660 words - 3 pages

There are some advantages in formulating the problem this way. First, the model solves the problem of having the discrete frequency levels of a real computing system. Second, the model is not concerned with individual task assignment; it provides more of a bigger view of an overall system performance. Third, the model can be generalised to any types of systems, i.e. a homogeneous system, where all processors are the same or a heterogeneous system, where processors have different power consumption models, CPU workload limitations, or operating speed/frequency limits.

The proposed optimization formulation from Section~\ref{sec:prob} is implemented in MATLAB. The SCIP solver is used to obtain the optimal solution \citep{Achterberg2009}. Figure~\ref{fig:solution} shows solutions of the entire workload space defined by CPU frequency and Duty cycle of different unit jobs and periods.

From Fig.~\ref{fig:solution}, the optimal solutions can be divided into three different regions. First, considered the region where the orignal CPU workload is small, i.e. the lower triangular of the figure. The results from our algorithm suggest an increase of the operating frequency to 2.6 GHz-2.7 GHz if the original operating frequency is lesser and a decrease of the operating frequency to 2.6 GHz-2.7 GHz otherwise. This implies that if the CPU workload is small due to running at low frequency, the optimal strategy is to finish the computations as fast as possible and let the CPU goes to idle state, by doing so will result in the reduced power consumption. On the contradiction, in the case of the small workload due to a low duty cycle, the optimal strategy is to increase the duty cycle by reducing the operating speed so that the minimum power consumption is achieved.

Similar strategy suggested by the algorithm can also be seen in the middle section of a Fig.~\ref{fig:solution}. For these cases,...

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