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DVFS is an efficient energy saving technique for processors during program execution time. In this paper, a critical speed-based DVFS mechanism that we have implemented on the Android operating system is introduced. Our studies indicate that due to memory accesses, decreasing the frequency may not always reduce the energy consumption. A critical speed is thus defined as the CPU frequency with which the energy consumption can be minimized. In our mechanism, a prediction equation based on the correlation of the memory access rate and the critical speed was constructed and used to choose a suitable frequency and voltage dynamically at run time. Our initial experiment results show that for real applications running on Android, the energy consumption can be effectively reduced.