\section{Related works}
\label{sec.relwork}
-Energy reduction process for a high performance clusters recently performed using
+Energy reduction process for high performance clusters recently performed using
dynamic voltage and frequency scaling (DVFS) technique. DVFS is a technique enabled
-in a modern processors to scaled down both of the voltage and the frequency of
+in modern processors to scaled down both of the voltage and the frequency of
the CPU while it is in the computing mode to reduce the energy consumption. DVFS is
also allowed in the graphical processors GPUs, to achieved the same goal. Applying
DVFS has a dramatical side effect if it is applied to minimum levels to gain more
-energy reduction, producing a high percentage of performance degradations for the
+energy reduction, producing a high percentage of performance degradations for the
parallel applications. Many researchers used different strategies to solve this
nonlinear problem for example in
~\cite{Hao_Learning.based.DVFS,Dhiman_Online.Learning.Power.Management}, their methods
add big overheads to the algorithm to select the suitable frequency.
In this paper we present a method
-to find the optimal set of frequency scaling factors for a heterogeneous cluster to
-simultaneously optimize both the energy and the execution time without adding a big
-overhead. This work is developed from our previous work of a homogeneous cluster~\cite{Our_first_paper}.
+to find the optimal set of frequency scaling factors for heterogeneous cluster to
+simultaneously optimize both the energy and the execution time without adding big
+overhead. This work is developed from our previous work of homogeneous cluster~\cite{Our_first_paper}.
Therefore we are interested to present some works that concerned the heterogeneous clusters
enabled DVFS. In general, the heterogeneous cluster works fall into two categorizes:
GPUs-CPUs heterogeneous clusters and CPUs-CPUs heterogeneous clusters. In GPUs-CPUs
-heterogeneous clusters some parallel tasks executed on a GPUs and the others executed
-on a CPUs. As an example of this works, Luley et al.
+heterogeneous clusters some parallel tasks executed on GPUs and the others executed
+on CPUs. As an example of this works, Luley et al.
~\cite{Luley_Energy.efficiency.evaluation.and.benchmarking}, proposed a heterogeneous
cluster composed of Intel Xeon CPUs and NVIDIA GPUs. Their main goal is to determined the
energy efficiency as a function of performance per watt, the best tradeoff is done when the
efficiency than other clusters composed of only CPUs.
The CPUs-CPUs heterogeneous clusters consist of number of computing nodes all of the type CPU.
Our work in this paper can be classified to this type of the clusters.
-As an example of this works see Naveen et al.~\cite{Naveen_Power.Efficient.Resource.Scaling} work,
+As an example of these works see Naveen et al.~\cite{Naveen_Power.Efficient.Resource.Scaling} work,
They developed a policy to dynamically assigned the frequency to a heterogeneous cluster.
The goal is to minimizing a fixed metric of $energy*delay^2$. Where our proposed method is automatically
optimized the relation between the energy and the delay of the iterative applications.
their algorithm divided the executed tasks into two types: the critical and
non critical tasks. The algorithm scaled down the frequency of the non critical tasks
as function to the amount of the slack and communication times that
-have with maximum of performance degradation percentage of 10\%. In our method there is no
+have with maximum of performance degradation percentage less than 10\%. In our method there is no
fixed bounds for performance degradation percentage and the bound is dynamically computed
according to the energy and the performance tradeoff relation of the executed application.
There are some approaches used a heterogeneous cluster composed from two different types
\label{eq:pd}
Pd = \alpha \cdot C_L \cdot V^2 \cdot F
\end{equation}
-The static power $P_{s}$ captures the leakage power as follows:
+The static power $Ps$ captures the leakage power as follows:
\begin{equation}
\label{eq:ps}
Ps = V \cdot N_{trans} \cdot K_{design} \cdot I_{leak}
