Power-aware operating systems/processor controllers ensure that the system temperature does not exceed a threshold by utilizing system-throttling, where the clock speed is scaled to an equilibrium load. We denote this as the Constant policy, and compare against Zig-Zag policies that alternate between phases of cooling and heating. In this paper, we characterize and calculate the best possible Zig-Zag policy, and argue that simple system-throttling rules are often optimal. In reality, however,

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... e system design often forces us to implement Zig-Zag policies. In particular, we consider the case where the processor can operate only at a few discrete states; thus it is required to alternate between cooling and heating phases. In such a setting, we develop an algorithm that outperforms all other Zig-Zag policies, and present computational experiments emphasizing the performance of our algorithm.