Applications with several tasks consuming huge energy during they are executed on modern high performance computing systems has not gone unnoticed. Fortunately, researchers have provided many solutions to reduce energy consumption by employing dynamic power management (DPM) and dynamic voltage frequency scaling (DVFS). We offer another perspective for studying this issue through increasing the actual amount of completed workload per unit energy consumption (i.e. efficiency of unit energy consumption). In order to Maximize the amount of Work under a Given Energy, an energy efficiency algorithm for tasks with time and precedence constraints, called MWGE, is proposed in this paper. For tasks with precedence constraints, we calculate the upward rank values to establish their scheduling order and tune processor speed according to the execution workload to achieve maximum efficiency. And for tasks with time constraints, we utilize the earliest deadline first (EDF) to schedule task and select the optimal speed to achieve our objective as well as guarantee that each task meets its deadline. Compared with greedy algorithm, our algorithm decreases the rate of speed switching and increases energy efficiency obviously. To demonstrate the effectiveness and accuracy of MWGE, the execution of two real-time applications with 100 tasks under a given budget energy are simulated. Our simulation results show that, on average, MWGE algorithm can achieve a 56.32% less switching rate and 13.42% higher energy efficiency compared to the existing greedy algorithm.
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