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Profitable Scheduling on Multiple Speed-Scalable Processors

Published: 08 September 2015 Publication History

Abstract

We present a new online algorithm for profit-oriented scheduling on multiple speed-scalable processors and provide a tight analysis of the algorithm’s competitiveness. Our results generalize and improve upon work by Chan et al. [2010], which considers a single speed-scalable processor. Using significantly different techniques, we can not only extend their model to multiprocessors but also prove an enhanced and tight competitive ratio for our algorithm.
In our scheduling problem, jobs arrive over time and are preemptable. They have different workloads, values, and deadlines. The scheduler may decide not to finish a job but instead to suffer a loss equaling the job’s value. However, to process a job’s workload until its deadline the scheduler must invest a certain amount of energy. The cost of a schedule is the sum of lost values and invested energy. In order to finish a job, the scheduler has to determine which processors to use and set their speeds accordingly. A processor’s energy consumption is power Pα(s) integrated over time, where Pα(s)=sα is the power consumption when running at speed s. Since we consider the online variant of the problem, the scheduler has no knowledge about future jobs. This problem was introduced by Chan et al. [2010] for the case of a single processor. They presented an online algorithm that is αα + 2eα-competitive. We provide an online algorithm for the case of multiple processors with an improved competitive ratio of αα.

References

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Susanne Albers, Antonios Antoniadis, and Gero Greiner. 2011. On multi-processor speed scaling with migration. In Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA’11). ACM, 279--288.
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Nikhil Bansal, Ho-Leung Chan, Kirk Pruhs, and Dmitriy Katz. 2009. Improved bounds for speed scaling in devices obeying the cube-root rule. In Proceedings of the 36th International Colloquium on Automata, Languages and Programming (ICALP’09). Springer, 144--155.
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Peter Kling and Peter Pietrzyk. 2013. Profitable scheduling on multiple speed-scalable processors. In Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA’13). ACM, New York, NY, 251--260.
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Cited By

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  • (2021)Timing Analysis in Multi-Core Real Time Systems2021 IEEE International Symposium on Smart Electronic Systems (iSES)10.1109/iSES52644.2021.00021(38-43)Online publication date: Dec-2021

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Published In

cover image ACM Transactions on Parallel Computing
ACM Transactions on Parallel Computing  Volume 2, Issue 3
Special Issue for SPAA 2013
October 2015
196 pages
ISSN:2329-4949
EISSN:2329-4957
DOI:10.1145/2821462
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 08 September 2015
Accepted: 01 June 2014
Received: 01 October 2013
Published in TOPC Volume 2, Issue 3

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Author Tags

  1. Convex programming
  2. energy
  3. online algorithms
  4. primal-dual
  5. scheduling

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  • Research-article
  • Research
  • Refereed

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  • German Research Foundation (DFG) within the Collaborative Research Center On-The-Fly Computing (SFB 901)
  • Graduate School on Applied Network Science (GSANS)

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View all
  • (2021)Timing Analysis in Multi-Core Real Time Systems2021 IEEE International Symposium on Smart Electronic Systems (iSES)10.1109/iSES52644.2021.00021(38-43)Online publication date: Dec-2021

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