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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.
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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 

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Footnotes

∗

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

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