Learning to Make Rent-to-Buy Decisions with Systems Applications

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 described in the paper. We develop a provably optimal and compu-tationally eecient algorithm for our formulation of the rent-to-buy problem. Our algorithm uses O(p t) time and space, and its expected cost for the tth resource use converges to optimal as O(p log 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 signiicantly improved power/response time performance over the non-adaptive 2-competitive algorithm which is optimal in the worst-case competitive analysis model.