\maketitle
\begin{abstract}
-
+Green computing emphasizes the importance of energy conservation, minimizing the negative impact
+on the environment while achieving high performance and minimizing operating costs. So, energy reduction
+process in a high performance clusters it can be archived using dynamic voltage and frequency
+scaling (DVFS) technique, through reducing the frequency of a CPU. Using DVFS to lower levels
+result in a high increase in performance degradation ratio. Therefore selecting the best frequencies
+must give the best possible tradeoff between the energy and the performance of parallel program.
+
+In this paper we present a new online heterogeneous scaling algorithm that selects the best vector
+of frequency scaling factors. These factors give the best tradeoff between the energy saving and the
+performance degradation. The algorithm has small overhead and works without training and profiling.
+We developed a new energy model for distributed iterative application running on heterogeneous cluster.
+The proposed algorithm experimented on Simgrid simulator that applying the NAS parallel benchmarks.
+It reduces the energy consumption up to 35\% while limits the performance degradation as much as possible.
\end{abstract}
\section{Introduction}
\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
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
+~\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.
+to be executed on CPU or 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,
+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}
\subsection{The results for different power consumption scenarios}
-
+\label{sec.compare}
The results of the previous section were obtained while using processors that consume during computation
an overall power which is 80\% composed of dynamic power and 20\% of static power. In this section,
these ratios are changed and two new power scenarios are considered in order to evaluate how the proposed
the work 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 for all the NAS parallel benchmarks
running class B on 8 or 9 nodes. The comparison showed that the proposed execution time model is very precise,
-the maximum normalized difference between the predicted execution time and the real execution time is equal
+the maximum normalized difference between the predicted execution time and the real execution time is equal
to 0.03 for all the NAS benchmarks.
Since the proposed algorithm is not an exact method and do not test all the possible solutions (vectors of scaling factors)
table~(\ref{table:platform}), it takes on average \np[ms]{0.04} for 4 nodes and \np[ms]{0.15} on average for 144 nodes
to compute the best scaling factors vector. The algorithm complexity is $O(F\cdot (N \cdot4) )$, where $F$ is the number
of iterations and $N$ is the number of computing nodes. The algorithm needs from 12 to 20 iterations to select the best
-vector of frequency scaling factors that gives the results of the section (\ref{sec.res}).
+vector of frequency scaling factors that gives the results of the sections (\ref{sec.res}) and (\ref{sec.compare}).
\section{Conclusion}
\label{sec.concl}
-
+In this paper, we have presented a new online heterogeneous scaling algorithm
+that selects the best possible vector of frequency scaling factors. This vector
+gives the maximum distance (optimal tradeoff) between the predicted energy and
+the predicted performance curves. In addition, we developed a new energy model for measuring
+and predicting the energy of distributed iterative applications running over heterogeneous
+cluster. The proposed method evaluated on Simgrid/SMPI simulator to built a heterogeneous
+platform to executes NAS parallel benchmarks. The results of the experiments showed the ability of
+the proposed algorithm to changes its behaviour to selects different scaling factors when
+the number of computing nodes and both of the static and the dynamic powers are changed.
+
+In the future, we plan to improve this method to apply on asynchronous iterative applications
+where each task does not wait the others tasks to finish there works. This leads us to develop a new
+energy model to an asynchronous iterative applications, where the number of iterations is not
+known in advance and depends on the global convergence of the iterative system.
\section*{Acknowledgment}
+
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