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

Author

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  • Alexander Kononov

    (Sobolev Institute of Mathematics SB RAS)

  • Yulia Zakharova

    (Sobolev Institute of Mathematics SB RAS)

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.

Suggested Citation

  • Alexander Kononov & Yulia Zakharova, 2022. "Speed scaling scheduling of multiprocessor jobs with energy constraint and makespan criterion," Journal of Global Optimization, Springer, vol. 83(3), pages 539-564, July.
    • Handle: RePEc:spr:jglopt:v:83:y:2022:i:3:d:10.1007_s10898-021-01115-x
    DOI: 10.1007/s10898-021-01115-x
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    References listed on IDEAS

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    1. Peter Brucker & Sigrid Knust & Duncan Roper & Yakov Zinder, 2000. "Scheduling UET task systems with concurrency on two parallel identical processors," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(3), pages 369-387, December.
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    7. Keqin Li, 1999. "Analysis of the List Scheduling Algorithm for Precedence Constrained Parallel Tasks," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 73-88, July.
    8. Evripidis Bampis & Alexander Kononov & Dimitrios Letsios & Giorgio Lucarelli & Maxim Sviridenko, 2018. "Energy-efficient scheduling and routing via randomized rounding," Journal of Scheduling, Springer, vol. 21(1), pages 35-51, February.
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