of a processor after scaling its frequency is computed as follows:
\begin{equation}
\label{eq:Estatic}
- E_\textit{s} = P_\textit{s} \cdot (Tcp \cdot S + MinTcm)
+ E_\textit{s} = P_\textit{s} \cdot (Tcp \cdot S + Tcm)
\end{equation}
In the considered heterogeneous platform, each processor $i$ might have different dynamic and static powers, noted as $P_{di}$ and $P_{si}$ respectively. Therefore, even if the distributed message passing iterative application is load balanced, the computation time of each CPU $i$ noted $T_{cpi}$ might be different and different frequency scaling factors might be computed in order to decrease the overall energy consumption of the application and reduce the slack times. The communication time of a processor $i$ is noted as $T_{cmi}$ and could contain slack times if it is communicating with slower nodes, see figure(\ref{fig:heter}). Therefore, all nodes do not have equal communication times. While the dynamic energy is computed according to the frequency scaling factor and the dynamic power of each node as in EQ(\ref{eq:Edyn}), the static energy is computed as the sum of the execution time of each processor multiplied by its static power. The overall energy consumption of a message passing distributed application executed over a heterogeneous platform during one iteration is the summation of all dynamic and static energies for each processor. It is computed as follows:
