adding the some corrections

diff --git a/Heter_paper.tex b/Heter_paper.tex
index 8aeea6b8dd30ec61d3af183d47cd723e6879b524..2fc854959ff4a138331b9011b0833c60010fe89b 100644 (file)
--- a/Heter_paper.tex
+++ b/Heter_paper.tex
@@ -129,26 +129,26 @@ Finally, we conclude in Section~\ref{sec.concl} with a summary and some future w
 
 \section{Related works}
 \label{sec.relwork}
 
 \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 
 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 
 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 
 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 
 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 
 ~\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 


@@ -161,7 +161,7 @@ a heterogeneous clusters enabled DVFS using GPUs and CPUs gave better energy and
 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. 
 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. 
 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. 


@@ -169,7 +169,7 @@ Other works such as Lizhe et al.~\cite{Lizhe_Energy.aware.parallel.task.scheduli
 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 
 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 
 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 


@@ -299,7 +299,7 @@ operational frequency $F$, as shown in EQ(\ref{eq:pd}).
   \label{eq:pd}
   Pd = \alpha \cdot C_L \cdot V^2 \cdot F
 \end{equation}
   \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}
 \begin{equation}
   \label{eq:ps}
    Ps  = V \cdot N_{trans} \cdot K_{design} \cdot I_{leak}