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This paper presents GRACE-OS, an energy-efficient soft real-time CPU scheduler for mobile devices that primarily run multimedia applications. The major goal of GRACE-OS is to support application quality of service and save energy. To achieve this goal, GRACE-OS integrates dynamic voltage scaling into soft real-time scheduling and decides how fast to execute applications in addition to when and how long to execute them. GRACE-OS makes such scheduling decisions based on the probability distribution of application cycle demands, and obtains the demand distribution via online profiling and estimation. We have implemented GRACE-OS in the Linux kernel and evaluated it on an HP laptop with a variable-speed CPU and multimedia codecs. Our experimental results show that (1) the demand distribution of the studied codecs is stable or changes smoothly. This stability implies that it is feasible to perform stochastic scheduling and voltage scaling with low overhead; (2) GRACE-OS delivers soft performance guarantees by bounding the deadline miss ratio under application-specific requirements; and (3) GRACE-OS reduces CPU idle time and spends more busy time in lower-power speeds. Our measurement indicates that compared to deterministic scheduling and voltage scaling, GRACE-OS saves energy by 7% to 72% while delivering statistical performance guarantees.