Abstract
We consider the setting of a sensor that consists of a speed-scalable processor, a battery, and a solar cell that harvests energy from its environment at a time-invariant recharge rate. The processor must process a collection of jobs of various sizes. Jobs arrive at different times and have different deadlines. The objective is to minimize the recharge rate, which is the rate at which the device has to harvest energy in order to feasibly schedule all jobs. The main result is a polynomial-time combinatorial algorithm for processors with a natural set of discrete speed/power pairs.
See [5] for the full version.
P. Kling—Supported by fellowships of the Postdoc-Programme of the German Academic Exchange Service (DAAD) and the Pacific Institute of Mathematical Sciences (PIMS). Work done while at the University of Pittsburgh.
K. Pruhs—Supported, in part, by NSF grants CCF-1115575, CNS-1253218, CCF-1421508, CCF-1535755, and an IBM Faculty Award.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Statements slightly simplified; Sect. 3 gives the full formal conditions.
- 2.
Figure 3 gives an example where the SLR can be observed: The orange and light-blue jobs run both in depletion interval \(I_3\) and \(I_4\). The orange job’s average speed “jumps” one discrete speed level from \(I_3\) to \(I_4\) (from below \(s_2\) to above \(s_2\)). Thus, the light-blue job must also jump one discrete speed level (from below \(s_3\) to above \(s_3\)).
- 3.
In fact, \(\varDelta _{i+1}>\varDelta _{i}\) is already sufficient. Also note that starting with the lower speed is essential: otherwise the battery’s energy level might become negative.
- 4.
The existence of such a schedule follows from standard speed scaling arguments. To see this, note that any schedule can be transformed to use earliest deadline first and interpolate an average speed in a depletion interval by at most one speed change between two discrete speeds. Thus, the number of job changes and speed changes is finite (depending on n) and we merely have to choose the time slots suitably small.
- 5.
If we restrict ourselves to normalized (earliest deadline first, only one speed change per job in a depletion interval) schedules, they are in fact also necessary.
- 6.
The formal definition is left for the full version.
References
Angelopoulos, S., Lucarelli, G., Nguyen, K.T.: Primal-dual and dual-fitting analysis of online scheduling algorithms for generalized flow time problems. In: Bansal, N., Finocchi, I. (eds.) ESA 2015. LNCS, vol. 9294, pp. 35–46. Springer, Heidelberg (2015)
Antoniadis, A., Barcelo, N., Consuegra, M.E., Kling, P., Nugent, M., Pruhs, K., Scquizzato, M.: Efficient computation of optimal energy and fractional weighted flow trade-off schedules. In: Symposium on Theoretical Aspects of Computer Science, pp. 63–74 (2014)
Bansal, N., Chan, H.L., Pruhs, K.: Speed scaling with a solar cell. Theor. Comput. Sci. 410(45), 4580–4587 (2009)
Bansal, N., Kimbrel, T., Pruhs, K.: Speed scaling to manage energy and temperature. J. ACM 54(1), 3:1–3:39 (2007)
Barcelo, N., Kling, P., Nugent, M., Pruhs, K.: Optimal speed scaling with a solar cell. arXiv:1609.02668 [cs.DS]
Brooks, D.M., Bose, P., Schuster, S.E., Jacobson, H., Kudva, P.N., Buyuktosunoglu, A., Wellman, J.D., Zyuban, V., Gupta, M., Cook, P.W.: Power-aware microarchitecture: design and modeling challenges for next-generation microprocessors. IEEE Micro 20(6), 26–44 (2000)
Cole, D., Letsios, D., Nugent, M., Pruhs, K.: Optimal energy trade-off schedules. In: International Green Computing Conference, pp. 1–10 (2012)
Pruhs, K., Uthaisombut, P., Woeginger, G.J.: Getting the best response for your ERG. ACM Trans. Algorithms 4(3), 38:1–38:17 (2008)
Remick, K., Quinn, D.D., McFarland, D.M., Bergman, L., Vakakis, A.: High-frequency vibration energy harvesting from impulsive excitation utilizing intentional dynamic instability caused by strong nonlinearity. J. Sound Vib. 370, 259–279 (2016)
Stephen, N.G.: On energy harvesting from ambient vibration. J. Sound Vib. 293(1–2), 409–425 (2006)
Vullers, R., van Schaijk, R., Doms, I., Hoof, C.V., Mertens, R.: Micropower energy harvesting. Solid-State Electron. 53(7), 684–693 (2009)
Yao, F.F., Demers, A.J., Shenker, S.: A scheduling model for reduced CPU energy. In: Foundations of Computer Science, pp. 374–382 (1995)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Barcelo, N., Kling, P., Nugent, M., Pruhs, K. (2016). Optimal Speed Scaling with a Solar Cell. In: Chan, TH., Li, M., Wang, L. (eds) Combinatorial Optimization and Applications. COCOA 2016. Lecture Notes in Computer Science(), vol 10043. Springer, Cham. https://doi.org/10.1007/978-3-319-48749-6_38
Download citation
DOI: https://doi.org/10.1007/978-3-319-48749-6_38
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48748-9
Online ISBN: 978-3-319-48749-6
eBook Packages: Computer ScienceComputer Science (R0)