I have commented everything related to multi-cores. Unless we have good clear results...

[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 c8f4cd0a73aea76b40aca0d7e4e8546eaf95d0b8..1caecff578b5103af079e6240275515f54036785 100644 (file)
--- a/mpi-energy2-extension/Heter_paper.tex
+++ b/mpi-energy2-extension/Heter_paper.tex
@@ -87,29 +87,31 @@
 
 
 \begin{abstract}
 
 
 \begin{abstract}

-\textcolor{blue}{
-  In recent years, green computing topic  has being became an important topic in 
-  the domain of the research. The increase in computing power of the computing 
-  platforms is increased the energy consumption and the carbon dioxide emissions.
-  Many techniques have being used to minimize the cost of the energy consumption 
-  and reduce environmental pollution. Dynamic voltage and frequency scaling (DVFS) 
-  is one of these techniques. It used to reduce the power consumption of the CPU 
-  while computing by lowering its frequency. Moreover, lowering the frequency of 
+
+  In recent years, green computing topic  has  become an important topic 
+  in the supercomputing research domain. However, the 
+  computing platforms are still  consuming more and
+more energy due to the increasing number of nodes composing
+them. To minimize the operating costs of these platforms many
+techniques have been used. Dynamic voltage and frequency
+scaling (DVFS) is one of them. It can be used to reduce the power consumption of the CPU 
+  while computing, by lowering its frequency. However, lowering the frequency of 

   a CPU may increase the execution time of an application running on that 
   processor. Therefore, the frequency that gives the best trade-off between 
   the energy consumption and the performance of an application must be selected. 
   a CPU may increase the execution time of an application running on that 
   processor. Therefore, the frequency that gives the best trade-off between 
   the energy consumption and the performance of an application must be selected. 

-  In this paper, a new online frequency selecting algorithm for heterogeneous
-  grid (heterogeneous CPUs) is presented.  It selects the frequencies and tries to give the best
+  In this paper, a new online frequency selecting algorithm for grids, composed of heterogeneous clusters, is presented.  
+  It selects the frequencies and tries to give the best

   trade-off between energy saving and performance degradation, for each node
   trade-off between energy saving and performance degradation, for each node

-  computing the message passing iterative application. The algorithm has a small
+  computing the message passing iterative application. 
+  The algorithm has a small

   overhead and works without training or profiling. It uses a new energy model
   overhead and works without training or profiling. It uses a new energy model

-  for message passing iterative applications running on a heterogeneous
-  grid. The proposed algorithm is evaluated on real testbed, grid'5000 platform, while
+  for message passing iterative applications running on a  grid. 
+  The proposed algorithm is evaluated on a real grid , the grid'5000 platform, while

   running the NAS parallel benchmarks.  The experiments show that it reduces the
   running the NAS parallel benchmarks.  The experiments show that it reduces the

-  energy consumption on average up to \np[\%]{30} while declines the performance
+  energy consumption on average by \np[\%]{30} while  the performance  is only degraded

   on average by \np[\%]{3}. Finally, the algorithm is 
   on average by \np[\%]{3}. Finally, the algorithm is 

-  compared to an existing method, the comparison results show that it outperforms the
-  latter in term of energy and performance trade-off.}
+  compared to an existing method. The comparison results show that it outperforms the
+  latter in terms of energy consumption reduction and performance.

 \end{abstract}
 
 
 \end{abstract}
 
 


@@ -149,7 +151,7 @@ homogeneous  and heterogeneous clusters respectively.
 The results of the experiments showed significant energy
 consumption reductions. All the experimental results were conducted over 
 Simgrid simulator \cite{SimGrid}, which offers easy tools to create a homogeneous and heterogeneous platforms and run message passing parallel applications over them. In this paper, a new frequencies selecting algorithm,
 The results of the experiments showed significant energy
 consumption reductions. All the experimental results were conducted over 
 Simgrid simulator \cite{SimGrid}, which offers easy tools to create a homogeneous and heterogeneous platforms and run message passing parallel applications over them. In this paper, a new frequencies selecting algorithm,

-adapted to  grid platforms, is presented. It is applied to the NAS parallel benchmarks and evaluated over a real testbed, 
+adapted to  grid platforms composed of heterogeneous clusters, is presented. It is applied to the NAS parallel benchmarks and evaluated over a real testbed, 

 the grid'5000 platform \cite{grid5000}. It selects  for a grid platform running a message passing iterative
 application the vector of
 frequencies  that simultaneously tries to offer the maximum energy reduction and
 the grid'5000 platform \cite{grid5000}. It selects  for a grid platform running a message passing iterative
 application the vector of
 frequencies  that simultaneously tries to offer the maximum energy reduction and


@@ -167,8 +169,8 @@ consumption while minimizing the degradation of the program's performance.
 Section~\ref{sec.optim} details the proposed frequencies selecting algorithm.
 Section~\ref{sec.expe} presents the results of applying the algorithm on the 
 NAS parallel benchmarks and executing them on the grid'5000 testbed. 
 Section~\ref{sec.optim} details the proposed frequencies selecting algorithm.
 Section~\ref{sec.expe} presents the results of applying the algorithm on the 
 NAS parallel benchmarks and executing them on the grid'5000 testbed. 

-It shows the results of running different scenarios using multi-cores and one core per node 
-and comparing them. It also evaluates the algorithm over three different power scenarios. Moreover, it shows the
+%It shows the results of running different scenarios using multi-cores and one core per node and comparing them. 
+It also evaluates the algorithm over three different power scenarios. Moreover, it shows the

 comparison results between the proposed method and an existing method.  Finally,
 in Section~\ref{sec.concl} the paper ends with a summary and some future works.
 
 comparison results between the proposed method and an existing method.  Finally,
 in Section~\ref{sec.concl} the paper ends with a summary and some future works.
 


@@ -472,13 +474,13 @@ characteristics of each processor (computation power, range of frequencies,
 dynamic and static powers) and the task executed (computation/communication
 ratio). The aim being to reduce the overall energy consumption and to avoid
 increasing significantly the execution time.
 dynamic and static powers) and the task executed (computation/communication
 ratio). The aim being to reduce the overall energy consumption and to avoid
 increasing significantly the execution time.

-\textcolor{blue}{  In our previous
-works~\cite{Our_first_paper} and \cite{pdsec2015}, we proposed a methods that select the optimal
-frequency scaling factors for a homogeneous and a heterogeneous clusters respectively. 
-Both of the two methods executing a message passing
-iterative synchronous application while giving the best trade-off between the
-energy consumption and the performance for such applications.  In this work we
-are interested in heterogeneous grid as described above.}
+In our previous
+works, \cite{Our_first_paper} and \cite{pdsec2015}, two methods that select the optimal
+frequency scaling factors for a homogeneous and a heterogeneous cluster respectively, were proposed. 
+Both methods selects the frequencies that gives the best tradeoff between 
+energy consumption reduction and performance for  message passing
+iterative synchronous applications.   In this work we
+are interested in grids that are composed of heterogeneous clusters were the nodes have different characteristics such  as  dynamic power, static power, computation power, frequencies range, network latency and bandwidth. 

 Due to the
 heterogeneity of the processors, a vector of scaling factors should be selected
 and it must give the best trade-off between energy consumption and performance.
 Due to the
 heterogeneity of the processors, a vector of scaling factors should be selected
 and it must give the best trade-off between energy consumption and performance.


@@ -998,143 +1000,139 @@ which increase the computations to communications ratio  and the latter uses lon
 
 
 
 
 
 

-\subsection{The experimental results of multi-cores clusters}
-\label{sec.res-mc}
-The  clusters of grid'5000 have different number of cores embedded in their nodes
-as shown in Table \ref{table:grid5000}. 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 
-benchmarks, class D, over these four different scenarios are presented 
-in the figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.
-
-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. 
-   
- \textcolor{blue}{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.   ???????
-}
-
-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.
-
-The computations to communications ratios of the NAS benchmarks are higher over 
-the one site one core scenario  when compared to the ratios of the other scenarios. 
-More energy reduction was achieved when this ratio is increased because the proposed scaling algorithm selects smaller frequencies that decrease the dynamic power consumption. 
-
-  \textcolor{blue}{ Whereas, the energy consumption in the two sites one core scenario is higher than the energy consumption of the two sites multi-core scenario. This is according to the increase in the execution time of the two sites one core scenario. }
-
-
-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.
-
-
-The energy saving percentages of all NAS benchmarks running over these four scenarios are presented in the figure \ref{fig:eng-s-mc}. It shows that  the energy saving percentages   over the two sites multi-cores scenario 
-and over the two sites one core scenario are on average  equal to 22\% and 18\%
-respectively. The energy saving percentages   are higher in the former scenario because  its computations to communications  ratio is higher than the ratio of the latter scenario  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 shows 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.  
-
-
-When the benchmarks are executed  over the one 
-site one core scenario, their performance degradation percentages are equal  on average
-to 10\% and are higher than those executed over the one site multi-cores scenario, 
-which on average is equal to 7\%. 
-
-\textcolor{blue}{
-The performance degradation percentages over one site multi-cores is lower because  the computations to communications ratio is decreased. Therefore, selecting bigger 
-frequencies by the scaling algorithm are proportional to this ratio, and thus the execution time do not increase significantly.}
-
-
-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 verify which scenario is the best in terms of energy reduction and performance. The figure shows that using muti-cores in both of the one site and two sites scenarios gives bigger  tradeoff distance percentages, on overage equal to 17.6\% and 15.3\% respectively, than using one core per node in both of one site and two sites scenarios,  on average  equal to 14.7\% and 13.3\% respectively. 
-
-\begin{table}[]
-\centering
-\caption{The multicores scenarios}
-
-\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 experimental results of multi-cores clusters}
+%\label{sec.res-mc}
+%The  clusters of grid'5000 have different number of cores embedded in their nodes
+%as shown in Table \ref{table:grid5000}. In 
+%this section, the proposed scaling algorithm is evaluated over the grid'5000 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 
+%benchmarks, class D, over these four different scenarios are presented 
+%in the figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.
+%
+%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 and. Moreover, the cores of a node share the memory bus which can be also saturated and become a bottleneck. 
+%   
+%
+%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 memory bus 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.
+%
+%The computations to communications ratios of the NAS benchmarks are higher over 
+%the one site one core scenario  when compared to the ratios of the other scenarios. 
+%More energy reduction was achieved when this ratio is increased because the proposed scaling algorithm selects smaller frequencies that decrease the dynamic power consumption. 
+%
+%  \textcolor{blue}{ Whereas, the energy consumption in the two sites one core scenario is higher than the energy consumption of the two sites multi-core scenario. This is according to the increase in the execution time of the two sites one core scenario. }
+%
+%
+%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.
+%
+%
+%The energy saving percentages of all NAS benchmarks running over these four scenarios are presented in the figure \ref{fig:eng-s-mc}. It shows that  the energy saving percentages   over the two sites multi-cores scenario 
+%and over the two sites one core scenario are on average  equal to 22\% and 18\%
+%respectively. The energy saving percentages   are higher in the former scenario because  its computations to communications  ratio is higher than the ratio of the latter scenario  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 shows 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.  
+%
+%
+%When the benchmarks are executed  over the one 
+%site one core scenario, their performance degradation percentages are equal  on average
+%to 10\% and are higher than those executed over the one site multi-cores scenario, 
+%which on average is equal to 7\%. 
+%
+%\textcolor{blue}{
+%The performance degradation percentages over one site multi-cores is lower because  the computations to communications ratio is decreased. Therefore, selecting bigger 
+%frequencies by the scaling algorithm are proportional to this ratio, and thus the execution time do not increase significantly.}
+%
+%
+%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 verify which scenario is the best in terms of energy reduction and performance. The figure shows that using muti-cores in both of the one site and two sites scenarios gives bigger  tradeoff distance percentages, on overage equal to 17.6\% and 15.3\% respectively, than using one core per node in both of one site and two sites scenarios,  on average  equal to 14.7\% and 13.3\% respectively. 
+%
+%\begin{table}[]
+%\centering
+%\caption{The multicores scenarios}
+%
+%\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{Experiments with different static and dynamic powers consumption scenarios}
 \label{sec.pow_sen}
 
 \subsection{Experiments with different static and dynamic powers consumption scenarios}
 \label{sec.pow_sen}


@@ -1265,7 +1263,7 @@ To evaluate the proposed method on a real heterogeneous grid platform, it was ap
  NAS parallel benchmarks   and the  class D instance was executed over the  grid'5000 testbed platform. 
  The experimental results showed that the algorithm reduces  on average 30\% of the energy consumption
 for all the NAS benchmarks   while  only degrading by 3\% on average  the performance. 
  NAS parallel benchmarks   and the  class D instance was executed over the  grid'5000 testbed platform. 
  The experimental results showed that the algorithm reduces  on average 30\% of the energy consumption
 for all the NAS benchmarks   while  only degrading by 3\% on average  the performance. 

-The Maxdist algorithm was also evaluated in different scenarios that vary in the distribution of the computing nodes between different clusters' sites,  use one core or multi-cores per node or assume different values for the consumed static power. The algorithm selects different vector of frequencies according to the 
+The Maxdist algorithm was also evaluated in different scenarios that vary in the distribution of the computing nodes between different clusters' sites or in the values of the consumed static power. The algorithm selects different vector of frequencies according to the 

 computations and communication times ratios, and  the values of the static and measured dynamic powers of the CPUs. 
 Finally, the proposed algorithm was compared to another method that uses
 the well known energy and delay product as an objective function. The comparison results showed 
 computations and communication times ratios, and  the values of the static and measured dynamic powers of the CPUs. 
 Finally, the proposed algorithm was compared to another method that uses
 the well known energy and delay product as an objective function. The comparison results showed