ADAPTIVE DISK SPINDOWN VIA OPTIMAL RENT-TO-BUY IN PROBABILISTIC ENVIRONMENTS

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 un it time or buy it once and for all for $c. In this paper we study algo rithms that make a sequence of single rent-to-buy decisions, using the assumption that the resource use times are independently drawn from a n unknown probability distribution. Our study of this rent-to-buy prob lem is motivated by important systems applications, specifically, prob lems arising from deciding when to spindown disks to conserve energy i n mobile computers [4], [13], [15], thread blocking decisions during l ock acquisition in multiprocessor applications [7], and virtual circui t holding times in IP-over-ATM networks [11], [19]. We develop a prova bly optimal and computationally efficient algorithm for the rent-to-bu y problem. Our algorithm uses O (root t) time and space, and its expec ted cost for the tth resource use converges to optimal as O (root logt /t), for any bounded probability distribution on the resource use time s. Alternatively, using O(1) time and space, the algorithm almost conv erges to optimal. We describe the experimental results for the applica tion of our algorithm to one of the motivating systems problems: the q uestion 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 p ower/response time performance over the nonadaptive 2-competitive algo rithm which is optimal in the worst-case competitive analysis model.