Speed scaling scheduling of multiprocessor jobs with energy constraint and makespan criterion

Alexander Kononov () and Yulia Zakharova ()
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Alexander Kononov: Sobolev Institute of Mathematics SB RAS
Yulia Zakharova: Sobolev Institute of Mathematics SB RAS

Journal of Global Optimization, 2022, vol. 83, issue 3, No 8, 539-564

Abstract: Abstract We are given a set of parallel jobs that have to be executed on a set of speed-scalable processors varying their speeds dynamically. Running a job at a slower speed is more energy-efficient, however, it takes a longer time and affects the performance. Every job is characterized by the processing volume and the number or the set of the required processors. Our objective is to minimize the maximum completion time so that the energy consumption is not greater than a given energy budget. For various particular cases, we propose polynomial-time approximation algorithms, consisting of two stages. At the first stage, we give an auxiliary convex program. By solving this problem, we get processing times of jobs and a lower bound on the makespan. Then, at the second stage, we transform our problem into the corresponding scheduling problem with the constant speed of processors and construct a feasible schedule. We also obtain an “almost exact” solution for the preemptive settings based on a configuration linear program.

Keywords: Multiprocessor job; Speed scaling; Energy; Scheduling; Approximation algorithm (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-021-01115-x

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