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We present a Markov Decision Process (MDP) approach to compute the optimal on-line speed scaling policy to minimize the energy consumption of a processor executing a finite or infinite set of jobs with real-time constraints. The policy is computed off-line but used on-line. We provide several qualitative properties of the optimal policy: monotonicity with respect to the jobs parameters, comparison with on-line deterministic algorithms. Numerical experiments show that our proposition performs well when compared with off-line optimal solutions and out-performs on-line solutions oblivious to statistical information on the jobs.