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Non-preemptive Scheduling in a Smart Grid Model and Its Implications on Machine Minimization

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Abstract

We study a scheduling problem arising in demand response management in smart grid. Consumers send in power requests with a flexible feasible time interval during which their requests can be served. The grid controller, upon receiving power requests, schedules each request within the specified interval. The electricity cost is measured by a convex function of the load in each timeslot. The objective is to schedule all requests with the minimum total electricity cost. Previous work has studied cases where jobs have unit power requirement and unit duration. We extend the study to arbitrary power requirement and duration, which has been shown to be NP-hard. We give the first online algorithm for the general problem and prove that the problem is fixed parameter tractable. We also show that the online algorithm is the best-possible in an asymptotically sense when the objective is to minimize the peak load. In addition, we observe that the classical non-preemptive machine minimization problem is a special case of the smart grid problem with min-peak objective and show that we can achieve the best-possible competitive ratio in an asymptotically sense when solving the non-preemptive machine minimization problem.

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Acknowledgements

Prudence W.H. Wong is partially supported by Networks Sciences and Technologies, University of Liverpool. Hsiang-Hsuan Liu is partially supported by a studentship from the University of Liverpool-National Tsing-Hua University Dual PhD programme.

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Authors and Affiliations

  1. Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan

    Fu-Hong Liu

  2. Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands

    Hsiang-Hsuan Liu

  3. Department of Computer Science, University of Liverpool, Liverpool, UK

    Prudence W. H. Wong

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A preliminary version of this paper titled “Optimal Nonpreemptive Scheduling in a Smart Grid Model” appeared in Proceedings of the 27th International Symposium on Algorithms and Computation, ISAAC 2016 [30] and some results are improved in this version.

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Liu, FH., Liu, HH. & Wong, P.W.H. Non-preemptive Scheduling in a Smart Grid Model and Its Implications on Machine Minimization. Algorithmica 82, 3415–3457 (2020). https://doi.org/10.1007/s00453-020-00733-3

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