Abstract
In this paper, we study a system where the speed of a processor depends on the current number of jobs. We propose a queueing model in which jobs consist of a variable number of tasks, and priority is given to the job with the fewest remaining tasks. The number of processor frequency levels determines the dimensionality of the queueing process. The objective is to evaluate the trade-offs between holding cost and energy cost when setting the processor frequency. We obtain exact results for two and three frequency levels, and accurate approximations that can be further generalized. Numerical and simulation results show the high accuracy of the approximate solutions that we propose. Our experiments suggest that a parsimonius model with only two frequency levels is sufficient, since more elaborate models provide negligible improvements when optimizing the system.
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Andrew, L., Lin, M., Wierman, A.: Optimality, fairness, and robustness in speed scaling designs. In: Proceedings of ACM SIGMETRICS, pp. 37–48 (2010)
Bansal, N., Chan, H., Pruhs, K.: Speed scaling with an arbitrary power function. In: Proceedings of ACM-SIAM Symposium on Discrete Algorithms (2009)
Bansal, N., Harchol-Balter, M.: Analysis of SRPT scheduling: investigating unfairness. In: Proceedings of ACM SIGMETRICS, pp. 279–290 (2001)
Bansal, N., Kimbrel, T., Pruhs, K.: Speed scaling to manage energy and temperature. J. ACM 54, 3 (2007)
Cox, D.R.: A use of complex probabilities in the theory of stochastic processes. Math. Proc. Cambridge Philos. Soc. 51(2), 313–319 (1955)
Elahi, M., Williamson, C.: Autoscaling effects in speed scaling systems. In: Proceedings of IEEE MASCOTS, pp. 307–312 (2016)
George, J., Harrison, J.: Dynamic control of a queue with adjustable service rate. Oper. Res. 49(5), 720–731 (2001)
Harchol-Balter, M., Bansal, N., Shroeder, B., Agrawal, M.: Implementation of SRPT scheduling in web servers. In: Proceedings of IEEE International Parallel & Distributed Processing Symposium (IPDS), pp. 1–24 (2001)
Kleinrock, L.: Queueing Systems: Computer Applications, vol. 2. Wiley, New York (1976)
Pakes, A.G.: Some conditions for ergodicity and recurrence of Markov chains. Oper. Res. 17(6), 1058–1061 (1969)
Rai, I.A., Urvoy-Keller, G., Vernon, M.K., Biersack, E.W.: Performance analysis of LAS-based scheduling disciplines in a packet switched network. In: Proceedings of the Joint International Conference on Measurement and Modeling of Computer Systems (SIGMETRICS 2004/Performance 2004), pp. 106–117 (2004)
Schrage, L.: A proof of the optimality of the shortest remaining processing time discipline. Oper. Res. 16, 678–690 (1968)
Skrenes, A., Williamson, C.: Experimental calibration and validation of a speed scaling simulator. In: Proceedings of IEEE MASCOTS, pp. 105–114 (2016)
Wierman, A.: Fairness and scheduling in single server queues. Surv. Oper. Res. Manage. Sci. 6(1), 39–48 (2011)
Wierman, A., Andrew, L., Tang, A.: Power-aware speed scaling in processor sharing systems. In: Proceedings of IEEE INFOCOM (2009)
Wierman, A., Andrew, L., Tang, A.: Power-aware speed scaling in processor sharing systems: optimality and robustness. Perform. Eval. 69, 601–622 (2012)
Yao, F., Demers, A., Shenker, S.: A scheduling model for reduced CPU energy. In: Proceedings of ACM Foundations of Computer Systems (FOCS), pp. 374–382 (1995)
Acknowledgments
The work described in this paper has been partially supported by the Università Ca’ Foscari Venezia - DAIS within the IRIDE program.
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Marin, A., Mitrani, I., Elahi, M., Williamson, C. (2018). Control and Optimization of the SRPT Service Policy by Frequency Scaling. In: McIver, A., Horvath, A. (eds) Quantitative Evaluation of Systems. QEST 2018. Lecture Notes in Computer Science(), vol 11024. Springer, Cham. https://doi.org/10.1007/978-3-319-99154-2_16
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DOI: https://doi.org/10.1007/978-3-319-99154-2_16
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