dynamic and the static power. This general power formulation is used by many
researchers~\cite{9,3,15,26}. The dynamic power of the CMOS processors
$P_{dyn}$ is related to the switching activity $\alpha$, load capacitance $C_L$,
-the supply voltage $V$ and operational frequency $f$ respectively as follow :
+the supply voltage $V$ and operational frequency $f$ respectively as follow:
\begin{equation}
\label{eq:pd}
P_\textit{dyn} = \alpha \cdot C_L \cdot V^2 \cdot f
2.5 GHz to 800 MHz, there is 100 MHz difference between two successive
frequencies. For more details on the characteristics of the platform refer to
table~(\ref{table:platform}). This lead to 18 run states for each program. We
-use seven MPI programs of the NAS parallel benchmarks : CG, MG, EP, FT, BT, LU
+use seven MPI programs of the NAS parallel benchmarks: CG, MG, EP, FT, BT, LU
and SP. The average normalized errors between the predicted execution time and
the real time (SimGrid time) for all programs is between 0.0032 to 0.0133. AS an
example, we are present the execution times of the NAS benchmarks as in the
is not straightforward. Moreover, they are not measured using the same metric.
For solving this problem, we normalize the energy by calculating the ratio
between the consumed energy with scaled frequency and the consumed energy
-without scaled frequency :
+without scaled frequency:
\begin{multline}
\label{eq:enorm}
E_\textit{Norm} = \frac{ E_\textit{Reduced}}{E_\textit{Original}} \\
P_\textit{dyn} \cdot \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
P_\textit{static} \cdot T_1 \cdot N }
\end{multline}
-By the same way we can normalize the performance as follows :
+By the same way we can normalize the performance as follows:
\begin{equation}
\label{eq:pnorm}
P_\textit{Norm} = \frac{T_\textit{New}}{T_\textit{Old}}
optimize both energy and performance simultaneously without adding big
overheads. Our solution for this problem is to make the optimization process
have the same direction. Therefore, we inverse the equation of normalize
-performance as follows :
+performance as follows:
\begin{equation}
\label{eq:pnorm_en}
P^{-1}_\textit{Norm} = \frac{ T_\textit{Old}}{ T_\textit{New}}
After obtaining the optimal scale factor from the EPSA algorithm. The program
calculates the new frequency $F_i$ for each task proportionally to its time
value $T_i$. By substitution of the EQ~(\ref{eq:s}) in the EQ~(\ref{eq:si}), we
-can calculate the new frequency $F_i$ as follows :
+can calculate the new frequency $F_i$ as follows:
\begin{equation}
\label{eq:fi}
F_i = \frac{F_\textit{max} \cdot T_i}{S_\textit{optimal} \cdot T_\textit{max}}
