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Adaptive Disk Spindown via Optimal Rent-to-Buy in Probabilistic Environments
Krishnan, P. Long, Philip M. Vitter, Jeffrey Scott
Krishnan, P.
Long, Philip M.
Vitter, Jeffrey Scott
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Abstract
In the single rent-to-buy decision problem, without a priori knowledge of the amount of time
a resource will be used we need to decide when to buy the resource, given that we can rent the
resource for $1 per unit time or buy it once and for all for $c. In this paper we study algorithms
that make a sequence of single rent-to-buy decisions, using the assumption that the resource use
times are independently drawn from an unknown probability distribution. Our study of this rent-
to-buy problem is motivated by important systems applications, speci cally, problems arising
from deciding when to spindown disks to conserve energy in mobile computers [DKM, LKH,
MDK], thread blocking decisions during lock acquisition in multiprocessor applications [KLM],
and virtual circuit holding times in IP-over-ATM networks [KLP, SaK].
We develop a provably optimal and computationally e cient algorithm for the rent-to-buy
problem. Our algorithm uses O(pt) time and space, and its expected cost for the tth resource use
converges to optimal as O(plog t=t), for any bounded probability distribution on the resource
use times. Alternatively, using O(1) time and space, the algorithm almost converges to optimal.
We describe the experimental results for the application of our algorithm to one of the
motivating systems problems: the question of when to spindown a disk to save power in a mobile
computer. Simulations using disk access traces obtained from an HP workstation environment
suggest that our algorithm yields signi cantly improved power/response time performance over
the non-adaptive 2-competitive algorithm which is optimal in the worst-case competitive analysis
model.
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The original publication is available at www.springerlink.com
Date
1999-01
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Springer Verlag
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Citation
P. Krishnan, P. M. Long, and J. S. Vitter. “Adaptive Disk Spindown via Optimal Rent-to-Buy in Probabilistic Environments,” Algorithmica, 23(1), January 1999, 31–56. An extended abstract appears in “Learning to Make Rent-to-Buy Decisions in Probabilistic Environments with Systems Applications,” Proceedings of the 12th International Conference on Machine Learning (ML ’95), Tahoe City, CA, July 1995, 322–330. http://dx.doi.org/10.1007/PL00009249