IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v37y2019i4d10.1007_s10878-018-0352-0.html
   My bibliography  Save this article

Speed scaling on parallel processors with migration

Author

Listed:
  • Eric Angel

    (Université d’Évry Val d’Essonne)

  • Evripidis Bampis

    (Sorbonne Université)

  • Fadi Kacem

    (Carthage University)

  • Dimitrios Letsios

    (Technische Universität München
    Imperial College London)

Abstract

We study the problem of scheduling a set of jobs with release dates, deadlines and processing requirements (or works) on parallel speed scalable processors so as to minimize the total energy consumption. We consider that both preemptions and migrations of jobs are allowed. For this problem, there exists an optimal polynomial-time algorithm which uses as a black box an algorithm for linear programming. Here, we formulate the problem as a convex program and we propose a combinatorial polynomial-time algorithm which is based on finding maximum flows. Our algorithm runs in $$O({ nf}(n)\log U)$$ O ( nf ( n ) log U ) time, where n is the number of jobs, U is the range of all possible values of processors’ speeds divided by the desired accuracy and f(n) is the time needed for computing a maximum flow in a layered graph with O(n) vertices.

Suggested Citation

  • Eric Angel & Evripidis Bampis & Fadi Kacem & Dimitrios Letsios, 2019. "Speed scaling on parallel processors with migration," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1266-1282, May.
    • Handle: RePEc:spr:jcomop:v:37:y:2019:i:4:d:10.1007_s10878-018-0352-0
    DOI: 10.1007/s10878-018-0352-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-018-0352-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-018-0352-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Robert McNaughton, 1959. "Scheduling with Deadlines and Loss Functions," Management Science, INFORMS, vol. 6(1), pages 1-12, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alexander Kononov & Yulia Kovalenko, 2020. "Approximation algorithms for energy-efficient scheduling of parallel jobs," Journal of Scheduling, Springer, vol. 23(6), pages 693-709, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu Guiqing & Li Kai & Cheng Bayi, 2015. "Preemptive Scheduling with Controllable Processing Times on Parallel Machines," Journal of Systems Science and Information, De Gruyter, vol. 3(1), pages 68-76, February.
    2. Hoogeveen, J. A. & Lenstra, J. K. & Veltman, B., 1996. "Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard," European Journal of Operational Research, Elsevier, vol. 89(1), pages 172-175, February.
    3. Yung-Chia Chang & Kuei-Hu Chang & Ching-Ping Zheng, 2022. "Application of a Non-Dominated Sorting Genetic Algorithm to Solve a Bi-Objective Scheduling Problem Regarding Printed Circuit Boards," Mathematics, MDPI, vol. 10(13), pages 1-21, July.
    4. Scholl, Armin & Becker, Christian, 2006. "State-of-the-art exact and heuristic solution procedures for simple assembly line balancing," European Journal of Operational Research, Elsevier, vol. 168(3), pages 666-693, February.
    5. Leah Epstein, 2023. "Parallel solutions for preemptive makespan scheduling on two identical machines," Journal of Scheduling, Springer, vol. 26(1), pages 61-76, February.
    6. Han, Bin & Zhang, Wenjun & Lu, Xiwen & Lin, Yingzi, 2015. "On-line supply chain scheduling for single-machine and parallel-machine configurations with a single customer: Minimizing the makespan and delivery cost," European Journal of Operational Research, Elsevier, vol. 244(3), pages 704-714.
    7. Chen, Lin & Ye, Deshi & Zhang, Guochuan, 2018. "Parallel machine scheduling with speed-up resources," European Journal of Operational Research, Elsevier, vol. 268(1), pages 101-112.
    8. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    9. Zeynep Adak & Mahmure Övül Arıoğlu Akan & Serol Bulkan, 0. "Multiprocessor open shop problem: literature review and future directions," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-23.
    10. Jiang, Xiaojuan & Lee, Kangbok & Pinedo, Michael L., 2021. "Ideal schedules in parallel machine settings," European Journal of Operational Research, Elsevier, vol. 290(2), pages 422-434.
    11. Viswanath Nagarajan & Joel Wolf & Andrey Balmin & Kirsten Hildrum, 2019. "Malleable scheduling for flows of jobs and applications to MapReduce," Journal of Scheduling, Springer, vol. 22(4), pages 393-411, August.
    12. Yumei Huo, 2019. "Parallel machine makespan minimization subject to machine availability and total completion time constraints," Journal of Scheduling, Springer, vol. 22(4), pages 433-447, August.
    13. Sterna, Malgorzata, 2011. "A survey of scheduling problems with late work criteria," Omega, Elsevier, vol. 39(2), pages 120-129, April.
    14. Akiyoshi Shioura & Natalia V. Shakhlevich & Vitaly A. Strusevich, 2017. "Machine Speed Scaling by Adapting Methods for Convex Optimization with Submodular Constraints," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 724-736, November.
    15. Xiaoqiang Cai & George L. Vairaktarakis, 2012. "Coordination of Outsourced Operations at a Third-Party Facility Subject to Booking, Overtime, and Tardiness Costs," Operations Research, INFORMS, vol. 60(6), pages 1436-1450, December.
    16. Lenstra, J. K. & Rinnooy Kan, A. H. G., 1980. "An Introduction To Multiprocessor Scheduling," Econometric Institute Archives 272258, Erasmus University Rotterdam.
    17. Leah Epstein & Lene M. Favrholdt & Jens S. Kohrt, 2006. "Separating online scheduling algorithms with the relative worst order ratio," Journal of Combinatorial Optimization, Springer, vol. 12(4), pages 363-386, December.
    18. Van Dam, Peter & Gaalman, Gerard J. C. & Sierksma, Gerard, 1998. "Designing scheduling systems for packaging in process industries: A tobacco company case," International Journal of Production Economics, Elsevier, vol. 56(1), pages 649-659, September.
    19. Akiyoshi Shioura & Natalia V. Shakhlevich & Vitaly A. Strusevich, 2020. "Scheduling problems with controllable processing times and a common deadline to minimize maximum compression cost," Journal of Global Optimization, Springer, vol. 76(3), pages 471-490, March.
    20. Wan, Guohua & Vakati, Sudheer R. & Leung, Joseph Y.-T. & Pinedo, Michael, 2010. "Scheduling two agents with controllable processing times," European Journal of Operational Research, Elsevier, vol. 205(3), pages 528-539, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:37:y:2019:i:4:d:10.1007_s10878-018-0352-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.