliation:
University of Leiden
Flos Spieksma*
Affiliation:
University of Leiden
*
Postal address for both authors: Institute of Applied Mathematics and Computer Science, University of Leiden, Niels Bohrweg 1, Leiden, The Netherlands.
Postal address for both authors: Institute of Applied Mathematics and Computer Science, University of Leiden, Niels Bohrweg 1, Leiden, The Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider an exponential queue with arrival and service rates depending on the number of jobs present in the queue. The queueing system is controlled by restricting arrivals. Typically, a good policy should provide a proper balance between throughput and congestion. A mathematical model for computing such a policy is a Markov decision chain with rewards and a constrained cost function. We give general conditions on the reward and cost function which guarantee the existence of an optimal threshold or thinning policy. An efficient algorithm for computing an optimal policy is constructed.

Keywords

FLOW CONTROLLINEAR PROGRAMMINGCONVEX COMBINATION OF STATIONARY DISTRIBUTIONS ON ACTIONS AND STATESTHRESHOLD OPTIMAL POLICYTHINNING OPTIMAL POLICY
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 2 , June 1989 , pp. 409 - 431
Copyright
Copyright © Applied Probability Trust 1989 

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

∗

The research of this author was supported by the Netherlands Organization for Scientific Research, N.W.O.

References

Beutler, F. J. and Ross, K. W. (1986) Time-average optimal constrained semi-Markov decision processes. Adv. Appl. Prob. 18, 341–359.Google Scholar
Cooper, R. B. (1981) Introduction to Queueing Theory. North-Holland, New York.Google Scholar
Hordijk, A. (1983) Insensitivity for stochastic networks. In Mathematical Computer Performance and Reliability, eds. Iazeolla, G., Courtois, P. J., Hordijk, A., North-Holland, Amsterdam, 77–94.Google Scholar
Hordijka, A. and Kallenberg, L. C. M. (1984) Constrained undiscounted stochastic dynamic programming. Math. Operat. Res. 9, 277–289.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
Lazar, A. A. (1983) Optimal flow control of a class of queueing networks in equilibrium. IEEE Trans. Autom. Control 28, 1001–1007.Google Scholar
Ross, K. W. (1986) Optimal and suboptimal policies for Markov decision processes. To appear.Google Scholar
Schoute, F. C. (1979) Optimal control and call acceptance in an SPC exchange. Ninth International Teletraffic Congress.Google Scholar
Serfozo, R. F. (1979) An equivalence between continuous and discrete time Markov decision processes. Operat. Res. 27, 616–620.Google Scholar
Shwartz, A., Ma, D.-J. and Makowski, A. M. (1986) Estimation and optimal control for constrained Markov chains. Proc. 25th Conf. Decision and Control, Athens, December 1986, 994–999.Google Scholar
Stidham, S. Jr., (1985) Optimal control of admission to a queueing system. IEEE Trans. Autom. Control 30, 705–713.Google Scholar
Stidham, Sh. Jr. and Weber, R. R. (1984) Monotonic and insensitive optimal policies for control of queues with undiscounted costs. Unpublished.Google Scholar