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For real-time embedded systems, schedulability and energy efficiency are two highly co-related important design issues. In this paper, we explore how to improve the schedulability and energy efficiency for real-time systems with weakly hard temporal constraints. The weakly hard temporal constraints are modeled by the (m, k)-constraints, which require that at least m out of any k consecutive jobs of a task meet their deadlines. Two off-line approaches are proposed for managing the appropriate mandatory/optional job partition for a given task set with (m, k)-constraints. Through extensive experiments, the results demonstrate that our proposed techniques significantly outperform previous approaches in both schedulability and energy performance for weakly hard real-time embedded systems.