Stochastic Analysis of Energy Consumption in Pool Depletion Systems

  • Davide CerottiEmail author
  • Marco Gribaudo
  • Riccardo Pinciroli
  • Giuseppe Serazzi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9629)


The evolutions of digital technologies and software applications have introduced a new computational paradigm that involves initially the creation of a large pool of jobs followed by a phase in which all the jobs are executed in systems with limited capacity. For example, a number of libraries have started digitizing their old books, or video content providers, such as YouTube or Netflix, need to transcode their contents to improve playback performances. Such applications are characterized by a huge number of jobs with different requests of computational resources, like CPU and GPU. Due to the very long computation time required by the execution of all the jobs, strategies to reduce the total energy consumption are very important.

In this work we present an analytical study of such systems, referred to as pool depletion systems, aimed at showing that very simple configuration parameters may have a non-trivial impact on the performance and especially on the energy consumption. We apply results from queueing theory coupled with the absorption time analysis for the depletion phase. We show that different optimal settings can be found depending on the considered metric.


Stochastic models Energy efficiency Performance evaluation 



This work was partially funded by the European Commission under the grant ANTAREX H2020 FET-HPC-671623.


  1. 1.
    Albers, S., Fujiwara, H.: Energy-efficient algorithms for flow time minimization. ACM Trans. Algorithms (TALG) 3(4), 49 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Andrew, L.L., Lin, M., Wierman, A.: Optimality, fairness, and robustness in speed scaling designs. In: ACM SIGMETRICS Performance Evaluation Review, vol. 38, pp. 37–48. ACM (2010)Google Scholar
  3. 3.
    Bansal, N., Chan, H.L., Pruhs, K.: Speed scaling with an arbitrary power function. In: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 693–701. Society for Industrial and Applied Mathematics (2009)Google Scholar
  4. 4.
    Cerotti, D., Gribaudo, M., Piazzolla, P., Pinciroli, R., Serazzi, G.: Multi-class queuing networks models for energy optimization. In: Proceedings of the 8th International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2014, ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering), ICST, Brussels, Belgium, pp. 98–105 (2014).
  5. 5.
    Chen, D., Goldberg, G., Kahn, R., Kat, R., Meth, K.: Leveraging disk drive acoustic modes for power management. In: 2010 IEEE 26th Symposium on Mass Storage Systems and Technologies (MSST), pp. 1–9, May 2010Google Scholar
  6. 6.
    Diaz-Sanchez, D., Marin-Lopez, A., Almenarez, F., Sanchez-Guerrero, R., Arias, P.: A distributed transcoding system for mobile video delivery. In: Wireless and Mobile Networking Conference (WMNC), 2012 5th Joint IFIP, pp. 10–16, September 2012Google Scholar
  7. 7.
    Fan, X., Weber, W.D., Barroso, L.A.: Power provisioning for a warehouse-sized computer. In: Proceedings of the 34th Annual International Symposium on Computer Architecture, ISCA 2007, pp. 13–23. ACM, New York (2007).
  8. 8.
    Gandhi, A., Gupta, V., Harchol-Balter, M., Kozuch, M.A.: Optimality analysis of energy-performance trade-off for server farm management. Perform. Eval. 67(11), 1155–1171 (2010)CrossRefGoogle Scholar
  9. 9.
    Gonzalez, R., Horowitz, M.: Energy dissipation in general purpose microprocessors. IEEE J. Solid-State Circuits 31(9), 1277–1284 (1996)CrossRefGoogle Scholar
  10. 10.
    Hyytiä, E., Righter, R., Aalto, S.: Task assignment in a heterogeneous server farm with switching delays and general energy-aware cost structure. Perform. Eval. 75, 17–35 (2014)CrossRefGoogle Scholar
  11. 11.
    Kang, C.W., Abbaspour, S., Pedram, M.: Buffer sizing for minimum energy-delay product by using an approximating polynomial. In: Proceedings of the 13th ACM Great Lakes Symposium on VLSI, pp. 112–115. ACM (2003)Google Scholar
  12. 12.
    Kant, K.: A control scheme for batching dram requests to improve power efficiency. In: Proceedings of the ACM SIGMETRICS Joint International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2011, pp. 139–140. ACM (2011)Google Scholar
  13. 13.
    Kaxiras, S., Martonosi, M.: Computer architecture techniques for power-efficiency. Synth. Lect. Comput. Archit. 3(1), 1–207 (2008)CrossRefGoogle Scholar
  14. 14.
    Muppala, J., Malhotra, M., Trivedi, K.: Markov dependability models of complex systems: analysis techniques. In: Ozekici, S. (ed.) Reliability and Maintenance of Complex Systems, vol. 154, pp. 442–486. Springer, Heidelberg (1996). Scholar
  15. 15.
    Rivoire, S., Ranganathan, P., Kozyrakis, C.: A comparison of high-level full-system power models. HotPower 8, 3 (2008)Google Scholar
  16. 16.
    Rosti, E., Schiavoni, F., Serazzi, G.: Queueing network models with two classes of customers. In: Proceedings of the Fifth International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems, MASCOTS 1997, pp. 229–234. IEEE (1997)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Davide Cerotti
    • 1
    Email author
  • Marco Gribaudo
    • 1
  • Riccardo Pinciroli
    • 1
  • Giuseppe Serazzi
    • 1
  1. 1.Dip. di Elettronica, Informazione e BioingengeriaPolitecnico di MilanoMilanoItaly

Personalised recommendations