-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
-performance per watt function is maximized. In the work of Kia Ma et al.
-~\cite{KaiMa_Holistic.Approach.to.Energy.Efficiency.in.GPU-CPU}, They developed a scheduling
-algorithm to distributed different workloads proportional to the computing power of the node
-to be executed on a CPU or a GPU, emphasize all tasks must be finished in the same time.
-Recently, Rong et al.~\cite{Rong_Effects.of.DVFS.on.K20.GPU}, Their study explain that
-a heterogeneous clusters enabled DVFS using GPUs and CPUs gave better energy and performance
-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,
-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.
-Other works such as Lizhe et al.~\cite{Lizhe_Energy.aware.parallel.task.scheduling},
-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
-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
-of Intel and AMD processors such as~\cite{Joshi_Blackbox.prediction.of.impact.of.DVFS}
-and \cite{Spiliopoulos_Green.governors.Adaptive.DVFS}, they predicated both the energy
-and the performance for each frequency gear, then the algorithm selected the best gear that gave
-the best tradeoff. In contrast our algorithm works over a heterogeneous platform composed of
-four different types of processors. Others approaches such as
-\cite{Shelepov_Scheduling.on.Heterogeneous.Multicore} and \cite{Li_Minimizing.Energy.Consumption.for.Frame.Based.Tasks},
-they are selected the best frequencies for a specified heterogeneous clusters offline using some
-heuristic methods. While our proposed algorithm works online during the execution time of
-iterative application. Greedy dynamic approach used by Chen et al.~\cite{Chen_DVFS.under.quality.of.service.requirements},
-minimized the power consumption of a heterogeneous severs with time/space complexity, this approach
-had considerable overhead. In our proposed scaling algorithm has very small overhead and
-it is works without any previous analysis for the application time complexity.
+cluster composed of Intel Xeon CPUs and NVIDIA GPUs. Their main goal was to maximize the
+energy efficiency of the platform during computation by maximizing the number of FLOPS per watt generated.
+In~\cite{KaiMa_Holistic.Approach.to.Energy.Efficiency.in.GPU-CPU}, Kai Ma et al. developed a scheduling
+algorithm that distributes workloads proportional to the computing power of the nodes which could be a GPU or a CPU. All the tasks must be completed at the same time.
+In~\cite{Rong_Effects.of.DVFS.on.K20.GPU}, Rong et al. showed that
+a heterogeneous (GPUs and CPUs) cluster that enables DVFS gave better energy and performance
+efficiency than other clusters only composed of CPUs.
+
+The work presented in this paper concerns the second type of platform, with heterogeneous CPUs.
+Many methods were conceived to reduce the energy consumption of this type of platform. Naveen et al.~\cite{Naveen_Power.Efficient.Resource.Scaling}
+developed a method that minimizes the value of $energy*delay^2$ (the delay is the sum of slack times that happen during synchronous communications) by dynamically assigning new frequencies to the CPUs of the heterogeneous cluster.. Lizhe et al.~\cite{Lizhe_Energy.aware.parallel.task.scheduling} propose
+an algorithm that divides the executed tasks into two types: the critical and
+non critical tasks. The algorithm scales down the frequency of non critical tasks proportionally to their slack and communication times while limiting the performance degradation percentage to less than 10\%. In~\cite{Joshi_Blackbox.prediction.of.impact.of.DVFS}
+ a heterogeneous cluster composed of two types
+of Intel and AMD processors. They use a gradient method to predict the impact of DVFS operations on performance.
+In~\cite{Shelepov_Scheduling.on.Heterogeneous.Multicore} and \cite{Li_Minimizing.Energy.Consumption.for.Frame.Based.Tasks},
+ the best frequencies for a specified heterogeneous cluster are selected offline using some
+heuristic. Chen et al.~\cite{Chen_DVFS.under.quality.of.service.requirements} used a greedy dynamic programming approach to
+minimize the power consumption of heterogeneous severs while respecting given time constraints. This approach
+had considerable overhead.
+In contrast to the above described papers, this paper presents the following contributions :
+\begin{enumerate}
+\item two new energy and performance models for message passing iterative synchronous applications running over
+ a heterogeneous platform. Both models takes into account the communication and slack times. The models can predict the required energy and the execution time of the application.
+
+\item a new online frequency selecting algorithm for heterogeneous platforms. The algorithm has a very small
+ overhead and does not need for any training or profiling. It uses a new optimization function which simultaneously maximizes the performance and minimizes the energy consumption of a message passing iterative synchronous application .
+
+
+\end{enumerate}
