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On the structure of value functions for threshold policies in queueing models

Part of: Special processes Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

Sandjai Bhulai  and
Ger Koole
Sandjai Bhulai
Affiliation:
Vrije Universiteit Amsterdam
Ger Koole*
Affiliation:
Vrije Universiteit Amsterdam
*
∗∗Postal address: Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
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Abstract

We study the multiserver queue with Poisson arrivals and identical independent servers with exponentially distributed service times. Customers arriving at the system are admitted or rejected according to a fixed threshold policy. Moreover, the system is subject to holding, waiting, and rejection costs. We give a closed-form expression for the average costs and the value function for this multiserver queue. The result will then be used in a single step of policy iteration in the model where a controller has to route to several finite-buffer queues with multiple servers. We numerically show that the improved policy has a close to optimal value.

Keywords

Difference equationmultiserver queueone-step policy improvementthreshold policyvalue function

MSC classification

Primary: 93E25: Other computational methods
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 613 - 622
Copyright
Copyright © Applied Probability Trust 2003 

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Footnotes

∗

Current address: Bell Laboratories, Lucent Technologies, 700 Mountain Avenue, Room 2C-313, Murray Hill, NJ 07974-0636, USA. Email address: sbhulai@research.bell-labs.com

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