adding power senarios section

[mpi-energy2.git] / mpi-energy2-extension / Heter_paper.tex

diff --git a/mpi-energy2-extension/Heter_paper.tex b/mpi-energy2-extension/Heter_paper.tex
index e30d62cdb03dbe5f6b62ecc1975f51d67eadee73..b2c2c21e7a3a5dea5693aac7e66121ceb2fe2195 100644 (file)
--- a/mpi-energy2-extension/Heter_paper.tex
+++ b/mpi-energy2-extension/Heter_paper.tex
@@ -54,7 +54,7 @@
 \newcommand{\Sopt}[1][]{\Xsub{S}{opt}_{#1}}
 \newcommand{\Tcm}[1][]{\Xsub{T}{cm}_{\fxheight{#1}}}
 \newcommand{\Tcp}[1][]{\Xsub{T}{cp}_{#1}}
 \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}}
 \newcommand{\Pidle}[1][]{\Xsub{P}{idle}_{\fxheight{#1}}}
 \newcommand{\TcpOld}[1][]{\Xsub{T}{cpOld}_{#1}}
 \newcommand{\Tnew}{\Xsub{T}{New}}


@@ -183,7 +183,7 @@ used in the method to optimize both the energy consumption and the performance
 of iterative methods, which is presented in the following sections.
 
 
 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,
 
 Many researchers~\cite{Malkowski_energy.efficient.high.performance.computing,
   Rauber_Analytical.Modeling.for.Energy,Zhuo_Energy.efficient.Dynamic.Task.Scheduling,


@@ -567,7 +567,7 @@ maximum distance between the energy curve and the performance curve is, which re
 
 \section{Experimental results}
 \label{sec.expe}
 
 \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}
 in this paper real experiments were conducted over the grid'5000 platform. 
 
 \subsection{Grid'5000 architature and power consumption}


@@ -583,14 +583,14 @@ Two types of local networks are used, Ethernet or Infiniband networks which have
 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 $j$, 
 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}
 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 $j$, 
 \end{equation}
 
 where $\Pd[j]$ is the dynamic power consumption for one core of node $j$, 


@@ -599,7 +599,7 @@ $\lbrace\Theta_1,\Theta_2\rbrace$ is the time interval for the measured  idle po
 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.
 
 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}).
 
 
 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}).
 


@@ -701,7 +701,7 @@ Table \ref{tab:sc} shows the number of nodes used from each cluster for each sce
 \centering
 \begin{tabular}{|*{4}{c|}}
 \hline
 \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} 
                                       & Cluster & Site           & No. of  nodes     \\ 
 \hline
 \multirow{3}{*}{Two sites / 16 nodes} & Taurus & Lyon                & 5                      \\ \cline{2-4} 


@@ -815,31 +815,35 @@ The best energy saving percentage was obtained in the one site scenario with 16
 
 
 Figure \ref{fig:per_d} presents the performance degradation percentages for all benchmarks.
 
 
 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. 
 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 
 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 
 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,
 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}
 
 \subsection{The experimental results of multicores clusters}
 \label{sec.res-mc}


@@ -861,29 +865,29 @@ benchmarks, class D, over these four different scenarios are represented
 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. 
 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 
 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 
 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 
 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 
 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 
 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 
 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 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 


@@ -892,44 +896,42 @@ communications in each of them.
 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 
 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 
 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 
 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\%. 
 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, 
 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
 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 
 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 
 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.

 
 
 
 
 
 


@@ -995,17 +997,107 @@ Scenario name                          & Cluster name & \begin{tabular}[c]{@{}c@
   \label{fig:dist-mc}
 \end{figure}
 
   \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}
 
 
 \label{sec.compare_EDP}
 
 

-
+  

 \section{Conclusion}
 \label{sec.concl}
 
 \section{Conclusion}
 \label{sec.concl}