Energy-efficient multiprocessor scheduling for flow time and makespan

Abstract

We consider energy-efficient scheduling on multiprocessors, where the speed of each processor can be individually scaled, and a processor consumes power s α when running at speed s, for α > 1. A scheduling algorithm needs to decide at any time both processor allocations and processor speeds for a set of parallel jobs with time-varying parallelism. The objective is to minimize the sum of the total energy consumption and certain performance metric, which in this paper includes total flow time and makespan. For both objectives, we present instantaneous parallelism-clairvoyant (IP-clairvoyant) algorithms that are aware of the instantaneous parallelism of the jobs at any time but not their future characteristics, such as remaining parallelism and work. For total flow time plus energy, we present an O(1)-competitive algorithm, which significantly improves upon the best known non-clairvoyant algorithm and is the first constant competitive result on multiprocessor speed scaling for parallel jobs. In the case of makespan plus energy, which is considered for the first time in the literature, we present an O(ln 1−1/α P )competitive algorithm, where P is the total number of processors. We show that this algorithm is asymptotically optimal by providing a matching lower bound. In addition, we also study non-clairvoyant scheduling for total flow time plus energy, and present an algorithm that achieves O(ln P )-competitive for jobs with arbitrary release time and O(ln 1/α P )-competitive for jobs with identical release time. Finally, we prove an Ω(ln 1/α P ) lower bound on the competitive ratio of any non-clairvoyant algorithm, matching the upper bound of our algorithm for jobs with identical release time.

Energy-Aware Online Non-Clairvoyant Scheduling Using Speed Scaling with Arbitrary Power Function

“…Lemma 1. (Young's Inequality [34]) Let f be any real-valued, continuous and strictly increasing function such that f(0) = 0. Then ∀ m, n≥0…”

Energy‐aware online non‐clairvoyant multiprocessor scheduling: multiprocessor priority round robin

“…Bell and Wong [16] studied an energy efficient deadline scheduling on multiprocessors and proposes a deterministic online algorithm for the general setting and showed that it is ‐competitive, where R is the ratio of the maximum to the minimum job size. Sun et al [17] gave an online non‐clairvoyant algorithm N‐EQUI for the objective of total flow time plus energy. In N‐EQUI, jobs arrived arbitrarily and the competitive ratio is , where and m is total number of processors.…”