-The grid'5000 is a large-scale testbed found in France \cite{grid5000}.
-The grid infrastructure consist of ten sites distributed over all France
-metropolitan regions. Each site in the grid'5000 composed from number of heterogeneous
-computing clusters, while each cluster includes a collection of homogeneous nodes.
-In general, the grid'5000 had one thousand of heterogeneous nodes and eight thousand of cores.
-All the sites are connected together via special long distance network called RENATER,
-which is the French National Telecommunication Network for Technology. Whereas inside each site
-the clusters and their nodes are connected throw high speed local area networks.
-There are different types of local networks used such as Ethernet and Infiniband netwoks,
-which allowed different gigabits bandwidth and latencies. On the other hand, the nodes inside each cluster
-are homogeneous, while they are different from the nodes of the other clusters. Therefore, there are
-a wide diversity of processors in grid'5000, that mainly had different processors families
-such as Intel Xeon and AMD Opteron families.
-
-In this paper we are interested to run NAS parallel v3.3 \cite{NAS.Parallel.Benchmarks} over grid'5000.
-We are used seven benchmarks, CG, MG, EP, LU, BT, SP and FT. These benchmarks used seven different types of classes.
-These classes are S, W, A, B, C, D, E, where S represents the smaller problem size that used by benchmark and
-E is represents the biggest class. In this work, the class D is used for all benchmarks in all the experiments that will
-be showed in the coming sections.
-Moreover, the NAS parallel benchmarks have different computations and communications ratios, then it is interested
-to study their energy consumption and their performance on real testbed such as grid'5000.
-In this work, the NAS benchmarks are executed over two sites, Lyon and Nancy sites, of grid'5000.
-These two sites had seven different types of computing clusters as in figure (\ref{fig:grid5000}).
+Grid'5000~\cite{grid5000} is a large-scale testbed that consists of ten sites distributed over all metropolitan France and Luxembourg. All the sites are connected together via a special long distance network called RENATER,
+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,
+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
+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}
+ \Pd[j] = \max_{x=\beta_1,\dots \beta_2} (P\max[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 $j$,
+$\lbrace \beta_1,\beta_2 \rbrace$ is the time interval for the measured peak 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
+measured value in peak 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.
+
+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}).
+
+Four clusters from the two sites were selected in the experiments: one cluster from
+Lyon's site, Taurus cluster, and three clusters from Nancy's site, Graphene,
+Griffon and Graphite. Each one of these clusters has homogeneous nodes inside, while nodes from different clusters are heterogeneous in many aspects such as: computing power, power consumption, available
+frequency ranges and local network features: the bandwidth and the latency. Table \ref{table:grid5000} shows
+the details characteristics of these four clusters. Moreover, the dynamic powers were computed using the equation (\ref{eq:pdyn}) for all the nodes in the
+selected clusters and are presented in table \ref{table:grid5000}.
+
+
+
