Abstract
This paper deals with power-aware scheduling of preemptable jobs on identical parallel processors to minimize schedule length when jobs are described by continuous, strictly concave functions relating their processing speed at time t to the amount of power allotted at the moment. Power is a continuous, doubly constrained resource, i.e. both: its availability at time t and consumption over scheduling horizon are constrained. Precedence constraints among jobs are represented by a task-on-arc graph. A methodology based on properties of optimal schedules is presented for solving the problem optimally for a given ordering of nodes in the graph. Heuristics for finding an ordering which leads to possibly short schedules are proposed and examined experimentally.
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Bansal, N., Kimbrel, T., & Pruhs, K. (2005). Dynamic speed scaling to manage energy and temperature. In Lecture notes in computer science (Vol. 3404, pp. 460–471).
Bansal, N., Chan, H. L., Lam, T. W., & Lee, L. K. (2008). Scheduling for speed bounded processors. In Proceedings of international colloquium on automata, languages and programming (ICALP) (pp. 409–420).
Boyer, F. R., Epassa, H. G., & Savaria, Y. (2006). Embedded power-aware cycle by cycle variable speed processor. In IEE Proceedings: Vol. 153/4. Computers and digital techniques (pp. 283–290).
Błażewicz, J., Ecker, K., Pesch, E., Schmidt, G., & Węglarz, J. (2007). Handbook on scheduling. Berlin: Springer.
Bunde, D. P. (2006). Power-aware scheduling for makespan and flow. In Proceedings of the eighteenth annual ACM symposium on parallelism in algorithms and architectures (pp. 190–196). Cambridge, MA, USA.
Er, M. C. (1985). Lexicographic ordering, ranking and unranking of combinations. International Journal of Computer Mathematics, 3, 277–283.
Irani, S., & Pruhs, K.b (2005). Algorithmic problems in power management. SIGACT News, 36(2), 63–76.
Józefowska, J., Mika, M., Różycki, R., Waligóra, G., & Węglarz, J. (2002). A heuristic approach to allocating the continuous resource in discrete-continuous scheduling problems to minimize the makespan. Journal of Scheduling, 5(6), 487–499.
Józefowska, J., Mika, M., Różycki, R., Waligóra, G., & Węglarz, J. (2004). An almost optimal heuristic for preemptive C max scheduling of dependent tasks on identical parallel processors. Annals of Operation Research, 129, 205–216.
Lawrence, C., Zhou, J. L., & Tits, A. L. User’s guide for CFSQP version 2.5: A C code for solving (large scale) constrained nonlinear (minimax) optimization problems, generating iterates satisfying all inequality constraints (1997). Available at: http://www.isr.umd.edu/Labs/CACSE/FSQP/c_manual.ps.
Pruhs, K., van Stee, R., & Uthaisombut, P. (2005). Speed scaling of tasks with precedence constraints. In Proceedings of WAOA (pp. 307–319).
Słowiński, R. (1978). A node ordering heuristic for network scheduling under resource constraints. Foundations of Control Engineering, 3, 19–27.
Węglarz, J. (1981). Project scheduling with continuously-divisible doubly constrained resources. Management Science, 27(9), 1040–1053.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Różycki, R., Węglarz, J. Power-aware scheduling of preemptable jobs on identical parallel processors to minimize makespan. Ann Oper Res 213, 235–252 (2014). https://doi.org/10.1007/s10479-011-0957-5
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DOI: https://doi.org/10.1007/s10479-011-0957-5