Abstract
We consider a scheduling problem which abstracts a model of demand-response management in Smart Grid. In the problem, there is a set of unrelated machines and each job j (representing a client demand) is characterized by a release date, and a power request function representing its request demand at specific times. Each machine has an energy power function and the energy cost incurred at a time depends on the load of the machine at that time. The goal is to find a non-migration schedule that minimizes the total energy (over all times).
We give a competitive algorithm for the problem in the online setting where the competitive ratio depends (only) on the power functions of machines. In the setting with typical energy function \(P(z) = z^{\nu }\), the algorithm is \(\varTheta (\nu ^{\nu })\)-competitive, which is optimal up to a constant factor. Our algorithm is robust in the sense that the guarantee holds for arbitrary request demands of clients. This enables flexibility on the choices of clients in shaping their demands — a desired property in Smart Grid.
We also consider a special case in offline setting in which jobs have unit processing time, constant power request and identical machines with energy function \(P(z) = z^{\nu }\). We present a \(2^{\nu }\)-approximation algorithm for this case.
V. Chau and S. Feng—Research supported by NSFC (no. 61433012, U1435215), by Shenzhen basic research grant JCYJ20160229195940462 and by National High-Tech R&D Program of China (863 Program) 2015AA050201.
N. K. Thang—Research supported by the ANR project OATA no. ANR-15-CE40-0015-01, Hadamard PGMO and DIM RFSI.
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Notes
- 1.
For convenience, we consider schedules up to a time T, which can be arbitrarily large but finite.
References
Albers, S.: Energy-efficient algorithms. Commun. ACM 53(5), 86–96 (2010)
Alford, R., Dean, M., Hoontrakul, P., Smith, P.: Power systems of the future: the case for energy storage, distributed generation, and microgrids. Zpryme Research & Consulting, Technical report (2012)
Azar, Y., Epstein, A.: Convex programming for scheduling unrelated parallel machines. In: Proceedings 37th Annual ACM Symposium on Theory of Computing, pp. 331–337 (2005)
Bell, P.C., Wong, P.W.H.: Multiprocessor speed scaling for jobs with arbitrary sizes and deadlines. J. Comb. Optim. 29(4), 739–749 (2015)
Burcea, M., Hon, W., Liu, H.H., Wong, P.W.H., Yau, D.K.Y.: Scheduling for electricity cost in a smart grid. J. Sched. 19(6), 687–699 (2016)
Chen, C., Nagananda, K., Xiong, G., Kishore, S., Snyder, L.V.: A communication-based appliance scheduling scheme for consumer-premise energy management systems. IEEE Trans. Smart Grid 4(1), 56–65 (2013)
Cohen, J., Dürr, C., Thang, N.K.: Smooth inequalities and equilibrium inefficiency in scheduling games. In: Goldberg, P.W. (ed.) WINE 2012. LNCS, vol. 7695, pp. 350–363. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-35311-6_26
Fang, K., Uhan, N.A., Zhao, F., Sutherland, J.W.: Scheduling on a single machine under time-of-use electricity tariffs. Ann. OR 238(1–2), 199–227 (2016)
Feng, X., Xu, Y., Zheng, F.: Online scheduling for electricity cost in smart grid. In: Lu, Z., Kim, D., Wu, W., Li, W., Du, D.-Z. (eds.) COCOA 2015. LNCS, vol. 9486, pp. 783–793. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-26626-8_58
Hamilton, K., Gulhar, N.: Taking demand response to the next level. IEEE Power Energy Mag. 8(3), 60–65 (2010)
Koutsopoulos, I., Tassiulas, L.: Control and optimization meet the smart power grid: scheduling of power demands for optimal energy management. In: e-Energy, pp. 41–50. ACM (2011)
Lenstra, J.K., Shmoys, D.B., Tardos, É.: Approximation algorithms for scheduling unrelated parallel machines. Math. Program. 46(1), 259–271 (1990)
Liu, F., Liu, H.H., Wong, P.W.H.: Optimal nonpreemptive scheduling in a smart grid model. In: Proceedings 27th Symposium on Algorithms and Computation, vol. 64, pp. 53:1–53:13 (2016)
Liu, F., Liu, H.H., Wong, P.W.H.: Optimal nonpreemptive scheduling in a smart grid model. CoRR abs/1602.06659 (2016). http://arxiv.org/abs/1602.06659
Lui, T.J., Stirling, W., Marcy, H.O.: Get smart. IEEE Power Energy Mag. 8(3), 66–78 (2010)
Maharjan, S., Zhu, Q., Zhang, Y., Gjessing, S., Basar, T.: Dependable demand response management in the smart grid: a stackelberg game approach. IEEE Trans. Smart Grid 4(1), 120–132 (2013)
Roughgarden, T.: Intrinsic robustness of the price of anarchy. J. ACM 62(5), 32 (2015)
Salinas, S., Li, M., Li, P.: Multi-objective optimal energy consumption scheduling in smart grids. IEEE Trans. Smart Grid 4(1), 341–348 (2013)
Thang, N.K.: Online primal-dual algorithms with configuration linear programs. CoRR abs/1708.04903 (2017)
US Department of Energy: The smart grid: an introduction (2009). https://energy.gov/oe/downloads/smart-grid-introduction-0
Yao, F.F., Demers, A.J., Shenker, S.: A scheduling model for reduced CPU energy. In: FOCS, pp. 374–382. IEEE Computer Society (1995)
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We thank Prudence W. H. Wong for insightful discussions and anonymous reviewers for useful comments that helps to improve the presentation.
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Chau, V., Feng, S., Thang, N.K. (2018). Competitive Algorithms for Demand Response Management in Smart Grid. In: Bender, M., Farach-Colton, M., Mosteiro, M. (eds) LATIN 2018: Theoretical Informatics. LATIN 2018. Lecture Notes in Computer Science(), vol 10807. Springer, Cham. https://doi.org/10.1007/978-3-319-77404-6_23
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