\newcommand{\Sopt}[1][]{\Xsub{S}{opt}_{#1}}
\newcommand{\Tcm}[1][]{\Xsub{T}{cm}_{\fxheight{#1}}}
\newcommand{\Tcp}[1][]{\Xsub{T}{cp}_{#1}}
-\newcommand{\Pmax}[1][]{\Xsub{P}{max}_{#1}}
+\newcommand{\Pmax}[1][]{\Xsub{P}{max}_{\fxheight{#1}}}
\newcommand{\Pidle}[1][]{\Xsub{P}{idle}_{\fxheight{#1}}}
\newcommand{\TcpOld}[1][]{\Xsub{T}{cpOld}_{#1}}
\newcommand{\Tnew}{\Xsub{T}{New}}
of iterative methods, which is presented in the following sections.
-\subsection{Energy model for heterogeneous platform}
+\subsection{Energy model for heterogeneous grid platform}
Many researchers~\cite{Malkowski_energy.efficient.high.performance.computing,
Rauber_Analytical.Modeling.for.Energy,Zhuo_Energy.efficient.Dynamic.Task.Scheduling,
\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.org},
+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.
\subsection{Grid'5000 architature and power consumption}
Since grid'5000 is dedicated for 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 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}. To just 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 consumption represents the
+ 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 consumption represents the
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})
\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])
+ \Pd[j] = \max_{x=\beta_1,\dots \beta_2} (\Pmax[jx]) - \min_{y=\Theta_1,\dots \Theta_2} (\Pidle[jy])
\end{equation}
where $\Pd[j]$ is the dynamic power consumption for one core of node $j$,
Therefore, the dynamic power of one core is computed as the difference between the maximum
measured value in maximum powers vector and the minimum measured value in the idle powers vector.
-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 np[\%]{20} of dynamic power consumption of the core.
+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}).
\centering
\begin{tabular}{|*{4}{c|}}
\hline
-\multirow{2}{*}{Scenario name} & \multicolumn{2}{c|} {The participating clusters} \\ \cline{2-4}
+\multirow{2}{*}{Scenario name} & \multicolumn{3}{c|} {The participating clusters} \\ \cline{2-4}
& Cluster & Site & No. of nodes \\
\hline
\multirow{3}{*}{Two sites / 16 nodes} & Taurus & Lyon & 5 \\ \cline{2-4}
Figure \ref{fig:per_d} presents the performance degradation percentages for all benchmarks.
-The performance degradation percentage for the benchmarks running on one site with
+The performance degradation percentage for the benchmarks running on two sites with
+16 or 32 nodes is on average equal to 8\% or 4\% respectively.
+
+ \textcolor{red}{
+The proposed scaling algorithm selecting smaller frequencies in two sites scenario,
+due to decreasing in the computations to communications ratio when the number of nodes is increased and
+leads to less performance degradation percentage.
+In contrast, the performance degradation percentage for the benchmarks running on one site with
16 or 32 nodes is on average equal to 3\% or 10\% respectively.
-
- \textcolor{red}{please correct the following paragraph because I do not understand it at all! Stop using we, this because, effected, while, ...}
-
-
-
- This because selecting smaller frequencies in the one site scenarios,
-when the computations grater than the communications , increase the number of the critical nodes
-when the number of nodes increased. The inverse happens in the tow sites scenario,
-this due to the lower computations to communications ratio that decreased with highest
-communications. Therefore, the number of the critical nodes are decreased. The average performance
-degradation for the two sites scenario with 16 nodes is equal to 8\% and for 32 nodes is equal to 4\%.
+The inverse is happens in this scenario when the number of computing nodes is increased
+the performance degradation percentage is decreased. So, using double number of computing
+nodes when the communications occur in high speed network not decreased the computations to
+communication ratio. Moreover, as shown in the figure \ref{fig:time_sen}, the execution time of one site scenario with 32 nodes
+are less by approximately double, linear speed-up, for most of the benchmarks comparing to the one site with 16 nodes scenario.
+This leads to increased the number of the critical nodes which any one of them may increased the overall the execution time of the benchmarks.
The EP benchmarks is gives the bigger performance degradation ratio, because there is no
-communications and no slack times in this benchmarks that is always their performance effected
-by selecting big or small frequencies.
-The tradeoff between these scenarios can be computed as in the trade-off function \ref{eq:max}.
+communications and no slack times in this benchmarks which their performance controlled by
+the computing powers of the nodes.
+The tradeoff between these scenarios can be computed as in the tradeoff function \ref{eq:max}.
Figure \ref{fig:dist}, presents the tradeoff distance for all benchmarks over all
platform scenarios. The one site scenario with 16 and 32 nodes had the best tradeoff distance
-compared to the two sites scenarios, because the increase in the communications as mentioned before.
+compared to the two sites scenarios, due to the increase or decreased in the communications as mentioned before.
The one site scenario with 16 nodes is the best scenario in term of energy and performance tradeoff,
-which on average is up 26\%. Then, the tradeoff distance is related linearly to the energy saving
-percentage. Finally, the best energy and performance tradeoff depends on the increase in all of:
-1) the computations to communications ratio, 2) the differences in computing powers
-between the computing nodes and 3) the differences in static and the dynamic powers of the nodes.
+which on average is up 26\%. Therefore, the tradeoff distance is related linearly to the energy saving
+percentage. Finally, the best energy and performance tradeoff depends on the all of the following:
+1) the computations to communications ratio when there is a communications and slack times, 2) the differences in computing powers
+between the computing nodes and 3) the differences in static and the dynamic powers of the nodes.}
+
+
\subsection{The experimental results of multicores clusters}
\label{sec.res-mc}
in the figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.
The execution times of NAS benchmarks over the one site multicores scenario
is higher than the execution time of those running over one site multicores scenario.
-This because in the one site multicores scenario the communication is increased significantly,
+The reason in the one site multicores scenario the communication is increased significantly,
and all node's cores share the same node network link which increased
-the communication times. While, the execution times of the NAS benchmarks over
+the communication times. Whereas, the execution times of the NAS benchmarks over
the two site multicores scenario is less than those executed over the two
-sites one core scenario. This because using multicores decrease the communications,
-while the cores shared same nodes' link but the communications between the cores
-are less than the communication times between the nodes over the long distance
+sites one core scenario. This goes back when using multicores is decreasing the communications.
+As explained previously, the cores shared same nodes' linkbut the communications between the cores
+are still less than the communication times between the nodes over the long distance
networks, and thus the over all execution time decreased. Generally, executing
-the NAS benchmarks over the one site one core gives smaller execution times
-comparing to other scenarios. This because each node in this scenario has it's
+the NAS benchmarks over the one site one core scenario gives smaller execution times
+comparing to other scenarios. This due to each node in this scenario has it's
dedicated network link that used independently by one core, while in the other
-scenarios the communication times are higher when using long distance communication
+scenarios the communication times are higher when using long distance communications
link or using the shared link communications between cores of each node.
On the other hand, the energy consumptions of the NAS benchmarks over the
one site one cores is less than the one site multicores scenario because
this scenario had less execution time as mentioned before. Also, in the
one site one core scenario the computations to communications ratio is
higher, then the new scaled frequencies are decreased the dynamic energy
-consumption, because the dynamic power consumption are decreased exponentially
+consumption which is decreased exponentially
with the new frequency scaling factors. These experiments also showed, the energy
consumption and the execution times of EP and MG benchmarks over these four
scenarios are not change a lot, because there are no or small communications
- which are increase or decrease the static power consumptions.
+which are increase or decrease the static power consumptions.
The other benchmarks were showed that their energy consumptions and execution times
are changed according to the decreasing or increasing in the communication
times that are different from scenario to other or due to the amount of
The energy saving percentages of all NAS benchmarks, as in figure
\ref{fig:eng-s-mc}, running over these four scenarios are presented. The figure
showed the energy saving percentages of NAS benchmarks over two sites multicores scenario is higher
-than two sites once core scenario, this because the the computation
-times in the two sites multicores scenario is higher than the computation times
-of the two sites one core scenario, then the more reduction in the
+than two sites once core scenario, because the computation
+times in this scenario is higher than the other one, then the more reduction in the
dynamic energy can be obtained as mentioned previously. In contrast, in the one site one
core and one site multicores scenarios the energy saving percentages
-are approximately equivalent, on average they are up to 25\%. This
-because in the both scenarios there are a small difference in the
+are approximately equivalent, on average they are up to 25\%. In these both scenarios there are a small difference in the
computations to communications ratio, leading the proposed scaling algorithm
to selects the frequencies proportionally to these ratios and keeping
as much as possible the energy saving percentages the same. The
performance degradation percentages of NAS benchmarks are presented in
figure \ref{fig:per-d-mc}. This figure indicates that performance
degradation percentages of running NAS benchmarks over two sites
-multocores, on average is equal to 7\%, gives more performance degradation percentage
+multocores scenario, on average is equal to 7\%, gives more performance degradation percentage
than two sites one core scenario, which on average is equal to 4\%.
-This because when using the two sites multicores scenario increased
-the computations to communications ratio, which may be increased the effect
-on the overall execution time when the proposed scaling algorithm is applied and scaling down the frequencies.
+Moreover, using the two sites multicores scenario increased
+the computations to communications ratio, which may be increased
+the overall execution time when the proposed scaling algorithm is applied and scaling down the frequencies.
The inverse was happened when the benchmarks are executed over one
site one core scenario their performance degradation percentages, on average
is equal to 10\%, are higher than those executed over one sit one core,
-which on average is equal to 7\%. This because in one site
+which on average is equal to 7\%. So, in one site
multicores scenario the computations to communications ratio is decreased
-as mentioned before, thus selecting new frequencies are less effect
-on the overall execution time. The tradeoff distances of all NAS
+as mentioned before, thus selecting new frequencies are not increased
+the overall execution time. The tradeoff distances of all NAS
benchmarks over all scenarios are presented in the figure \ref{fig:dist-mc}.
These tradeoff distances are used to verified which scenario is the best in term of
energy and performance ratio. The one sites multicores scenario is the best scenario in term of
energy and performance tradeoff, on average is equal to 17.6\%, when comparing to the one site one core
-scenario, one average is equal to 15.3\%. This because the one site multicores scenario
+scenario, one average is equal to 15.3\%. The one site multicores scenario
has the same energy saving percentages of the one site one core scenario but
with less performance degradation. The two sites multicores scenario is gives better
energy and performance tradeoff, one average is equal to 14.7\%, than the two sites
one core, on average is equal to 13.3\%.
Finally, using multicore in both scenarios increased the energy and performance tradeoff
-distance. This is because using multicores are increased the computations to communications
-ratio in two sites scenario and thus the energy saving increased over the performance degradation, whereas decreased this ratio
-in one site scenario causing the performance degradation decreased over the energy saving.
+distance. This generally due to using multicores was increased the computations to communications
+ratio in two sites scenario and thus the energy saving percentage increased over the performance degradation percentage, whereas this ratio was decreased
+in one site scenario causing the performance degradation percentage decreased over the energy saving percentage.
\label{fig:dist-mc}
\end{figure}
-\subsection{The results for different power consumption scenarios}
-\label{sec.compare}
+\subsection{The results of using different static power consumption scenarios}
+\label{sec.pow_sen}
+The static power consumption for one core of the computing node is the leakage power
+consumption when this core is in the idle state. The node's idle state power value that measured
+as in section \ref{sec.grid5000} had many power consumptions embedded such as
+all cores static powers in addition to the power consumption of the other devices. So, the static power for one core
+can't measured precisely. On the other hand, while the static power consumption of
+one core representing the core's power when there is no any computation, thus
+the majority of ratio of the total power consumption is depends on the dynamic power consumption.
+Despite that, the static power consumption is becomes more important when the execution time
+increased using DVFS. Therefore, the objective of this section is to verify the ability of the proposed
+frequencies selecting algorithm when the static power consumption is changed.
+
+All the results obtained in the previous sections depend on the measured dynamic power
+consumptions as in table \ref{table:grid5000}. Moreover, the static power consumption is assumed for
+one core represents 20\% of the measured dynamic power of that core.
+This assumption is extended in this section to taking into account others ratios for the static power consumption.
+In addition to the previous ratio of the static power consumption, two other scenarios are used which
+all of these scenarios can be denoted as follow:
+\begin{itemize}
+\item 10\% of static power scenario
+\item 20\% of static power scenario
+\item 30\% of static power scenario
+\end{itemize}
+
+These three scenarios represented the ratio of the static power consumption that can be computed from
+the dynamic power consumption of the core. The NAS benchmarks of class D are executed over 16 nodes
+in the Nancy site using three clusters: Graphite, Graphene and Griffon. As same as used before, the one site 16 nodes
+platform scenario explained in the last experiments, as in table \ref{tab:sc}, is uses to run
+the NAS benchmarks with these static power scenarios.
+
+ \begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/eng_pow.eps}
+ \caption{The energy saving percentages for NAS benchmarks of the three power scenario}
+ \label{fig:eng-pow}
+\end{figure}
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/per_pow.eps}
+ \caption{The performance degradation percentages for NAS benchmarks of the three power scenario}
+ \label{fig:per-pow}
+\end{figure}
+
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/dist_pow.eps}
+ \caption{The tradeoff distance for NAS benchmarks of the three power scenario}
+ \label{fig:dist-pow}
+\end{figure}
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.47]{fig/three_scenarios.pdf}
+ \caption{Comparing the selected frequencies of MG benchmarks for three static power scenarios}
+ \label{fig:fre-pow}
+\end{figure}
+The energy saving percentages of NAS benchmarks with these three static power scenarios are presented
+in figure \ref{fig:eng_sen}. This figure showed the 10\% of static power scenario
+gives the biggest energy saving percentage comparing to 20\% and 30\% static power
+scenario. When using smaller ratio of static power consumption, the proposed
+frequencies selecting algorithm selects smaller frequencies, bigger scaling factors,
+because the static energy consumption not increased significantly the overall energy
+consumption. Therefore, more energy reduction can be achieved when the frequencies are scaled down.
+For example figure \ref{fig:fre-pow}, illustrated that the proposed algorithm
+proportionally scaled down the new computed frequencies with the overall predicted energy
+consumption. The results of 30\% static power scenario gives the smallest energy saving percentages
+because the new selected frequencies produced smaller ratio in the reduced energy consumption.
+Furthermore, The proposed algorithm tries to limit selecting smaller frequencies that increased
+the static energy consumption if the static power consumption is increased.
+The performance degradation percentages are presented in the figure \ref{fig:per-pow},
+the 30\% of static power scenario had less performance degradation percentage, because
+bigger frequencies was selected due to the big ratio in the static power consumption.
+The inverse was happens in the 20\% and 30\% scenario, the algorithm was selected
+biggest frequencies, smaller scaling factors, according to this increased in the static power ratios.
+The tradoff distance for the NAS benchmarks with these three static powers scenarios
+are presented in the figure \ref{fig:dist}. The results showed that the tradeoff
+distance 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.
+In EP benchmarks, the results of energy saving, performance degradation and tradeoff
+distance are showed small differences when the these static power scenarios were used,
+because this benchmark not has communications. The proposed algorithm is selected
+same frequencies in this benchmark when all these static power scenarios are used.
+The small differences in the results are due to the static power is consumed during the computation
+times side by side to the dynamic power consumption, knowing that the dynamic power consumption
+representing the highest ratio in the total power consumption of the core, then any change in
+the static power during these times have less affect on the overall energy consumption. While the
+inverse was happens for the rest of the benchmarks which have the communications
+that increased the static energy consumption linearly to the mount of communications
+in these benchmarks.
+
-\subsection{The comparison of the proposed scaling algorithm }
+\subsection{The comparison of the proposed frequencies selecting algorithm }
\label{sec.compare_EDP}
-
+
\section{Conclusion}
\label{sec.concl}
