correcting the last sections

[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..1774eba61645015f7900a0f4a4ea93ed408824c7 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}).
 


@@ -672,22 +672,21 @@ The benchmarks have seven different classes, S, W, A, B, C, D and E, that repres
 
 \subsection{The experimental results of the scaling algorithm}
 \label{sec.res}
 
 \subsection{The experimental results of the scaling algorithm}
 \label{sec.res}

-In this section, the results of the the application of the scaling factors selection algorithm \ref{HSA} 
+In this section, the results of the application of the scaling factors selection algorithm \ref{HSA} 

 to the NAS parallel benchmarks are presented. 
 
 As mentioned previously, the experiments 
 to the NAS parallel benchmarks are presented. 
 
 As mentioned previously, the experiments 

-were conducted over two sites of grid'5000,   Lyon and Nancy sites. 
+were conducted over two sites of grid'5000,  Lyon and Nancy sites. 

 Two scenarios were considered while selecting the clusters from these two sites :
 \begin{itemize}
 \item In the first scenario, nodes from two sites and three heterogeneous clusters were selected. The two sites are connected 
 Two scenarios were considered while selecting the clusters from these two sites :
 \begin{itemize}
 \item In the first scenario, nodes from two sites and three heterogeneous clusters were selected. The two sites are connected 

-are connected via a long distance network.
-\item In the second scenario nodes from three clusters that are 
-located in one site, Nancy site.  
+ via a long distance network.
+\item In the second scenario nodes from three clusters that are located in one site, Nancy site.  

 \end{itemize}
 
 The main reason 
 behind using these two scenarios is to evaluate the influence of long distance communications (higher latency) on the performance of the 
 \end{itemize}
 
 The main reason 
 behind using these two scenarios is to evaluate the influence of long distance communications (higher latency) on the performance of the 

-scaling factors selection algorithm. Indeed, in the first scenario  the computations to communications ratio 
+scaling factors selection algorithm. Indeed, in the first scenario the computations to communications ratio 

 is very low due to the higher communication times which reduces the effect of DVFS operations.
 
 The NAS parallel benchmarks are executed over 
 is very low due to the higher communication times which reduces the effect of DVFS operations.
 
 The NAS parallel benchmarks are executed over 


@@ -701,7 +700,7 @@ 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} 


@@ -754,8 +753,8 @@ presented in the 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. 
 
 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 
+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.
 
 over one site with 16 and 32 nodes are also lower when  compared to those of the  two sites 
 scenario.
 


@@ -791,13 +790,12 @@ 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   
 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   

-than in the second one. Moreover, the frequency selecting algorithm selects smaller frequencies when the computations times are higher than the communication times which 
+than in the second one. Moreover, the frequency selecting algorithm selects smaller frequencies when the computations times are bigger than the communication times which 

 results in  a lower energy consumption. Indeed, the dynamic  consumed power
 is exponentially related to the CPU's frequency value. On the other side, the increase in the number of computing nodes can 
 increase the communication times and thus produces less energy saving depending on the 
 benchmarks being executed. The results of the benchmarks CG, MG, BT and FT show more 
 results in  a lower energy consumption. Indeed, the dynamic  consumed power
 is exponentially related to the CPU's frequency value. On the other side, the increase in the number of computing nodes can 
 increase the communication times and thus produces less energy saving depending on the 
 benchmarks being executed. The results of the benchmarks CG, MG, BT and FT show more 

-energy saving percentage in one site scenario when executed  over 16 nodes comparing to 32 nodes. While, LU and SP consume more energy with 16 nodes than 32 in one site  because there computations to 
-communications ratio is not affected by the increase of the number of local communications. 
+energy saving percentage in one site scenario when executed over 16 nodes comparing to 32 nodes. While, LU and SP consume more energy with 16 nodes than 32 in one site  because their computations to communications ratio is not affected by the increase of the number of local communications. 

 
 
 The energy saving percentage is reduced for all the benchmarks because of the long distance communications in the two sites 
 
 
 The energy saving percentage is reduced for all the benchmarks because of the long distance communications in the two sites 


@@ -805,135 +803,129 @@ scenario, except for the   EP benchmark which has  no communications. Therefore,
 dependent on the maximum difference between the computing powers of the heterogeneous computing nodes, for example 
 in the one site scenario, the graphite cluster is selected but in the two sits scenario 
 this cluster is replaced with Taurus cluster which is more powerful. 
 dependent on the maximum difference between the computing powers of the heterogeneous computing nodes, for example 
 in the one site scenario, the graphite cluster is selected but in the two sits scenario 
 this cluster is replaced with Taurus cluster which is more powerful. 

-Therefore, the energy saving of EP benchmarks are bigger in the two site scenario due 
+Therefore, the energy saving of EP benchmarks are bigger in the two sites scenario due 

 to the higher maximum difference between the computing powers of the nodes. 
 to the higher maximum difference between the computing powers of the nodes. 

-In fact,  high
-differences between the nodes' computing powers make the proposed frequencies selecting  
+
+In fact, high differences between the nodes' computing powers make the proposed frequencies selecting  

 algorithm  select smaller frequencies for the powerful nodes which 
 produces less energy consumption and thus more energy saving.
 algorithm  select smaller frequencies for the powerful nodes which 
 produces less energy consumption and thus more energy saving.

-The best energy saving percentage was obtained in the one site scenario with 16 nodes, The energy consumption was on average reduced up to 30\%.
+The best energy saving percentage was obtained in the one site scenario with 16 nodes, the energy consumption was on average reduced up to 30\%.

 
 
 
 

-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
-16 or 32  nodes is on average equal to 3\% or 10\% respectively. 
+Figure \ref{fig:per_d} presents the performance degradation percentages for all benchmarks over the two scenarios.
+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. 
+For this scenario, the proposed scaling algorithm selects smaller frequencies for the executions with 32 nodes  without significantly degrading their performance because the communication times are higher with 32 nodes which results in smaller  computations to communications ratio.  On the other hand, 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. In opposition to the two sites scenario, when the number of computing nodes is increased in the one site scenario, the performance degradation percentage is increased. Therefore, doubling the number of computing 
+nodes when the communications occur in high speed network does not decrease the computations to 
+communication ratio. 

 
 

- \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 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}.
-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.
-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.
-
-\subsection{The experimental results of multicores clusters}
+
+ 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{blue}{
+The performance degradation percentage of EP benchmark is the higher when it is compared with 
+the other benchmarks. There are no communication and slack times in this benchmark and its 
+performance degradation percentage depends on the frequency value selected in the computing node.
+The rest of the benchmarks showed different performance degradation percentages, which are decreased
+when the communication times are increased and vice versa.}
+
+\textcolor{blue}{Figure \ref{fig:dist} presents the tradeoff distance percentage between the energy saving  and the performance degradation for all benchmarks  over both  scenarios. The tradeoff distance percentage can be 
+computed as in the tradeoff function \ref{eq:max}. The one site scenario with 16 nodes gives the best energy and performance 
+tradeoff, on average is equal to  26\%. As a result, one site scenario using both 16 and 32 nodes had better energy and performance 
+tradeoff comparing to the two sites scenario. This because the former used high speed local communications 
+which increased the computations to communications ratio  and the latter used long distance communications which decreased this ratio. }   \textcolor{red}{The last paragraph has compared the two scenarios}
+
+
+ Finally, the best energy and performance tradeoff 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 of multi-cores clusters}

 \label{sec.res-mc}
 \label{sec.res-mc}

-The grid'5000 clusters have different number of cores embedded in their nodes
-as in the Table \ref{table:grid5000}. Moreover, the cores of each node are 
-connected via shared memory model, the data transfer between cores' local 
-memories achieved via the global memory \cite{rauber_book}. Therefore, in 
-this section the proposed scaling algorithm is implemented over the  grid'5000 
-clusters which are included multicores in the selected nodes as same as the 
-two previous platform scenarios that mentioned in the section \ref{sec.res}.
-The two platform scenarios, the two sites and one site scenarios,  with 32 
-nodes are reconfigured to used multicores for each node. For example if 
-the participating number of nodes from a certain cluster is equal to 12 nodes, 
-in the multicores scenario the selected nodes is equal to 3 nodes with using 
-4 cores for each of them to produced 12 cores. These scenarios with one  
-core and  multicores are  demonstrated in Table \ref{table:sen-mc}. 
+The  clusters of grid'5000 have different number of cores embedded in their nodes
+as shown in Table \ref{table:grid5000}. The cores of each node can exchange 
+data via the shared memory \cite{rauber_book}. In 
+this section, the proposed scaling algorithm is evaluated over the grid'5000 grid while using multi-core nodes 
+selected according to the two  platform scenarios described in the section \ref{sec.res}.
+The two platform scenarios, the two sites and one site scenarios, use  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 12, 
+in the multi-core scenario the selected nodes is equal to 3 nodes while using 
+4 cores from each node. The platforms with one  
+core per node and  multi-cores nodes are  shown in Table \ref{table:sen-mc}. 

 The energy consumptions and execution times of running the NAS parallel 
 The energy consumptions and execution times of running the NAS parallel 

-benchmarks, class D, over these four different scenarios are represented 
+benchmarks, class D, over these four different scenarios are presented 

 in the figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.
 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,
-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 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 
-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 
-dedicated network link that used independently by one core, while in the other 
-scenarios the communication times are higher when using long distance communication 
-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 
-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. 
-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 
-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 
-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 
-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 
-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
-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.  
-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 
-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 
-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 
-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.
-
-

 
 

+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. 
+
+\textcolor{blue}{Furthermore,  in two sites multi-cores per node scenario part of the communications happened via shared memory
+and the rest via long distance network. According to the high latency in the long distance network, the
+communication times are smaller compared to the  communication times of the shared memory. 
+Therefore, using the shared memory communications mixed with the long distance communications 
+has decreased the communication times, and thus the overall execution time is decreased.}
+
+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. 
+Indeed, in this scenario each core has a dedicated network link and all the communications are local.  
+Moreover, the energy consumptions of the NAS benchmarks are lower over the 
+one site one core scenario  than over the one site multi-cores scenario because 
+the first scenario had less execution time than the latter which results in less static energy being consumed.
+
+\textcolor{blue}{ 
+Therefore, the computations to communications ratios of the NAS benchmarks are higher over 
+the one site one core scenario  compared to the other scenarios. 
+More energy reduction has achieved when this ratio increased, because the proposed scaling algorithm selecting smaller frequencies that decreased the dynamic power consumption.  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.}
+
+
+These experiments also showed that the energy 
+consumption and the execution times of the EP and MG benchmarks do not change significantly over these four 
+scenarios  because there are no or small communications,  
+which could increase or decrease the static power consumptions. Contrary to EP and MG, the  energy consumptions 
+and the execution times of the rest of the  benchmarks  vary according to the  communication times that are different from one scenario to the other.
+
+\textcolor{blue}{
+The energy saving percentages of all NAS benchmarks running over these four scenarios are presented in the figure \ref{fig:eng-s-mc}. This figure 
+shows that  the energy saving percentages are higher  over the two sites multi-cores scenario 
+than over the two sites one core scenario, on average they are equal to 22\% and 18\%
+respectively. This is according to the increase or decrease in the computations to communications  ratio  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 
+are a small difference  in the computations to communications ratios, which leads 
+the proposed scaling algorithm to select similar frequencies for both scenarios.  
+
+The performance degradation percentages of the NAS benchmarks are presented in
+figure \ref{fig:per-d-mc}. 
+
+It indicates that the performance degradation percentages for the NAS benchmarks are higher over the two sites 
+multi-cores scenario than over the  two sites  one core scenario, equal on average to 7\% and 4\% respectively. 
+Moreover, using the two sites multi-cores scenario increased 
+the computations to communications ratio, which may increase 
+the overall execution time  when the proposed scaling algorithm is applied and the frequencies scaled down.  
+
+\textcolor{blue}{
+When the benchmarks are executed  over the one 
+site one core scenario their performance degradation percentages, on average
+is equal to 10\%, are higher than those executed over one site multi-cores, 
+which on average is equal to 7\%. This because using  multi-cores in one site scenario
+decreased the computations to communications ratio. Therefore, selecting small 
+frequencies by the scaling algorithm do not increase the execution time significantly.}

 
 

+\textcolor{blue}{
+The tradeoff distance percentages of the NAS 
+benchmarks over all scenarios are presented in the figure \ref{fig:dist-mc}.
+These  tradeoff distance percentages are used to verified which scenario is the best in term of the energy and performance ratio. The figure indicates that using muti-cores in both of the one site and two sites scenarios gives bigger  tradeoff distance percentages, on overage they are equal to 17.6\% and 15.3\% respectively. On the contrary, using one core per node in both of one site and two sites scenarios gives lower  tradeoff distance percentages, on average they are equal to 14.7\% and 13.3\% respectively. }

 
 \begin{table}[]
 \centering
 
 \begin{table}[]
 \centering


@@ -995,15 +987,142 @@ 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}
+\textcolor{blue}{
+The static power consumption for one core is the leakage power
+consumption when it is idle. The measured static  power of the node, 
+as in section \ref{sec.grid5000}, had a collection of power values such as 
+all cores static powers and the power consumptions of the other devices. Furthermore, the static power for one core is hard to measured precisely. On the other hand,  the core has consumed the static power during 
+the communication and computation times.  However, the static power consumption becomes more important  when the execution time is
+increased using DVFS. Therefore, the objective of this section is to verify the ability of the proposed 
+scaling algorithm to select the best frequencies when the static power consumption is changing. 
+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 for one core is represented by 20\% of the measured dynamic power consumption. 
+This assumption is extended in this section to taking into account other ratios for the static power consumption.
+In addition to the previous ratio of the static power consumption, two other static power ratios are used, which are 10\% and 30\% of the measured dynamic power of the core.
+As a result, all of these static power scenarios is 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}
+The NAS parallel benchmarks, class D, are executed over Nancy site. 
+The number of computing nodes used is 16 nodes distributed between three cluster, which are Graphite, Graphene and Griffon.  The NAS benchmarks rerun
+with these two new static power scenarios over one site scenario
+using one core per node. }
+
+ \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 frequency scaling factors of MG benchmark for three static power scenarios}
+  \label{fig:fre-pow}
+\end{figure}

 
 

+\textcolor{blue}{
+The energy saving percentages of NAS benchmarks with these three static power scenarios are presented 
+in figure \ref{fig:eng_sen}. This figure shows that  10\% of static power scenario 
+gives the biggest energy saving percentage comparing to 20\% and 30\% static power 
+scenarios. The smaller ratio of the static power consumption makes the proposed 
+scaling algorithm to select smaller frequencies, bigger scaling factors. 
+These smaller frequencies has reduced the dynamic energy consumption and thus the 
+overall energy consumption is decreased. 
+The energy saving percentages of 30\% static power scenario is the smallest between the other scenarios, because of the scaling algorithm selects bigger frequencies, smaller scaling factors, that increased the energy consumption. For example, figure \ref{fig:fre-pow}, illustrates that the proposed scaling algorithm is proportionally selected the best frequency scaling factors according to the static power consumption ratio being used.
+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.
+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.
+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.
+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. }

 
 

-\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}

-
+\textcolor{blue}{
+The tradeoff between the energy consumption and the performance of the parallel 
+applications had significant importance in the domain of the research. 
+Many researchers, \cite{EDP_for_multi_processors,Energy_aware_application_scheduling,Exploring_Energy_Performance_TradeOffs},
+have optimized the tradeoff between the energy and the performance using the well known  energy and delay product, $EDP=energy \times delay$. 
+This model is also used by Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS},
+the  objective is to select the frequencies that minimized EDP product for the multi-cores 
+architecture when DVFS is used. Moreover, their algorithm is applied online, which synchronously optimized the energy consumption 
+and the execution time. Both energy consumption and execution time of a processor are predicted by the their algorithm.
+In this section the proposed frequencies selection algorithm, called Maxdist is compared with Spiliopoulos et al. algorithm, called EDP.
+To make both of the algorithms follow the same direction and  fairly  comparing them, the same energy model,  equation \ref{eq:energy} and
+the execution time model, equation \ref{eq:perf}, are used in the prediction process to select the best vector of the frequencies. 
+In contrast, the proposed algorithm starts the search space from the lower bound computed as in equation the  \ref{eq:Fint}. Also, the algorithm
+stops  the search process when it is reached to the lower bound as mentioned before. In the same way, the EDP algorithm is developed to start from the 
+same upper bound used in Maxdist algorithm, and it stops the search process when  a minimum available frequencies is reached. 
+Finally, the resulting EDP algorithm is an exhaustive search algorithm that test all possible frequencies, starting from the initial frequencies, 
+and selecting those minimized the EDP product.
+Both algorithms were applied to NAS benchmarks, class D, over 16 nodes selected from grid'5000 clusters.
+The participating computing nodes are distributed between two sites and one site to have two different scenarios that used in the 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. 
+\begin{figure}
+  \centering
+  \includegraphics[scale=0.5]{fig/edp_eng}
+  \caption{Comparing of the energy saving for the proposed method with EDP method}
+  \label{fig:edp-eng}
+\end{figure}
+\begin{figure}
+  \centering
+  \includegraphics[scale=0.5]{fig/edp_per}
+  \caption{Comparing of the performance degradation for the proposed method with EDP method}
+  \label{fig:edp-perf}
+\end{figure}
+\begin{figure}
+  \centering
+  \includegraphics[scale=0.5]{fig/edp_dist}
+  \caption{Comparing of the tradeoff distance for the proposed method with EDP method}
+  \label{fig:edp-dist}
+\end{figure}
+As shown form these figures, the proposed frequencies selection algorithm, Maxdist, outperform the EDP algorithm in term of energy and performance for all of the benchmarks executed over the two scenarios. 
+Generally, the proposed algorithm gives better results for all benchmarks because it is
+optimized the distance between the energy saving and the performance degradation in the same time. 
+Moreover, the proposed scaling algorithm gives the same weight for these two metrics.
+Whereas, the EDP algorithm gives some times negative tradeoff values for some benchmarks in the two sites scenarios.
+These negative tradeoff values mean that the performance degradation percentage is higher than energy saving percentage.
+The higher positive value of the tradeoff 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. The proposed algorithm, Maxdist, has selected the best frequencies in a small execution time, 
+on average is equal to  0.01 $ms$, when it is executed over 32 nodes distributed between Nancy and Lyon sites.
+While the EDP algorithm was slower than Maxdist algorithm by ten times over the same number of nodes and same distribution, its execution time on average 
+is equal to 0.1 $ms$. 
+}

 
 
 \section{Conclusion}
 
 
 \section{Conclusion}