\maketitle
-\begin{abstract}
-
-
-\end{abstract}
-
\section{Introduction}
\label{sec.intro}
+\textcolor{blue}{
+The need for more computing power is continually increasing. To partially
+satisfy this need, most supercomputers constructors just put more computing
+nodes in their platform. The resulting platforms may achieve higher floating
+point operations per second (FLOPS), but the energy consumption and the heat
+dissipation are also increased. As an example, the Chinese supercomputer
+Tianhe-2 had the highest FLOPS in June 2015 according to the Top500 list
+\cite{TOP500_Supercomputers_Sites}. However, it was also the most power hungry
+platform with its over 3 million cores consuming around 17.8 megawatts.
+Moreover, according to the U.S. annual energy outlook 2015
+\cite{U.S_Annual.Energy.Outlook.2014}, the price of energy for 1 megawatt-hour
+was approximately equal to \$70. Therefore, the price of the energy consumed by
+the Tianhe-2 platform is approximately more than \$10 million each year. The
+computing platforms must be more energy efficient and offer the highest number
+of FLOPS per watt possible, such as the Shoubu-ExaScaler from RIKEN
+which became the top of the Green500 list in June 2015 \cite{Green500_List}.
+This heterogeneous platform executes more than 7 GFLOPS per watt while consuming
+50.32 kilowatts.
+}
+Besides platform improvements, there are many software and hardware techniques
+to lower the energy consumption of these platforms, such as scheduling, DVFS,
+\dots{} 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 may increase the execution
+time of the application running over that processor. Therefore, researchers use
+different optimization strategies to select the frequency that gives the best
+trade-off between the energy reduction and performance degradation ratio. In
+\cite{Our_first_paper} and \cite{pdsec2015} , a frequencies selecting algorithm was proposed to reduce
+the energy consumption of message passing iterative applications running over
+homogeneous and heterogeneous clusters respectively.
+The results of the experiments show significant energy
+consumption reductions. In this paper, a new frequency selecting algorithm
+adapted for heterogeneous platform is presented. It selects the vector of
+frequencies, for a heterogeneous grid platform running a message passing iterative
+application, that simultaneously tries to offer the maximum energy reduction and
+minimum performance degradation ratio. The algorithm has a very small overhead,
+works online and does not need any training or profiling.
+\textcolor{blue}{
+This paper is organized as follows: Section~\ref{sec.relwork} presents some
+related works from other authors. Section~\ref{sec.exe} describes how the
+execution time of message passing programs can be predicted. It also presents
+an energy model that predicts the energy consumption of an application running
+over a heterogeneous grid. Section~\ref{sec.compet} presents the
+energy-performance objective function that maximizes the reduction of energy
+consumption while minimizing the degradation of the program's performance.
+Section~\ref{sec.optim} details the proposed frequencies selecting algorithm.
+Section~\ref{sec.expe} presents the results of applying the algorithm on the
+NAS parallel benchmarks and executing them on a grid'5000 testbed.
+It shows the results of running different scenarios using multi-cores and one core per node
+and comparing them. It also shows the results of running
+three different power scenarios and comparing them. Moreover, it shows the
+comparison results between the proposed method and an existing method. Finally,
+in Section~\ref{sec.concl} the paper ends with a summary and some future works.}
\section{Related works}
\label{sec.relwork}
+DVFS is a technique used in modern processors to scale down both the voltage and
+the frequency of the CPU while computing, in order to reduce the energy
+consumption of the processor. DVFS is also allowed in GPUs to achieve the same
+goal. Reducing the frequency of a processor lowers its number of FLOPS and may
+degrade the performance of the application running on that processor, especially
+if it is compute bound. Therefore selecting the appropriate frequency for a
+processor to satisfy some objectives, while taking into account all the
+constraints, is not a trivial operation. Many researchers used different
+strategies to tackle this problem. Some of them developed online methods that
+compute the new frequency while executing the application, such
+as~\cite{Hao_Learning.based.DVFS,Spiliopoulos_Green.governors.Adaptive.DVFS}.
+Others used offline methods that may need to run the application and profile
+it before selecting the new frequency, such
+as~\cite{Rountree_Bounding.energy.consumption.in.MPI,Cochran_Pack_and_Cap_Adaptive_DVFS}.
+The methods could be heuristics, exact or brute force methods that satisfy
+varied objectives such as energy reduction or performance. They also could be
+adapted to the execution's environment and the type of the application such as
+sequential, parallel or distributed architecture, homogeneous or heterogeneous
+platform, synchronous or asynchronous application, \dots{}
+
+In this paper, we are interested in reducing energy for message passing
+iterative synchronous applications running over heterogeneous grid platforms. Some
+works have already been done for such platforms and they can be classified into
+two types of heterogeneous platforms:
+\begin{itemize}
+\item the platform is composed of homogeneous GPUs and homogeneous CPUs.
+\item the platform is only composed of heterogeneous CPUs.
+\end{itemize}
-\section{The performance and energy consumption measurements on heterogeneous architecture}
+For the first type of platform, the computing intensive parallel tasks are
+executed on the GPUs and the rest are executed on the CPUs. 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 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 $\mathit{energy}\times \mathit{delay}^2$ (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} proposed 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 \np[\%]{10}.
+In~\cite{Joshi_Blackbox.prediction.of.impact.of.DVFS}, they developed 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 servers
+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 grid platform. Both models
+ take into account 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 grid
+ platforms. The algorithm has a very small overhead and does not need 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}
+
+
+
+\section{The performance and energy consumption measurements on heterogeneous grid architecture}
\label{sec.exe}
\subsection{The execution time of message passing distributed iterative
\end{algorithm}
-
In this section, the scaling factors selection algorithm for grids, algorithm~\ref{HSA}, is presented. It selects the vector of the frequency
scaling factors that gives the best trade-off between minimizing the
energy consumption and maximizing the performance of a message passing
selected clusters and are presented in table \ref{table:grid5000}.
-
-
\begin{figure}[!t]
\centering
\includegraphics[scale=1]{fig/grid5000}
\label{fig:grid5000}
\end{figure}
-
The energy model and the scaling factors selection algorithm were applied to the NAS parallel benchmarks v3.3 \cite{NAS.Parallel.Benchmarks} and evaluated over grid'5000.
The benchmark suite contains seven applications: CG, MG, EP, LU, BT, SP and FT. These applications have different computations and communications ratios and strategies which make them good testbed applications to evaluate the proposed algorithm and energy model.
The benchmarks have seven different classes, S, W, A, B, C, D and E, that represent the size of the problem that the method solves. In this work, the class D was used for all benchmarks in all the experiments presented in the next sections.
For the majority of the benchmarks, the energy consumed while executing the NAS benchmarks over one site scenario
for 16 and 32 nodes is lower than the energy consumed while using two sites.
The long distance communications between the two distributed sites increase the idle time, which leads to more static energy consumption.
+
The execution times of these benchmarks
over one site with 16 and 32 nodes are also lower when compared to those of the two sites
-scenario.
+scenario. Moreover, most of the benchmarks running over the one site scenario their execution times are approximately divided by two when the number of computing nodes is doubled from 16 to 32 nodes (linear speed up according to the number of the nodes).
However, the execution times and the energy consumptions of EP and MG benchmarks, which have no or small communications, are not significantly affected
in both scenarios. Even when the number of nodes is doubled. On the other hand, the communications of the rest of the benchmarks increases when using long distance communications between two sites or increasing the number of computing nodes.
nodes when the communications occur in high speed network does not decrease the computations to
communication ratio.
-
- Figure \ref{fig:time_sen} presents the execution times for all the benchmarks over the two scenarios. For most of the benchmarks running over the one site scenario, their execution times are approximately divided by two when the number of computing nodes is doubled from 16 to 32 nodes (linear speed up according to the number of the nodes).
-\textcolor{red}{The transition between the execution times to the performance degradation is not clear}
-
-
The performance degradation percentage of the EP benchmark after applying the scaling factors selection algorithm is the highest in comparison to
the other benchmarks. Indeed, in the EP benchmark, there are no communication and slack times and its
performance degradation percentage only depends on the frequencies values selected by the algorithm for the computing nodes.
The execution times for most of the NAS benchmarks are higher over the one site multi-cores per node scenario
than the execution time of those running over one site single core per node scenario. Indeed,
- the communication times are higher in the one site multi-cores scenario than in the latter scenario because all the cores of a node share the same node network link which can be saturated when running communication bound applications. On the other hand, the execution times for most of the NAS benchmarks are lower over
-the two sites multi-cores scenario than those over the two sites one core scenario. In the two sites multi-cores scenario, There are three types of communications :
-\begin{itemize}
-\item between cores on the same node via shared memory
-\item between cores from distinct nodes but belonging to the same cluster or site via local network
-\item between cores from distinct sites via long distance network
-\end{itemize}
-The latency of the communications increases from shared memory to LAN to WAN.
-Therefore, using multi-cores communicating via shared memory
-has reduced the communication times, and thus the overall execution time is also decreased.
-
-
+ the communication times are higher in the one site multi-cores scenario than in the latter scenario because all the cores of a node share the same node network link which can be saturated when running communication bound applications.
+
+ \textcolor{blue}{On the other hand, the execution times for most of the NAS benchmarks are lower over
+the two sites multi-cores scenario than those over the two sites one core scenario. ???????
+}
The experiments showed that for most of the NAS benchmarks and between the four scenarios,
the one site one core scenario gives the best execution times because the communication times are the lowest.
the one site one core scenario when compared to the ratios of the other scenarios.
More energy reduction was achieved when this ratio is increased because the proposed scaling algorithm selects smaller frequencies that decrease the dynamic power consumption.
-
- \textcolor{red}{ The next sentence is completely false! It is impossible to have these results! Whereas, the energy consumption in the two sites multi-cores scenario is higher than the energy consumption
-of the two sites one core scenario.
-Actually, using multi-cores in this scenario decreased the communication times that decreased the static energy consumption.}
+ \textcolor{blue}{ Whereas, the energy consumption in the two sites one core scenario is higher than the energy consumption of the two sites multi-core scenario. This is according to the increase in the execution time of the two sites one core scenario. }
These experiments also showed that the energy
and over the two sites one core scenario are on average equal to 22\% and 18\%
respectively. The energy saving percentages are higher in the former scenario because its computations to communications ratio is higher than the ratio of the latter scenario as mentioned previously.
-
In contrast, in the one site one
core and one site multi-cores scenarios the energy saving percentages
are approximately equivalent, on average they are up to 25\%. In both scenarios there
to 10\% and are higher than those executed over the one site multi-cores scenario,
which on average is equal to 7\%.
-\textcolor{red}{the next sentence is completely false!
-The higher performance degradation percentages over the first scenario is due to the use of multi-cores which
-decreases the computations to communications ratio. Therefore, selecting small
-frequencies by the scaling algorithm do not increase the execution time significantly. }
+\textcolor{blue}{
+The performance degradation percentages over one site multi-cores is lower because the computations to communications ratio is decreased. Therefore, selecting small
+frequencies by the scaling algorithm are proportional to this ratio, and thus the execution time do not increase significantly.}
The tradeoff distance percentages of the NAS
These smaller frequencies reduce the dynamic energy consumption more than increasing the consumed static energy which gives less overall energy consumption.
The energy saving percentages of the 30\% static power scenario is the smallest between the other scenarios, because the scaling algorithm selects bigger frequencies for the CPUs which increases the energy consumption. Figure \ref{fig:fre-pow} demonstrates that the proposed scaling algorithm selects the best frequency scaling factors according to the static power consumption ratio being used.
-\textcolor{red}{ The following paragraph is not clear at all. Please rewrite.
-Furthermore, the proposed scaling algorithm tries to limit selecting smaller frequencies, which increased the execution time. Hence, the increase in the execution time is relatively increased the static energy consumption.
+\textcolor{blue}{
The performance degradation percentages are presented in the figure \ref{fig:per-pow},
the 30\% of static power scenario had less performance degradation percentage. This because
-bigger frequencies was selected due to the big ratio in the static power consumption.
-The inverse happens in the 20\% and 30\% scenarios, the scaling algorithm is selecting
-smaller frequencies, bigger scaling factors, according to the ratio of the static power.
+bigger frequencies are selected for the CPUs by the scaling algorithm. While,
+the inverse happens in the 20\% and 30\% scenarios, because the scaling algorithm selects bigger
+frequencies.
The tradeoff distance percentage for the NAS benchmarks with these three static power scenarios
are presented in the figure \ref{fig:dist}. It shows that the tradeoff
distance percentage is the best when the 10\% of static power scenario is used, and this percentage
-is decreased for the other two scenarios propositionally to their static power ratios.
+is decreased for the other two scenarios because of different frequencies have being selected by the scaling algorithm.
In EP benchmark, the results of energy saving, performance degradation and tradeoff
-distance are showed small differences when the these static power scenarios were used.
-The absent of the communications in this benchmark made the proposed scaling algorithm to select equivalent frequencies even if the static power values are different. While, the
-inverse has been shown for the rest of the benchmarks, which have different communication times
-that increased the static energy consumption proportionally. Therefore, the scaling algorithm relatively selects
-different frequencies for each benchmark when these static power scenarios are used. }
+distance are showed small differences when the these static power scenarios are used.
+In this benchmark there are no communications which leads the proposed scaling algorithm to select similar frequencies even if the static power values are different. While, the
+inverse has been shown for the rest of the benchmarks, which have different communication times.
+This makes the scaling algorithm proportionally selects big or small frequencies for each benchmark,
+because the communication times proportionally increase or decrease the static energy consumption. }
\subsection{The comparison of the proposed frequencies selecting algorithm }
\section{Conclusion}
\label{sec.concl}
-
+\textcolor{blue}{
+This paper has been presented a new online frequencies selection algorithm.
+It works based on objective function that maximized the tradeoff distance
+between the predicted energy consumption and the predicted execution time of the distributed
+iterative applications running over heterogeneous grid. The algorithm selects the best vector of the
+frequencies which maximized the objective function has been used. A new energy model
+used by the proposed algorithm for measuring and predicting the energy consumption
+of the distributed iterative message passing application running over grid architecture.
+To evaluate the proposed method on a real heterogeneous grid platform, it was applied on the
+NAS parallel benchmarks class D instance and executed over grid'5000 testbed platform.
+The experimental results showed that the algorithm saves the energy consumptions on average
+for all NAS benchmarks up to 30\% while gives only 3\% percentage on average for the performance
+degradation for the same instance. The algorithm also selecting different frequencies according to the
+computations and communication times ratio, and according to the values of the static and measured dynamic power of the CPUs. The computations to communications ratio was varied between different scenarios have been used, concerning to the distribution of the computing nodes between different clusters' sites and using one core or multi-cores per node.
+Finally, the proposed algorithm was compared to other algorithm which it
+used the will known energy and delay product as an objective function. The comparison results showed
+that the proposed algorithm outperform the other one in term of energy-time tradeoff.
+In the near future, we would like to develop a similar method that is adapted to
+asynchronous iterative applications where each task does not
+wait for other tasks to finish their works. The development of
+such a 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}
