\subsection{The experimental results of the scaling algorithm}
\label{sec.res}
-In this section, the scaling factor selection algorithm \ref{HSA}, is applied
-to NAS parallel benchmarks. Seven benchmarks, CG, MG, EP, LU, BT, SP and FT, of the class D
-are executed over grid'5000 computing clusters. As mentioned previously, the experiments
-of this paper obtained from a collection of many clusters distributed in two sites, Lyon and Nancy sites,
-of grid'5000. Four different clusters are selected from these two sites to generate two
-different scenarios. Each of these two scenarios used three clusters. The first scenario,
-is composed from three clusters that located in two sites, Lyon and Nancy sites. One of these three
-clusters is from Lyon site, Taurus cluster and the other two clusters are form Nancy site,
-Graphene and Griffon clusters. The second scenario, is composed from three clusters that are
-located in one site, Nancy site. These cluster are Graphite, Graphene and griffon. The main reason
-behind using these two scenarios is because the first one is executing the NAS parllel benchmarks over
-two sites that are connected via long distance network, then the computations to communications ratio
-is very low due to the increase in communication times, while in the second scenario, all of the three clusters are
-located in one site and they are connected via high speed local area networks, where the computations
-to communications ratio is higher. Therefore, it is very interested to know the performance behaviour
-and the energy consumption of NAS parallel benchmarks using the proposed method, when they run
-over these two different platform scenarios. Moreover, The NAS parallel benchmarks are executed over
+In this section, the results of the the application of the scaling factors selection algorithm \ref{HSA}
+to the NAS parallel benchmarks are presented.
+
+As mentioned previously, the experiments
+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
+are connected 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
+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
16 and 32 nodes for each scenario. The number of participating computing nodes form each cluster
-are different, this depends on the available number of nodes in each cluster.
-Table \ref{tab:sc} shows the details of these two scenarios and the number of nodes
-used from each cluster.
+are different because all the selected clusters do not have the same available number of nodes and all benchmarks do not require the same number of computing nodes.
+Table \ref{tab:sc} shows the number of nodes used from each cluster for each scenario.
\begin{table}[h]
\caption{The different clusters scenarios}
\centering
-\begin{tabular}{|*{3}{c|}}
+\begin{tabular}{|*{4}{c|}}
\hline
-\multirow{2}{*}{Scenario name} & \multicolumn{2}{c|} {The participating clusters} \\ \cline{2-3}
- & Cluster name & No. of nodes of each cluster \\
+\multirow{2}{*}{Scenario name} & \multicolumn{2}{c|} {The participating clusters} \\ \cline{2-4}
+ & Cluster & Site & No. of nodes \\
\hline
-\multirow{3}{*}{Two sites / 16 nodes} & Taurus & 5 \\ \cline{2-3}
- & Graphene & 5 \\ \cline{2-3}
- & Griffon & 6 \\
+\multirow{3}{*}{Two sites / 16 nodes} & Taurus & Lyon & 5 \\ \cline{2-4}
+ & Graphene & Nancy & 5 \\ \cline{2-4}
+ & Griffon & Nancy & 6 \\
\hline
-\multirow{3}{*}{Tow sites / 32 nodes} & Taurus & 10 \\ \cline{2-3}
- & Graphene & 10 \\ \cline{2-3}
- & Griffon & 12 \\
+\multirow{3}{*}{Tow sites / 32 nodes} & Taurus & Lyon & 10 \\ \cline{2-4}
+ & Graphene & Nancy & 10 \\ \cline{2-4}
+ & Griffon &Nancy & 12 \\
\hline
-\multirow{3}{*}{One site / 16 nodes} & Graphite & 4 \\ \cline{2-3}
- & Graphene & 6 \\ \cline{2-3}
- & Griffon & 6 \\
+\multirow{3}{*}{One site / 16 nodes} & Graphite & Nancy & 4 \\ \cline{2-4}
+ & Graphene & Nancy & 6 \\ \cline{2-4}
+ & Griffon & Nancy & 6 \\
\hline
-\multirow{3}{*}{One site / 32 nodes} & Graphite & 4 \\ \cline{2-3}
- & Graphene & 12 \\ \cline{2-3}
- & Griffon & 12 \\
+\multirow{3}{*}{One site / 32 nodes} & Graphite & Nancy & 4 \\ \cline{2-4}
+ & Graphene & Nancy & 12 \\ \cline{2-4}
+ & Griffon & Nancy & 12 \\
\hline
\end{tabular}
\label{tab:sc}
\end{figure}
The NAS parallel benchmarks are executed over these two platform
-scenarios with different number of nodes, as in Table \ref{tab:sc}.
-The overall energy consumption of all benchmark, class D, with
-applying 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
using the equation of the reduced energy consumption, equation
(\ref{eq:energy}). This model uses the measured dynamic and static
-power values that showed in Table \ref{table:grid5000}. The execution
-time is measured for all benchmarks over these different scenarios.
-The energy consumptions and the execution times for all benchmarks are
-demonstrated in the plots \ref{fig:eng_sen} and \ref{fig:time_sen} respectively.
-In general, the energy consumptions of NAS benchmarks over one site scenario
-for 16 and 32 nodes are less than those executed over the two sites
-scenarios. This because in the two sites scenario the communication times
-are higher, due to long distance communications between the two distributed sites.
-This leading to more static energy consumption which is linearly related to the
-increased in the communication time. The execution times of these benchmarks
-over one sites for 16 and 32 nodes are less comparing to the two sites
-scenario according to the increase in communications times.
-
-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.
+power values showed in Table \ref{table:grid5000}. The execution
+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.
+
+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.
+
+
+
+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
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
-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
-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
-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,
+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 one site with
+16 or 32 nodes is on average equal to 3\% or 10\% respectively.
+
+ \textcolor{red}{please correct the following paragraph because I do not understand it at all! Stop using we, this because, effected, while, ...}
+
+
+
+ This because selecting smaller frequencies in the one site scenarios,
when the computations grater than the communications , increase the number of the critical nodes
when the number of nodes increased. The inverse happens in the tow sites scenario,
this due to the lower computations to communications ratio that decreased with highest
