F. Yao, A. Demers, and S. Shenker, A scheduling model for reduced CPU energy, Proceedings of IEEE 36th Annual Foundations of Computer Science, pp.374-382, 1995.
DOI : 10.1109/SFCS.1995.492493
URL : http://www.cs.pitt.edu/~kirk/cs3150spring2010/yds.pdf

N. Bansal, T. Kimbrel, and K. Pruhs, Speed scaling to manage energy and temperature, Journal of the ACM, vol.54, issue.1, 2007.
DOI : 10.1145/1206035.1206038

F. Gruian, On energy reduction in hard real-time systems containing tasks with stochastic execution times, IEEE Workshop on Power Management for Real-Time and Embedded Systems, pp.11-16, 2001.

J. Lorch and A. Smith, Improving dynamic voltage scaling algorithms with pace, ACM SIGMETRICS 2001 Conference, pp.50-61, 2001.
DOI : 10.1145/384268.378429

P. Pillai and K. G. Shin, Real-time dynamic voltage scaling for low-power embedded operating systems, ACM SIGOPS Operating Systems Review, vol.35, issue.5, pp.89-102, 2001.
DOI : 10.1145/502059.502044

M. L. Puterman, Markov Decision Process : Discrete Stochastic Dynamic Programming. Wiley, wiley series in probability and statistics ed, 2005.

B. Gaujal, N. Navet, and C. Walsh, Shortest-path algorithms for real-time scheduling of FIFO tasks with minimal energy use, ACM Transactions on Embedded Computing Systems, vol.4, issue.4, 2005.
DOI : 10.1145/1113830.1113838
URL : https://hal.archives-ouvertes.fr/inria-00099957

W. Horn, Some simple scheduling algorithms, Naval Research Logistics Quarterly, vol.18, issue.1, pp.177-185, 1974.
DOI : 10.1002/nav.3800210113

A. Marshall and I. Olkin, Inequalitites: Theory of Majorization and Its Applications, Mathematics in Science and Engineering, vol.143, 1979.

A. Müller and D. Stoyan, Comparison Methods for Stochastic Models and Risks, in Wiley Series in Probability and Statistics, 2002.

D. Bertsekas and J. Tsitsiklis, Neuro-dynamic programming, 1996.
DOI : 10.1007/0-306-48332-7_333

P. Hilton and J. Pedersen, Catalan Numbers, Their Generalization, and Their Uses, The Mathematical Intelligencer, vol.5, issue.4, pp.64-75, 1991.
DOI : 10.1007/BF03026506

H. Yun and J. Kim, On energy-optimal voltage scheduling for fixed-priority hard real-time systems, ACM Transactions on Embedded Computing Systems, vol.2, issue.3, pp.393-430, 2003.
DOI : 10.1145/860176.860183

M. Li and F. F. Yao, An Efficient Algorithm for Computing Optimal Discrete Voltage Schedules, SIAM Journal on Computing, vol.35, issue.3, pp.658-671, 2005.
DOI : 10.1137/050629434
URL : http://www.cs.cityu.edu.hk/~minmli/files/MFCS2005.pdf

R. N°-9101 and R. Centre-grenoble-?-rhône-alpes, Inovallée 655 avenue de l'Europe Montbonnot 38334 Saint Ismier Cedex Publisher Inria Domaine de Voluceau -Rocquencourt BP 105 -78153 Le Chesnay Cedex inria, pp.249-6399