Abstract
Basic algorithms have been proposed in the field of low-power (Yao, F., et al. in Proceedings of lEEE annual foundations of computer science, pp. 374–382, 1995) which compute the minimum energy-schedule for a set of non-recurrent tasks (or jobs) scheduled under EDF on a dynamically variable voltage processor. In this study, we propose improvements upon existing algorithms with lower average and worst-case complexities. They are based on a new EDF feasibility test that helps to identify the “critical intervals”. The complexity of this feasibility test depends on structural characteristics of the set of jobs. More precisely, it depends on how tasks are included one in the other. The first step of the algorithm is to construct the Hasse diagram of the set of tasks where the partial order is defined by the inclusion relation on the tasks. Then, the algorithm constructs the shortest path in a geometrical representation at each level of the Hasse diagram. The optimal processor speed is chosen according to the maximal slope of each path.
Similar content being viewed by others
References
AbouGhazaleh N, Mosse D, Childers B, Melhem R, Craven M (2003) Collaborative operating system and compiler power management for real-time applications. In: 9th IEEE real-time and embedded technology and applications symposium, pp 133–143
Aldous D, Diaconis P (1995) Hammersley’s interacting particle process and longest increasing subsequences. Probab Theory Relat Fields 103(2):199–213
Aydin H, Melhem R, Mossé D, Mejia-Alvarez P (2001) Dynamic and Aggressive Scheduling techniques for power aware real-time systems. In: 22th real-time systems symposium, pp 95–105
Aydin H, Melhem R, Mossé D, Mejia-Alvarez P (2004) Power-aware scheduling for periodic real-time tasks. IEEE Trans Comput 53(5):584–600
Barlow RE, Proschan F (1981) Statistical theory of reliability and life testing: probability models, 2nd edn. To Begin With, Silver Spring, MD ISBN-10:0960676406
Boissonnat J, Yvinec M (1998) Algorithmic geometry. Cambridge University Press, Cambridge
Fishburn P (1985) Interval orders and interval graphs: a study of partially ordered sets. Interscience series in discrete mathematics. Wiley, New York
Gaujal B, Navet N, Walsh C (2003) Real-time scheduling for optimal energy use. In: Journées d’étude faible tension—faible consommation (FTFC’03), pp 159–166
Gaujal B, Navet N, Walsh C (2005) Shortest-path algorithms for real-time scheduling of FIFO tasks with minimal energy use. ACM Trans. Embed. Comput. Syst. 4(4):907–933. Preliminary version available as INRIA Research Report RR-4886, http://www.inria.fr/rrrt/rr-4886.html
Gruian F (2001) On energy reduction in hard real-time systems containing tasks with stochastic execution times. In: IEEE workshop on power management for real-time and embedded systems, pp 11–16.
Gruian F (2002) Energy-centric scheduling for real-time systems. PhD thesis, Lund Institute of Technology
Leung J-T, Whitehead J (1982) On the complexity of fixed-priority scheduling of periodic, real-time tasks. Perform Eval 2:237–250
Liu Y, Mok A (2003) An integrated approach for applying dynamic voltage scaling to hard real-time systems. In: 9th IEEE real-time and embedded technology and applications symposium, pp 116–123
Lorch J, Smith A (2001) Improving dynamic voltage scaling algorithms with PACE. In: ACM SIGMETRICS 2001 conference, pp 50–61
Mossè D, Aydin H, Childers B, Melhem R (2000) Compiler-assisted dynamic power-aware scheduling for real-time applications. In: Workshop on compiler and operating systems for low-power
Pillai P, Shin K (2001) Real-time dynamic voltage scaling for low-power embedded systems. Oper Syst Rev 35(5):89–102
Qadi A, Goddard S, Farritor S (2003) A dynamic voltage scaling algorithm for sporadic tasks. In: 24th IEEE international real-time systems symposium, pp 52–62
Quan G, Hu X (2001) Energy efficient fixed-priority scheduling for real-time systems on variable voltage processors. In: Design automation conference, pp 828–833
Quan G, Hu X (2002) Minimum energy fixed-priority scheduling for variable voltage processors. In: Design, automation and test in Europe conference and exhibition (DATE’02)
Scordino C, Lipari G (2006) A resource reservation algorithm for power-aware scheduling of periodic and aperiodic real-time tasks. IEEE Trans Comput 55(12):1509–1522
Shin Y, Choi K (1999) Power conscious fixed priority scheduling for hard real-time systems. In: Design automation conference, pp 134–139
Shin D, Kim J, Lee S (2001) Intra-task voltage scheduling for low-energy hard real-time applications. IEEE Des Test Comput 18(2)
Stankovic J, Spuri M, Ramamritham K, Buttazo G (1998) Deadline scheduling for real-time systems: EDF and related algorithms. Kluwer Academic, Dordrecht
Weisstein E (1999) The CRC concise encyclopedia of mathematics. CRC Press, Boca Raton
Xu R, Xi C, Melhem R, Moss D (2004) Practical PACE for embedded systems. In: Proceedings of the 4th ACM international conference on embedded software (EMSOFT’04). ACM Press, New York, pp 54–63
Yao F (2003) Complexity of the Yao Demers Shenker algorithm. Private communication
Yao F, Demers A, Shenker S (1995) A scheduling model for reduced CPU energy. In: Proceedings of lEEE annual foundations of computer science, pp 374–382
Yun H-S, Kim J (2003) On energy-optimal voltage scheduling for fixed-priority hard real-time systems. ACM Trans Embed Comput Syst 2(3):393–430
Zhang F, Chanson S (2002) Processor voltage scheduling for real-time tasks with non-preemptible sections. In: 23th real-time systems symposium, pp 235–245
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gaujal, B., Navet, N. Dynamic voltage scaling under EDF revisited. Real-Time Syst 37, 77–97 (2007). https://doi.org/10.1007/s11241-007-9029-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11241-007-9029-y