Optimal index rules for single resource allocation to stochastic dynamic competitors

Jacko, Peter (2011) Optimal index rules for single resource allocation to stochastic dynamic competitors. In: VALUETOOLS '11 Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools. ACM, GBR, pp. 425-433. ISBN 978193968091

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Abstract

In this paper we present a generic Markov decision process model of optimal single resource allocation to a collection of stochastic dynamic competitors. The main goal is to identify sufficient conditions under which this problem is optimally solved by an index rule. The main focus is on the frozen-if-not-allocated assumption, which is notoriously found in problems including the multi-armed bandit problem, tax problem, Klimov network, job sequencing, object search and detection. The problem is approached by a Lagrangian relaxation and decomposed into a collection of normalized parametric single-competitor subproblems, which are then optimally solved by the well-known Gittins index. We show that the problem is equivalent to solving a time sequence of its Lagrangian relaxations. We further show that our approach gives insights on sufficient conditions for optimality of index rules in restless problems (in which the frozen-if-not-allocated assumption is dropped) with single resource; this paper is the first to prove such conditions.

Item Type:
Contribution in Book/Report/Proceedings
Additional Information:
© ACM, 2011.This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in VALUETOOLS '11 Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools http://doi.acm.org/10.4108/icst.valuetools.2011.245797
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/aacsb/disciplinebasedresearch
Subjects:
ID Code:
71355
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Deposited On:
21 Oct 2014 13:48
Refereed?:
Yes
Published?:
Published
Last Modified:
02 Dec 2020 07:43