became the top of the Green500 list in November 2014 \cite{Green500_List}.
This heterogeneous platform executes more than 5 GFLOPS per watt while consumed 57.15 kilowatts.
-Besides hardware improvements, there are many software techniques to lower the energy consumption of these platforms,
+Besides platform improvements, there are many software and hardware techniques to lower the energy consumption of these platforms,
such as scheduling, DVFS, ... DVFS is a widely used process to reduce the energy consumption of a processor by lowering
its frequency \cite{Rizvandi_Some.Observations.on.Optimal.Frequency}. However, it also reduces the number of FLOPS
executed by the processor which might increase the execution time of the application running over that processor.
\begin{figure}[t]
\centering
- \includegraphics[scale=0.5]{fig/commtasks}
+ \includegraphics[scale=0.6]{fig/commtasks}
\caption{Parallel tasks on a heterogeneous platform}
\label{fig:heter}
\end{figure}
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 (\ref{eq:Edyn}), the static energy is
-computed as the sum of the execution time of each processor multiplied by its static power.
+computed as the sum of the execution time of one iteration multiplied by static power of each processor.
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:
toward lower frequencies. The algorithm iterates on all left frequencies, from the higher bound until all
nodes reach their minimum frequencies, to compute their overall energy consumption and performance, and select
the optimal frequency scaling factors vector. At each iteration the algorithm determines the slowest node
-according to (\ref{eq:perf}) and keeps its frequency unchanged, while it lowers the frequency of
+according to the equation (\ref{eq:perf}) and keeps its frequency unchanged, while it lowers the frequency of
all other nodes by one gear.
The new overall energy consumption and execution time are computed according to the new scaling factors.
The optimal set of frequency scaling factors is the set that gives the highest distance according to the objective
The precision of the proposed algorithm mainly depends on the execution time prediction model defined in
(\ref{eq:perf}) and the energy model computed by (\ref{eq:energy}).
The energy model is also significantly dependent on the execution time model because the static energy is
-linearly related the execution time and the dynamic energy is related to the computation time. So, all of
+linearly related to the execution time and the dynamic energy is related to the computation time. So, all of
the works presented in this paper is based on the execution time model. To verify this model, the predicted
execution time was compared to the real execution time over SimGrid/SMPI simulator, v3.10~\cite{casanova+giersch+legrand+al.2014.versatile},
for all the NAS parallel benchmarks NPB v3.3
outperforms their algorithm in term of energy-time tradeoff.
In the near future, this method will be applied to real heterogeneous platforms to evaluate its performance in a real study case. It would also be interesting to evaluate its scalability over large scale heterogeneous platform and measure the energy consumption reduction it can produce. Afterward, we would like to develop a similar method that is adapted to asynchronous iterative applications
-where each task does not wait for others tasks to finish there works. The development of such method might require a new
+where each task does not wait for others tasks to finish their works. The development of such method might require a new
energy model because the number of iterations is not
known in advance and depends on the global convergence of the iterative system.
\section*{Acknowledgment}
This work has been partially supported by the Labex
-ACTION project (contract “ANR-11-LABX-01-01”). As a PhD student,
+ACTION project (contract “ANR-11-LABX-01-01”). As a PhD student,
Mr. Ahmed Fanfakh, would like to thank the University of
-Babylon (Iraq) for supporting his work.
+Babylon (Iraq) for supporting his work.
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