The algorithm has a small
overhead and works without training or profiling. It uses a new energy model
for message passing iterative applications running on a grid.
- The proposed algorithm is evaluated on a real grid, the grid'5000 platform, while
+ The proposed algorithm is evaluated on a real grid, the Grid'5000 platform, while
running the NAS parallel benchmarks. The experiments on 16 nodes, distributed on three clusters, show that it reduces on average the
energy consumption by \np[\%]{30} while the performance is on average only degraded
by \np[\%]{3.2}. Finally, the algorithm is
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
+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
homogeneous and heterogeneous clusters respectively.
The results of the experiments showed significant energy
consumption reductions. All the experimental results were conducted over the
-Simgrid simulator \cite{SimGrid}, which offers easy tools to create homogeneous and heterogeneous platforms and runs message passing parallel applications over them. In this paper, a new frequency selecting algorithm,
+SimGrid simulator \cite{SimGrid}, which offers easy tools to create homogeneous and heterogeneous platforms and runs message passing parallel applications over them. In this paper, a new frequency selecting algorithm,
adapted to grid platforms composed of heterogeneous clusters, is presented. It is applied to the NAS parallel benchmarks and evaluated over a real testbed,
-the grid'5000 platform \cite{grid5000}. It selects for a grid platform running a message passing iterative
+the Grid'5000 platform \cite{grid5000}. It selects for a grid platform running a message passing iterative
application the vector of
frequencies that simultaneously tries to offer the maximum energy reduction and
minimum performance degradation ratios. The algorithm has a very small overhead,
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 the grid'5000 testbed.
+NAS parallel benchmarks and executing them on the Grid'5000 testbed.
It also evaluates the algorithm over multi-cores per node architectures and over three different power scenarios. 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.
The main objective of DVFS operation is to reduce the overall energy
consumption~\cite{Le_DVFS.Laws.of.Diminishing.Returns}. The operational
frequency $F$ depends linearly on the supply voltage $V$, i.e., $V = \beta \cdot
-F$ with some constant $\beta$.~This equation is used to study the change of the
+F$ with some constant $\beta$. This equation is used to study the change of the
dynamic voltage with respect to various frequency values
in~\cite{Rauber_Analytical.Modeling.for.Energy}. The reduction process of the
frequency can be expressed by the scaling factor $S$ which is the ratio between
In our previous
works, \cite{Our_first_paper} and \cite{pdsec2015}, two methods that select the optimal
frequency scaling factors for a homogeneous and a heterogeneous cluster respectively, were proposed.
-Both methods selects the frequencies that gives the best tradeoff between
+Both methods selects the frequencies that gives the best trade-off between
energy consumption reduction and performance for message passing
iterative synchronous applications. In this work we
are interested in grids that are composed of heterogeneous clusters were the nodes have different characteristics such as dynamic power, static power, computation power, frequencies range, network latency and bandwidth.
While the main goal is to optimize the energy and execution time at the same
time, the normalized energy and execution time curves do not evolve (increase/decrease) in the same way.
-According to the equations~(\ref{eq:pnorm}) and (\ref{eq:enorm}), the
+According to Equations~\ref{eq:pnorm} and \ref{eq:enorm}, the
vector of frequency scaling factors $S_1,S_2,\dots,S_N$ reduce both the energy
and the execution time simultaneously. But the main objective is to produce
maximum energy reduction with minimum execution time reduction.
\item[{$\Ps[ij]$}] array of the static powers for all nodes.
\item[{$\Fdiff[ij]$}] array of the differences between two successive frequencies for all nodes.
\end{description}
- \Ensure $\Sopt[11],\Sopt[12] \dots, \Sopt[NM_i]$, a vector of scaling factors that gives the optimal tradeoff between energy consumption and execution time
+ \Ensure $\Sopt[11],\Sopt[12] \dots, \Sopt[NM_i]$, a vector of scaling factors that gives the optimal trade-off between energy consumption and execution time
\State $\Scp[ij] \gets \frac{\max_{i=1,2,\dots,N}(\max_{j=1,2,\dots,M_i}(\Tcp[ij]))}{\Tcp[ij]} $
\State $F_{ij} \gets \frac{\Fmax[ij]}{\Scp[i]},~{i=1,2,\cdots,N},~{j=1,2,\dots,M_i}.$
\If{(not the first frequency)}
\State $F_{ij} \gets F_{ij}+\Fdiff[ij],~i=1,\dots,N,~{j=1,\dots,M_i}.$
\EndIf
- \State $\Told \gets $ computed as in equations (\ref{eq:told}).
- \State $\Eoriginal \gets $ computed as in equations (\ref{eq:eorginal}) .
+ \State $\Told \gets $ computed as in Equation \ref{eq:told}.
+ \State $\Eoriginal \gets $ computed as in Equation \ref{eq:eorginal}.
\State $\Sopt[ij] \gets 1,~i=1,\dots,N,~{j=1,\dots,M_i}. $
\State $\Dist \gets 0 $
\While {(all nodes have not reached their minimum \newline\hspace*{2.5em} frequency \textbf{or} $\Pnorm - \Enorm < 0 $)}
\State $F_{ij} \gets F_{ij} - \Fdiff[ij],~{i=1,\dots,N},~{j=1,\dots,M_i}$.
\State $S_{ij} \gets \frac{\Fmax[ij]}{F_{ij}},~{i=1,\dots,N},~{j=1,\dots,M_i}.$
\EndIf
- \State $\Tnew \gets $ computed as in equations (\ref{eq:perf}).
- \State $\Ereduced \gets $ computed as in equations (\ref{eq:energy}).
+ \State $\Tnew \gets $ computed as in Equation \ref{eq:perf}.
+ \State $\Ereduced \gets $ computed as in Equation \ref{eq:energy}.
\State $\Pnorm \gets \frac{\Told}{\Tnew}$, $\Enorm\gets \frac{\Ereduced}{\Eoriginal}$
\If{$(\Pnorm - \Enorm > \Dist)$}
\State $\Sopt[ij] \gets S_{ij},~i=1,\dots,N,~j=1,\dots,M_i. $
of the slowest node and the computation time of the node $i$ as follows:
\begin{equation}
\label{eq:Scp}
- \Scp[ij] = \frac{ \mathop{\max_{i=1,\dots N}}_{j=1,\dots,M}(\Tcp[ij])} {\Tcp[ij]}
+ \Scp[ij] = \frac{ \mathop{\max\limits_{i=1,\dots N}}\limits_{j=1,\dots,M}(\Tcp[ij])} {\Tcp[ij]}
\end{equation}
Using the initial frequency scaling factors computed in (\ref{eq:Scp}), the
algorithm computes the initial frequencies for all nodes as a ratio between the
bound until all nodes reach their minimum frequencies or their lower bounds, to compute the overall
energy consumption and performance and selects the optimal vector of the frequency scaling
factors. At each iteration the algorithm determines the slowest node
-according to the equation (\ref{eq:perf}) and keeps its frequency unchanged,
+according to Equation~\ref{eq:perf} and keeps its frequency unchanged,
while it lowers the frequency of all other nodes by one gear. The new overall
energy consumption and execution time are computed according to the new scaling
factors. The optimal set of frequency scaling factors is the set that gives the
-highest distance according to the objective function (\ref{eq:max}).
+highest distance according to the objective function~\ref{eq:max}.
Figures~\ref{fig:r1} and \ref{fig:r2} illustrate the normalized performance and
consumed energy for an application running on a homogeneous cluster and a
\section{Experimental results}
\label{sec.expe}
While in~\cite{pdsec2015} the energy model and the scaling factors selection algorithm were applied to a heterogeneous cluster and evaluated over the SimGrid simulator~\cite{SimGrid},
-in this paper real experiments were conducted over the grid'5000 platform.
+in this paper real experiments were conducted over the Grid'5000 platform.
\subsection{Grid'5000 architecture and power consumption}
\label{sec.grid5000}
which is the French National Telecommunication Network for Technology.
Each site of the grid is composed of a few heterogeneous
computing clusters and each cluster contains many homogeneous nodes. In total,
-grid'5000 has about one thousand heterogeneous nodes and eight thousand cores. In each site,
+Grid'5000 has about one thousand heterogeneous nodes and eight thousand cores. In each site,
the clusters and their nodes are connected via high speed local area networks.
Two types of local networks are used, Ethernet or Infiniband networks which have different characteristics in terms of bandwidth and latency.
-Since grid'5000 is dedicated to testing, contrary to production grids it allows a user to deploy its own customized operating system on all the booked nodes. The user could have root rights and thus apply DVFS operations while executing a distributed application. Moreover, the grid'5000 testbed provides at some sites a power measurement tool to capture
+Since Grid'5000 is dedicated to testing, contrary to production grids it allows a user to deploy its own customized operating system on all the booked nodes. The user could have root rights and thus apply DVFS operations while executing a distributed application. Moreover, the Grid'5000 testbed provides at some sites a power measurement tool to capture
the power consumption for each node in those sites. The measured power is the overall consumed power by all the components of a node at a given instant, such as CPU, hard drive, main-board, memory, ... For more details refer to
\cite{Energy_measurement}. In order to correctly measure the CPU power of one core in a node $j$,
firstly, the power consumed by the node while being idle at instant $y$, noted as $\Pidle[jy]$, was measured. Then, the power was measured while running a single thread benchmark with no communication (no idle time) over the same node with its CPU scaled to the maximum available frequency. The latter power measured at time $x$ with maximum frequency for one core of node $j$ is noted $\Pmax[jx]$. The difference between the two measured power consumptions represents the
-dynamic power consumption of that core with the maximum frequency, see figure(\ref{fig:power_cons}).
+dynamic power consumption of that core with the maximum frequency, see Figure~\ref{fig:power_cons}.
-The dynamic power $\Pd[j]$ is computed as in equation (\ref{eq:pdyn})
+The dynamic power $\Pd[j]$ is computed as in Equation~\ref{eq:pdyn}
\begin{equation}
\label{eq:pdyn}
\Pd[j] = \max_{x=\beta_1,\dots \beta_2} (\Pmax[jx]) - \min_{y=\Theta_1,\dots \Theta_2} (\Pidle[jy])
On the other hand, the static power consumption by one core is a part of the measured idle power consumption of the node. Since in Grid'5000 there is no way to measure precisely the consumed static power and in~\cite{Our_first_paper,pdsec2015,Rauber_Analytical.Modeling.for.Energy} it was assumed that the static power represents a ratio of the dynamic power, the value of the static power is assumed as 20\% of dynamic power consumption of the core.
-In the experiments presented in the following sections, two sites of grid'5000 were used, Lyon and Nancy sites. These two sites have in total seven different clusters as in figure (\ref{fig:grid5000}).
+In the experiments presented in the following sections, two sites of Grid'5000 were used, Lyon and Nancy sites. These two sites have in total seven different clusters as in Figure~\ref{fig:grid5000}.
Four clusters from the two sites were selected in the experiments: one cluster from
Lyon's site, Taurus, and three clusters from Nancy's site, Graphene,
Griffon and Graphite. Each one of these clusters has homogeneous nodes inside, while nodes from different clusters are heterogeneous in many aspects such as: computing power, power consumption, available
-frequency ranges and local network features: the bandwidth and the latency. Table \ref{table:grid5000} shows
-the detailed characteristics of these four clusters. Moreover, the dynamic powers were computed using equation (\ref{eq:pdyn}) for all the nodes in the
-selected clusters and are presented in table \ref{table:grid5000}.
+frequency ranges and local network features: the bandwidth and the latency. Table~\ref{table:grid5000} shows
+the detailed characteristics of these four clusters. Moreover, the dynamic powers were computed using Equation~\ref{eq:pdyn} for all the nodes in the
+selected clusters and are presented in Table~\ref{table:grid5000}.
\begin{figure}[!t]
\centering
\includegraphics[scale=1]{fig/grid5000}
- \caption{The selected two sites of grid'5000}
+ \caption{The selected two sites of Grid'5000}
\label{fig:grid5000}
\end{figure}
\begin{figure}[!t]
The NAS parallel benchmarks are executed over
16 and 32 nodes for each scenario. The number of participating computing nodes from each cluster
is different because all the selected clusters do not have the same available number of nodes and all benchmarks do not require the same number of computing nodes.
-Table \ref{tab:sc} shows the number of nodes used from each cluster for each scenario.
+Table~\ref{tab:sc} shows the number of nodes used from each cluster for each scenario.
\begin{table}[h]
The NAS parallel benchmarks are executed over these two platforms
- with different number of nodes, as in Table \ref{tab:sc}.
+ with different number of nodes, as in Table~\ref{tab:sc}.
The overall energy consumption of all the benchmarks solving the class D instance and
using the proposed frequency selection algorithm is measured
-using the equation of the reduced energy consumption, equation
-(\ref{eq:energy}). This model uses the measured dynamic power showed in Table \ref{table:grid5000} and the static
+using the equation of the reduced energy consumption, Equation~\ref{eq:energy}. This model uses the measured dynamic power showed in Table~\ref{table:grid5000}
+and the static
power is assumed to be equal to 20\% of the dynamic power. The execution
time is measured for all the benchmarks over these different scenarios.
The energy consumptions and the execution times for all the benchmarks are
-presented in plots \ref{fig:eng_sen} and \ref{fig:time_sen} respectively.
+presented in Plots~\ref{fig:eng_sen} and \ref{fig:time_sen} respectively.
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 energy saving percentage is computed as the ratio between the reduced
-energy consumption, equation (\ref{eq:energy}), and the original energy consumption,
-equation (\ref{eq:eorginal}), for all benchmarks as in figure \ref{fig:eng_s}.
+energy consumption, Equation~\ref{eq:energy}, and the original energy consumption,
+Equation~\ref{eq:eorginal}, for all benchmarks as in Figure~\ref{fig:eng_s}.
This figure shows that the energy saving percentages of one site scenario for
16 and 32 nodes are bigger than those of the two sites scenario which is due
to the higher computations to communications ratio in the first scenario
\includegraphics[width=.48\textwidth]{fig/eng_s.eps}\label{fig:eng_s}} \hspace{0.4cm}%
\subfloat[The performance degradation of the NAS benchmarks over different scenarios]{%
\includegraphics[width=.48\textwidth]{fig/per_d.eps}\label{fig:per_d}}\hspace{0.4cm}%
- \subfloat[The tradeoff distance between the energy reduction and the performance of the NAS benchmarks
+ \subfloat[The trade-off distance between the energy reduction and the performance of the NAS benchmarks
over different scenarios]{%
\includegraphics[width=.48\textwidth]{fig/dist.eps}\label{fig:dist}}
\label{fig:exp-res}
The rest of the benchmarks showed different performance degradation percentages, which decrease
when the communication times increase and vice versa.
-Figure \ref{fig:dist} presents the distance percentage between the energy saving and the performance degradation for each benchmark over both scenarios. The tradeoff distance percentage can be
-computed as in equation \ref{eq:max}. The one site scenario with 16 nodes gives the best energy and performance
-tradeoff, on average it is equal to 26.8\%. The one site scenario using both 16 and 32 nodes had better energy and performance
-tradeoff comparing to the two sites scenario because the former has high speed local communications
+Figure \ref{fig:dist} presents the distance percentage between the energy saving and the performance degradation for each benchmark over both scenarios. The trade-off distance percentage can be
+computed as in Equation~\ref{eq:max}. The one site scenario with 16 nodes gives the best energy and performance
+trade-off, on average it is equal to 26.8\%. The one site scenario using both 16 and 32 nodes had better energy and performance
+trade-off comparing to the two sites scenario because the former has high speed local communications
which increase the computations to communications ratio and the latter uses long distance communications which decrease this ratio.
- Finally, the best energy and performance tradeoff depends on all of the following:
+ Finally, the best energy and performance trade-off depends on all of the following:
1) the computations to communications ratio when there are communications and slack times, 2) the heterogeneity of the computing powers of the nodes and 3) the heterogeneity of the consumed static and dynamic powers of the nodes.
\subsection{The experimental results over multi-cores clusters}
\label{sec.res-mc}
-The clusters of grid'5000 have different number of cores embedded in their nodes
-as shown in Table \ref{table:grid5000}. In
-this section, the proposed scaling algorithm is evaluated over the grid'5000 platform while using multi-cores nodes selected according to the one site scenario described in the section \ref{sec.res}.
+The clusters of Grid'5000 have different number of cores embedded in their nodes
+as shown in Table~\ref{table:grid5000}. In
+this section, the proposed scaling algorithm is evaluated over the Grid'5000 platform while using multi-cores nodes selected according to the one site scenario described in Section~\ref{sec.res}.
The one site scenario uses 32 cores from multi-cores nodes instead of 32 distinct nodes. For example if
the participating number of cores from a certain cluster is equal to 14,
in the multi-core scenario the selected nodes is equal to 4 nodes while using
3 or 4 cores from each node. The platforms with one
-core per node and multi-cores nodes are shown in Table \ref{table:sen-mc}.
+core per node and multi-cores nodes are shown in Table~\ref{table:sen-mc}.
The energy consumptions and execution times of running class D of the NAS parallel
benchmarks over these two different scenarios are presented
-in figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.
+in Figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.
+
\begin{table}[]
\centering
\subfloat[The performance degradation of running NAS benchmarks over one core and multicores scenarios
]{%
\includegraphics[width=.48\textwidth]{fig/per_d_mc.eps}\label{fig:per-d-mc}}\hspace{0.4cm}%
- \subfloat[The tradeoff distance of running NAS benchmarks over one core and multicores scenarios]{%
+ \subfloat[The trade-off distance of running NAS benchmarks over one core and multicores scenarios]{%
\includegraphics[width=.48\textwidth]{fig/dist_mc.eps}\label{fig:dist-mc}}
- \label{fig:exp-res}
+ \label{fig:exp-res2}
\caption{The experimental results of one core and multi-cores scenarios}
\end{figure*}
-The energy saving percentages of all NAS benchmarks running over these two scenarios are presented in figure \ref{fig:eng-s-mc}.
+The energy saving percentages of all NAS benchmarks running over these two scenarios are presented in Figure~\ref{fig:eng-s-mc}.
The figure shows that the energy saving percentages in the one
core and the multi-cores scenarios
are approximately equivalent, on average they are equal to 25.9\% and 25.1\% respectively.
The performance degradation percentages of the NAS benchmarks are presented in
-figure \ref{fig:per-d-mc}. It shows that the performance degradation percentages is higher for the NAS benchmarks over the one core per node scenario (on average equal to 10.6\%) than over the multi-cores scenario (on average equal to 7.5\%). The performance degradation percentages over the multi-cores scenario is lower because the computations to communications ratio is smaller than the ratio of the other scenario.
+Figure\ref{fig:per-d-mc}. It shows that the performance degradation percentages are higher for the NAS benchmarks over the one core per node scenario (on average equal to 10.6\%) than over the multi-cores scenario (on average equal to 7.5\%). The performance degradation percentages over the multi-cores scenario are lower because the computations to communications ratios are smaller than the ratios of the other scenario.
-The tradeoff distance percentages of the NAS benchmarks over the two scenarios are presented
-in figure \ref{fig:dist-mc}. These tradeoff distance between energy consumption reduction and performance are used to verify which scenario is the best in both terms at the same time. The figure shows that the tradeoff distance percentages are on average bigger over the multi-cores scenario (17.6\%) than over the one core per node scenario (15.3\%).
+The trade-off distances percentages of the NAS benchmarks over the two scenarios are presented
+in ~Figure~\ref{fig:dist-mc}. These trade-off distances between energy consumption reduction and performance are used to verify which scenario is the best in both terms at the same time. The figure shows that the trade-off distance percentages are on average bigger over the multi-cores scenario (17.6\%) than over the one core per node scenario (15.3\%).
\subsection{Experiments with different static power scenarios}
\label{sec.pow_sen}
-In section \ref{sec.grid5000}, since it was not possible to measure the static power consumed by a CPU, the static power was assumed to be equal to 20\% of the measured dynamic power. This power is consumed during the whole execution time, during computation and communication times. Therefore, when the DVFS operations are applied by the scaling algorithm and the CPUs' frequencies lowered, the execution time might increase and consequently the consumed static energy will be increased too.
+In Section~\ref{sec.grid5000}, since it was not possible to measure the static power consumed by a CPU, the static power was assumed to be equal to 20\% of the measured dynamic power. This power is consumed during the whole execution time, during computation and communication times. Therefore, when the DVFS operations are applied by the scaling algorithm and the CPUs' frequencies lowered, the execution time might increase and consequently the consumed static energy will be increased too.
The aim of this section is to evaluate the scaling algorithm while assuming different values of static powers.
In addition to the previously used percentage of static power, two new static power ratios, 10\% and 30\% of the measured dynamic power of the core, are used in this section.
\includegraphics[width=.48\textwidth]{fig/eng_pow.eps}\label{fig:eng-pow}} \hspace{0.4cm}%
\subfloat[The performance degradation percentages for the NAS benchmarks over the three power scenarios]{%
\includegraphics[width=.48\textwidth]{fig/per_pow.eps}\label{fig:per-pow}}\hspace{0.4cm}%
- \subfloat[The tradeoff distance between the energy reduction and the performance of the NAS benchmarks over the three power scenarios]{%
+ \subfloat[The trade-off distance between the energy reduction and the performance of the NAS benchmarks over the three power scenarios]{%
\includegraphics[width=.48\textwidth]{fig/dist_pow.eps}\label{fig:dist-pow}}
\label{fig:exp-pow}
\end{figure}
The energy saving percentages of the NAS benchmarks with the three static power scenarios are presented
-in figure \ref{fig:eng_sen}. This figure shows that the 10\% of static power scenario
+in Figure\ref{fig:eng_sen}. This figure shows that the 10\% of static power scenario
gives the biggest energy saving percentages in comparison to the 20\% and 30\% static power
scenarios. The small value of the static power consumption makes the proposed
scaling algorithm select smaller frequencies for the CPUs.
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.
-The performance degradation percentages are presented in figure \ref{fig:per-pow}.
+The performance degradation percentages are presented in Figure\ref{fig:per-pow}.
The 30\% static power scenario had less performance degradation percentage because the scaling algorithm
had selected big frequencies for the CPUs. While,
-the inverse happens in the 10\% and 20\% scenarios because the scaling algorithm had selected CPUs' frequencies smaller than those of the 30\% scenario. The tradeoff distance percentage for the NAS benchmarks with these three static power scenarios
-are presented in figure \ref{fig:dist}.
-It shows that the best tradeoff
+the inverse happens in the 10\% and 20\% scenarios because the scaling algorithm had selected CPUs' frequencies smaller than those of the 30\% scenario. The trade-off distance percentage for the NAS benchmarks with these three static power scenarios
+are presented in Figure~\ref{fig:dist}.
+It shows that the best trade-off
distance percentage is obtained with the 10\% static power scenario and this percentage
is decreased for the other two scenarios because the scaling algorithm had selected different frequencies according to the static power values.
-In the EP benchmark, the energy saving, performance degradation and tradeoff
+In the EP benchmark, the energy saving, performance degradation and trade-off
distance percentages for these static power scenarios are not significantly different because there is no communication in this benchmark. Therefore, the static power is only consumed during computation and the proposed scaling algorithm selects similar frequencies for the three scenarios. On the other hand, for the rest of the benchmarks, the scaling algorithm selects the values of the frequencies according to the communication times of each benchmark because the static energy consumption increases proportionally to the communication times.
\subsection{Comparison of the proposed frequencies selecting algorithm }
\label{sec.compare_EDP}
-Finding the frequencies that give the best tradeoff between the energy consumption and the performance for a parallel
+Finding the frequencies that give the best trade-off between the energy consumption and the performance for a parallel
application is not a trivial task. Many algorithms have been proposed to tackle this problem.
In this section, the proposed frequencies selecting algorithm is compared to a method that uses the well known energy and delay product objective function, $EDP=energy \times delay$, that has been used by many researchers \cite{EDP_for_multi_processors,Energy_aware_application_scheduling,Exploring_Energy_Performance_TradeOffs}.
This objective function was also used by Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS} where they select the frequencies that minimize the EDP product and apply them with DVFS operations to the multi-cores
architecture. Their online algorithm predicts the energy consumption and execution time of a processor before using the EDP method.
-To fairly compare the proposed frequencies scaling algorithm to Spiliopoulos et al. algorithm, called Maxdist and EDP respectively, both algorithms use the same energy model, equation \ref{eq:energy} and
-execution time model, equation \ref{eq:perf}, to predict the energy consumption and the execution time for each computing node.
-Moreover, both algorithms start the search space from the upper bound computed as in equation \ref{eq:Fint}.
+To fairly compare the proposed frequencies scaling algorithm to Spiliopoulos et al. algorithm, called Maxdist and EDP respectively, both algorithms use the same energy model, Equation~\ref{eq:energy} and
+execution time model, Equation~\ref{eq:perf}, to predict the energy consumption and the execution time for each computing node.
+Moreover, both algorithms start the search space from the upper bound computed as in Equation~\ref{eq:Fint}.
Finally, the resulting EDP algorithm is an exhaustive search algorithm that tests all the possible frequencies, starting from the initial frequencies (upper bound),
and selects the vector of frequencies that minimize the EDP product.
Both algorithms were applied to class D of the NAS benchmarks over 16 nodes.
-The participating computing nodes are distributed according to the two scenarios described in section \ref{sec.res}.
-The experimental results, the energy saving, performance degradation and tradeoff distance percentages, are
-presented in the figures \ref{fig:edp-eng}, \ref{fig:edp-perf} and \ref{fig:edp-dist} respectively.
+The participating computing nodes are distributed according to the two scenarios described in Section~\ref{sec.res}.
+The experimental results, the energy saving, performance degradation and trade-off distance percentages, are
+presented in Figures~\ref{fig:edp-eng}, \ref{fig:edp-perf} and \ref{fig:edp-dist} respectively.
\begin{figure*}[t]
\includegraphics[width=.48\textwidth]{fig/edp_eng}\label{fig:edp-eng}} \hspace{0.4cm}%
\subfloat[The performance degradation induced by the Maxdist method and the EDP method]{%
\includegraphics[width=.48\textwidth]{fig/edp_per}\label{fig:edp-perf}}\hspace{0.4cm}%
- \subfloat[The tradeoff distance between the energy consumption reduction and the performance for the Maxdist method and the EDP method]{%
+ \subfloat[The trade-off distance between the energy consumption reduction and the performance for the Maxdist method and the EDP method]{%
\includegraphics[width=.48\textwidth]{fig/edp_dist}\label{fig:edp-dist}}
\label{fig:edp-comparison}
\caption{The comparison results}
The proposed algorithm gives better results than EDP because it
maximizes the energy saving and the performance at the same time.
Moreover, the proposed scaling algorithm gives the same weight for these two metrics.
-Whereas, the EDP algorithm gives sometimes negative tradeoff values for some benchmarks in the two sites scenarios.
-These negative tradeoff values mean that the performance degradation percentage is higher than the energy saving percentage.
-The high positive values of the tradeoff distance percentage mean that the energy saving percentage is much higher than the performance degradation percentage.
+Whereas, the EDP algorithm gives sometimes negative trade-off values for some benchmarks in the two sites scenarios.
+These negative trade-off values mean that the performance degradation percentage is higher than the energy saving percentage.
+The high positive values of the trade-off distance percentage mean that the energy saving percentage is much higher than the performance degradation percentage.
The time complexity of both Maxdist and EDP algorithms are $O(N \cdot M \cdot F)$ and
$O(N \cdot M \cdot F^2)$ respectively, where $N$ is the number of the clusters, $M$ is the number of nodes and $F$ is the
maximum number of available frequencies. When Maxdist is applied to a benchmark that is being executed over 32 nodes distributed between Nancy and Lyon sites, it takes on average $0.01 ms$ to compute the best frequencies while EDP is on average ten times slower over the same architecture.
\label{sec.concl}
This paper presents a new online frequencies selection algorithm.
The algorithm selects the best vector of
-frequencies that maximizes the tradeoff distance
+frequencies that maximizes the trade-off distance
between the predicted energy consumption and the predicted execution time of the distributed
iterative applications running over a heterogeneous grid. A new energy model
is used by the proposed algorithm to predict the energy consumption
computations and communication times ratios, and the values of the static and measured dynamic powers of the CPUs.
Finally, the proposed algorithm was compared to another method that uses
the well known energy and delay product as an objective function. The comparison results showed
-that the proposed algorithm outperforms the latter by selecting a vector of frequencies that gives a better tradeoff between energy consumption reduction and performance.
+that the proposed algorithm outperforms the latter by selecting a vector of frequencies that gives a better trade-off between energy consumption reduction and performance.
In the near future, we would like to develop a similar method that is adapted to
asynchronous iterative applications where iterations are not synchronized and communications are overlapped with computations.
\end{document}
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