Advances in Applied Probability

The performance of index-based policies for bandit problems with stochastic machine availability

R. T. Dunn and K. D. Glazebrook

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Abstract

We consider generalisations of two classical stochastic scheduling models, namely the discounted branching bandit and the discounted multi-armed bandit, to the case where the collection of machines available for processing is itself a stochastic process. Under rather mild conditions on the machine availability process we obtain performance guarantees for a range of controls based on Gittins indices. Various forms of asymptotic optimality are established for index-based limit policies as the discount rate approaches 0.

Article information

Source
Adv. in Appl. Probab. Volume 33, Number 2 (2001), 365-390.

Dates
First available: 30 August 2001

Permanent link to this document
http://projecteuclid.org/euclid.aap/999188319

Digital Object Identifier
doi:10.1239/aap/999188319

Mathematical Reviews number (MathSciNet)
MR1842298

Zentralblatt MATH identifier
1017.90049

Subjects
Primary: 90B36: Scheduling theory, stochastic [See also 68M20]
Secondary: 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B22: Queues and service [See also 60K25, 68M20]

Keywords
average-overtaking optimal average-reward optimal branching bandit discounted rewards Gittins index machine breakdowns multi-armed bandit problem parallel machines suboptimality bound

Citation

Dunn, R. T.; Glazebrook, K. D. The performance of index-based policies for bandit problems with stochastic machine availability. Advances in Applied Probability 33 (2001), no. 2, 365--390. doi:10.1239/aap/999188319. http://projecteuclid.org/euclid.aap/999188319.


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