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Tax problems in the undiscounted case

Part of: Computer system organization Operations research and management science Stochastic processes

Published online by Cambridge University Press:  14 July 2016

P. Whittle
P. Whittle*
Affiliation:
University of Cambridge
*
∗Postal address: Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK. Email address: whittle@statslab.cam.ac.uk
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Abstract

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The aim of this paper is to evaluate the performance of the optimal policy (the Gittins index policy) for open tax problems of the type considered by Klimov in the undiscounted limit. In this limit, the state-dependent part of the cost is linear in the state occupation numbers for the multi-armed bandit, but is quadratic for the tax problem. The discussion of the passage to the limit for the tax problem is believed to be largely new; the principal novelty is our evaluation of the matrix of the quadratic form. These results are confirmed by a dynamic programming analysis, which also suggests how the optimal policy should be modified when resources can be freely deployed only within workstations, rather than system-wide.

Keywords

Tax problemmulti-armed bandittime sharingundiscounted limitdynamic programming

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 90B36: Scheduling theory, stochastic 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 754 - 765
Copyright
© Applied Probability Trust 2005 

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