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This paper derives simple, yet fundamental formulas to describe the interplay between parallelism of an application, program performance, and energy consumption. Given the ratio of serial and parallel portions in an application and the number of processors, the authors derive optimal frequencies allocated to the serial and parallel regions in an application to either minimize the total energy consumption or minimize the energy-delay product. The impact of static power is revealed by considering the ratio between static and dynamic power and quantifying the advantages of adding to the architecture capability to turn off individual processors and save static energy. They further determine the conditions under which one can obtain both energy and speed improvement, as well as the amount of improvement.
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