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Adaptive Disk Spindown via Optimal Rent-to-Buy in Probabilistic Environments
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Adaptive Disk Spindown via Optimal Rent-to-Buy in Probabilistic Environments
P. Krishnan1, P. M. Long2 and J. S. Vitter3
| (1) |
Bell Laboratories, 101 Crawfords Corner Road, Holmdel, NJ 07733, USA. pk@research.bell-labs.com., US |
| (2) |
ISCS Department, National University of Singapore, Singapore 119260, Republic of Singapore. plong@iscs.nus.sg., SG |
| (3) |
Department of Computer Science, Duke University, Durham, NC 27708-0129, USA. jsv@cs.duke.edu., US |
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, specifically, problems arising from deciding when to spindown disks to conserve energy
in mobile computers [4], [13], [15], thread blocking decisions during lock acquisition in multiprocessor applications [7],
and virtual circuit holding times in IP-over-ATM networks [11], [19].
We develop a provably optimal and computationally efficient algorithm for the rent-to-buy problem. Our algorithm uses time and space, and its expected cost for the t th resource use converges to optimal as , 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 significantly improved power/ response time performance over the nonadaptive 2-competitive algorithm which is optimal in the worst-case competitive analysis
model.
Key words. Mobile computing, On-line algorithms, Machine learning, Power conservation, Disk spindown, Rent-to-buy, Multiprocessor
spin / block, IP-over-ATM, Virtual circuit holding time.
Received October 22, 1996; revised September 25, 1997.
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