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We investigate a very basic problem in dynamic speed scaling where a sequence of jobs, each specified by an arrival time, a deadline and a processing volume, has to be processed so as to minimize energy consumption. We study multi-processor environments with m parallel variable-speed processors assuming that job migration is allowed, i.e. whenever a job is preempted it may be moved to a different processor. We first study the offline problem and show that optimal schedules can be computed efficiently in polynomial time, given any convex non-decreasing power function. In contrast to a previously known strategy, our algorithm does not resort to linear programming. For the online problem, we extend two algorithms Optimal Available and Average Rate proposed by Yao et al. [15] for the single processor setting. Here we concentrate on power functions P (s) = s α , where s is the processor speed and α > 1 is a constant.

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Given n jobs with release dates, deadlines and processing times we consider the problem of scheduling them on m parallel machines so as to minimize the total energy consumed. Machines can enter a sleep state and they consume no energy in this state. Each machine requires Q units of energy to awaken from the sleep state and in its active state the machine can process jobs and consumes a unit of energy per unit time. We allow for preemption and migration of jobs and provide the first constant approximation algorithm for this problem.

No abstract