correcting the last paragraph

[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 8ada2a0b96a2b372d42beb6546a4207014bc4886..09061339d3811524f420617c4b8318cb95b838cb 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{\Ppeak}[1][]{\Xsub{P}{peak}_{#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}}


@@ -350,9 +350,9 @@ maximum frequency for all  nodes:
 \end{equation}
 
 Where $\Ereduced$  is computed using (\ref{eq:energy}) and $\Eoriginal$ is 
 \end{equation}
 
 Where $\Ereduced$  is computed using (\ref{eq:energy}) and $\Eoriginal$ is 

-computed as in ().
+computed as in (\ref{eq:eorginal}).
+

 
 

-\textcolor{red}{A reference is missing}

 \begin{equation}
   \label{eq:eorginal}
     \Eoriginal = \sum_{i=1}^{N} \sum_{j=1}^{M} ( \Pd[ij] \cdot  \Tcp[ij])  + 
 \begin{equation}
   \label{eq:eorginal}
     \Eoriginal = \sum_{i=1}^{N} \sum_{j=1}^{M} ( \Pd[ij] \cdot  \Tcp[ij])  + 


@@ -477,9 +477,7 @@ in~\cite{Zhuo_Energy.efficient.Dynamic.Task.Scheduling,Rauber_Analytical.Modelin
   \label{dvfs}
 \end{algorithm}
 
   \label{dvfs}
 \end{algorithm}
 

-\subsection{The algorithm details}

 
 

-\textcolor{red}{Delete the subsection if there's only one.}

 
 In this section, the scaling factors selection algorithm for  grids, algorithm~\ref{HSA}, is presented. It selects the vector of the frequency
 scaling factors  that gives the best trade-off between minimizing the
 
 In this section, the scaling factors selection algorithm for  grids, algorithm~\ref{HSA}, is presented. It selects the vector of the frequency
 scaling factors  that gives the best trade-off between minimizing the


@@ -569,7 +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}


@@ -578,31 +576,30 @@ Grid'5000~\cite{grid5000} is a large-scale testbed that consists of ten sites di
 which is the French National Telecommunication Network for Technology.
 Each site of the grid is composed of few heterogeneous 
 computing clusters and each cluster contains many homogeneous nodes. In total,
 which is the French National Telecommunication Network for Technology.
 Each site of the grid is composed of few heterogeneous 
 computing clusters and each cluster contains many homogeneous nodes. In total,

- grid'5000 has about  one thousand heterogeneous nodes and eight thousand cores.  In each site,
+grid'5000 has about  one thousand heterogeneous nodes and eight thousand cores.  In each site,

 the clusters and their nodes are connected via  high speed local area networks. 
 Two types of local networks are used, Ethernet or Infiniband networks which have  different characteristics in terms of bandwidth and latency.  
 
 Since grid'5000 is dedicated 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 $j$, 
 the clusters and their nodes are connected via  high speed local area networks. 
 Two types of local networks are used, Ethernet or Infiniband networks which have  different characteristics in terms of bandwidth and latency.  
 
 Since grid'5000 is dedicated 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 $P\max[jx]$. 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}). 
 
 dynamic power consumption of that core with the maximum frequency, see  figure(\ref{fig:power_cons}). 
 

-\textcolor{red}{why maximum and minimum, change peak in the equation and the figure}

 
 The dynamic power $\Pd[j]$ is computed as in equation (\ref{eq:pdyn})
 \begin{equation}
   \label{eq:pdyn}
 
 The dynamic power $\Pd[j]$ is computed as in equation (\ref{eq:pdyn})
 \begin{equation}
   \label{eq:pdyn}

-    \Pd[j] = \max_{x=\beta_1,\dots \beta_2} (P\max[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 $j$, 

-$\lbrace \beta_1,\beta_2 \rbrace$ is the time interval for the measured peak power values, 
+$\lbrace \beta_1,\beta_2 \rbrace$ is the time interval for the measured maximum power values, 

 $\lbrace\Theta_1,\Theta_2\rbrace$ is the time interval for the measured  idle power values.
 Therefore, the dynamic power of one core is computed as the difference between the maximum 
 $\lbrace\Theta_1,\Theta_2\rbrace$ is the time interval for the measured  idle power values.
 Therefore, the dynamic power of one core is computed as the difference between the maximum 

-measured value in peak powers vector and the minimum measured value in the idle powers vector.
+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}).
 


@@ -704,7 +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} 


@@ -743,7 +740,7 @@ Table \ref{tab:sc} shows the number of nodes used from each cluster for each sce
   \label{fig:time_sen}
 \end{figure}
 
   \label{fig:time_sen}
 \end{figure}
 

-The NAS parallel benchmarks are executed over these two platform
+The NAS parallel benchmarks are executed over these two platforms

  with different number of nodes, as in Table \ref{tab:sc}. 
 The overall energy consumption of all the benchmarks solving the class D instance and
 using the proposed frequency selection algorithm is measured 
  with different number of nodes, as in Table \ref{tab:sc}. 
 The overall energy consumption of all the benchmarks solving the class D instance and
 using the proposed frequency selection algorithm is measured 


@@ -755,21 +752,15 @@ time is measured for all the benchmarks over these different scenarios.
 The energy consumptions  and the execution times for all the benchmarks are 
 presented in the plots \ref{fig:eng_sen} and \ref{fig:time_sen} respectively. 
 
 The energy consumptions  and the execution times for all the benchmarks are 
 presented in the plots \ref{fig:eng_sen} and \ref{fig:time_sen} respectively. 
 

-In general, the energy consumed while executing  the NAS benchmarks over one site scenario 
-for  16 and 32 nodes is lower than the energy consumed while executing over the two sites. 
-The long distance communications between the two distributed sites increases the idle time which leads to more static energy consumption. 
+For the majority of the benchmarks, the energy consumed while executing  the NAS benchmarks over one site scenario 
+for  16 and 32 nodes is lower than the energy consumed while using two sites. 
+The long distance communications between the two distributed sites increase the idle time which leads to more static energy consumption. 

  The execution times of these benchmarks 
 over one site with 16 and 32 nodes are also lower when  compared to those of the  two sites 
 scenario.
 
  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.
 

-
-
-The EP and MG benchmarks, where there are no or small communications, showed 
-that their execution times and the energy consumptions are not effected 
-significantly in both scenarios and when the number of nodes is increase, 
-while the other benchmarks showed the inverse, because they have more communications 
-that proportionally increase the communication times if there are slow 
-communications or using more number of nodes or both of them.
+However, the  execution times and the energy consumptions of EP and MG benchmarks, which have no or small communications, are not significantly affected 
+ in both scenarios. Even when the number of nodes is doubled. On the other hand, the communications of the rest of the benchmarks increases when using long distance communications between two sites or increasing the number of computing nodes.

 
 \begin{figure}
   \centering
 
 \begin{figure}
   \centering


@@ -798,58 +789,209 @@ The energy saving percentage is computed as the ratio between the reduced
 energy consumption, equation (\ref{eq:energy}), and the original energy consumption,
 equation (\ref{eq:eorginal}), for all benchmarks as in figure \ref{fig:eng_s}. 
 This figure shows that the energy saving percentages of one site scenario for
 energy consumption, equation (\ref{eq:energy}), and the original energy consumption,
 equation (\ref{eq:eorginal}), for all benchmarks as in figure \ref{fig:eng_s}. 
 This figure shows that the energy saving percentages of one site scenario for

-16 and 32 nodes are bigger than those of the two sites scenario. This is because
-the computations to communications ratio in  one site scenario is higher 
-than the ratio of the two sites scenarios, due to the increase in the communication
-times. Moreover, the frequencies selecting algorithm selects smaller frequencies, bigger
-scaling factors, when the computations times are higher than communication times, 
-producing  smaller energy consumption, because the dynamic energy consumption 
-is decreased linearly with computation times that decreased exponentially with 
-scaling factors. On the other side, the increase in the number of computing nodes can be 
-increase the communication times and thus producing less energy saving depending on the 
-benchmarks being executed. 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 
-the benchmarks  LU and SP showed the inverse, because there computations to 
-communications ratio is not effected to the increase in local site communications. 
-While all benchmarks are effected by the long distance communications in the two sites 
-scenarios, except  EP benchmarks. In EP benchmark  there is no communications 
-in their iterations, then it is independent from the effect of local and long 
-distance communications. Therefore, the energy saving percentage of this benchmarks is 
-depend on differences between the computing powers of the computing nodes, for example 
+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 
+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. 
+
+
+The energy saving percentage is reduced for all the benchmarks because of the long distance communications in the two sites 
+scenario, except for the   EP benchmark which has  no communications. Therefore, the energy saving percentage of this benchmark is 
+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 
 in the one site scenario, the graphite cluster is selected but in the two sits scenario 

-this cluster is replaced with Taurus cluster that be more powerful in computing power. 
+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 site scenario due 

-to increase in the differences between the computing powers of the nodes. This means, the higher 
+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  
 differences between the nodes' computing powers make the proposed frequencies selecting  

-algorithm  to selects smaller frequencies in the nodes of the higher computing power, 
-producing less energy consumption and thus more energy saving.
-The best energy saving percentage was for one site scenario with 16 nodes, on average it
-saves the energy consumption up to 30\%. 
-
-Figure \ref{fig:per_d}, presents the performance degradation percentages for all benchmarks.
-It shows that the performance degradation percentages  of the one site scenario with
-32 nodes, on average equal to 10\%, is higher than the performance degradation of one 16 nodes, 
-which on average equal to 3\%. 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\%.
+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\%.
+
+
+Figure \ref{fig:per_d} presents the performance degradation percentages for all benchmarks.
+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. 
+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 govern 
+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}
+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 energy consumptions and execution times of running the NAS parallel 
+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. 
+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. 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 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 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 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 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. 
+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, 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\%. 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 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\%. 
+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\%. So, in one site 
+multicores scenario the computations to communications ratio is decreased
+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\%.  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 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.
+
+
+
+
+
+\begin{table}[]
+\centering
+\caption{The multicores scenarios}

 
 

-\subsection{The experimental results of multi-cores clusters}
-\label{sec.res}
+\begin{tabular}{|*{4}{c|}}
+\hline
+Scenario name                          & Cluster name & \begin{tabular}[c]{@{}c@{}}No. of  nodes\\ in each cluster\end{tabular} & 
+                                       \begin{tabular}[c]{@{}c@{}}No. of  cores\\ for each node\end{tabular}  \\ \hline
+\multirow{3}{*}{Two sites/ one core}   & Taurus       & 10              & 1                   \\ \cline{2-4}
+                                       & Graphene     & 10              & 1                   \\ \cline{2-4}
+                                       & Griffon      & 12              & 1                   \\ \hline
+\multirow{3}{*}{Two sites/ multicores} & Taurus       & 3               & 3 or 4              \\ \cline{2-4}
+                                       & Graphene     & 3               & 3 or 4              \\  \cline{2-4}
+                                       & Griffon      & 3               & 4                   \\ \hline
+\multirow{3}{*}{One site/ one core}    & Graphite     & 4               & 1                   \\  \cline{2-4}
+                                       & Graphene     & 12              & 1                   \\  \cline{2-4}
+                                       & Griffon      & 12              & 1                   \\ \hline
+\multirow{3}{*}{One site/ multicores}  & Graphite     & 3               & 3 or 4              \\  \cline{2-4}
+                                       & Graphene     & 3               & 3 or 4              \\  \cline{2-4}
+                                       & Griffon      & 3               & 4                   \\ \hline
+\end{tabular}
+\label{table:sen-mc}
+\end{table}
+
+\begin{figure}
+  \centering
+  \includegraphics[scale=0.5]{fig/eng_con.eps}
+  \caption{Comparing the  energy consumptions of running NAS benchmarks over one core and multicores scenarios }
+  \label{fig:eng-cons-mc}
+\end{figure}
+
+
+  \begin{figure}
+  \centering
+  \includegraphics[scale=0.5]{fig/time.eps}
+  \caption{Comparing the  execution times of running NAS benchmarks over one core and multicores scenarios }
+  \label{fig:time-mc}
+\end{figure}
+
+ \begin{figure}
+  \centering
+  \includegraphics[scale=0.5]{fig/eng_s_mc.eps}
+  \caption{The energy saving of running NAS benchmarks over one core and multicores scenarios }
+  \label{fig:eng-s-mc}
+\end{figure}
+
+\begin{figure}
+  \centering
+  \includegraphics[scale=0.5]{fig/per_d_mc.eps}
+  \caption{The performance degradation of running NAS benchmarks over one core and multicores scenarios }
+  \label{fig:per-d-mc}
+\end{figure}
+
+\begin{figure}
+  \centering
+  \includegraphics[scale=0.5]{fig/dist_mc.eps}
+  \caption{The tradeoff distance of running NAS benchmarks over one core and multicores scenarios }
+  \label{fig:dist-mc}
+\end{figure}

 
 \subsection{The results for different power consumption scenarios}
 \label{sec.compare}
 
 \subsection{The results for different power consumption scenarios}
 \label{sec.compare}