time of the application running over that processor. Therefore, researchers use
different optimization strategies to select the frequency that gives the best
trade-off between the energy reduction and performance degradation ratio. In
-\cite{Our_first_paper} and \cite{pdsec2015} , a frequency selecting algorithm was proposed to reduce
-the energy consumption of message passing iterative applications running over
-homogeneous and heterogeneous clusters respectively.
-The results of the experiments showed significant energy
-consumption reductions. All the experimental results were conducted over the
-SimGrid simulator \cite{SimGrid}, which offers easy tools to create homogeneous and heterogeneous platforms and runs message passing parallel applications over them. In this paper, a new frequency selecting algorithm,
-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
-minimum performance degradation ratios. The algorithm has a very small overhead,
-works online and does not need any training or profiling.
+\cite{Our_first_paper} and \cite{pdsec2015} , a frequency selecting algorithm
+was proposed to reduce the energy consumption of message passing iterative
+applications running over homogeneous and heterogeneous clusters respectively.
+The results of the experiments showed significant energy consumption
+reductions. All the experimental results were conducted over the SimGrid
+simulator \cite{SimGrid}, which offers easy tools to create homogeneous and
+heterogeneous platforms and runs message passing parallel applications over
+them. %
+\AG{[\dots], which offers easy tools to describe homogeneous and heterogeneous
+ platforms, and to simulate the execution of message passing parallel
+ applications over them.}%
+In this paper, a new frequency selecting algorithm, 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 minimum performance degradation
+ratios. The algorithm has a very small overhead, works online and does not need
+any training or profiling.
This paper is organized as follows: Section~\ref{sec.relwork} presents some
goal was to maximize the energy efficiency of the platform during computation by
maximizing the number of FLOPS per watt generated.
In~\cite{KaiMa_Holistic.Approach.to.Energy.Efficiency.in.GPU-CPU}, Kai Ma et
-al. developed a scheduling algorithm that distributes workloads proportional to
+al. developed a scheduling algorithm that distributes workload proportional to
the computing power of the nodes which could be a GPU or a CPU. All the tasks
must be completed at the same time. In~\cite{Rong_Effects.of.DVFS.on.K20.GPU},
Rong et al. showed that a heterogeneous (GPUs and CPUs) cluster that enables
\item a new online frequency selecting algorithm for heterogeneous grid
platforms. The algorithm has a very small overhead and does not need any
- training or profiling. It uses a new optimization function which
+ training nor profiling. It uses a new optimization function which
simultaneously maximizes the performance and minimizes the energy consumption
of a message passing iterative synchronous application.
heterogeneous computing clusters interconnected via a long distance network which has lower bandwidth
and higher latency than the local networks of the clusters. Each computing cluster in the grid is composed of homogeneous nodes that are connected together via high speed network. Therefore, each cluster has different characteristics such as computing power (FLOPS), energy consumption, CPU's frequency range, network bandwidth and latency.
-\begin{figure}[!t]
- \centering
- \includegraphics[scale=0.6]{fig/commtasks}
- \caption{Parallel tasks on a heterogeneous platform}
- \label{fig:heter}
-\end{figure}
-
The overall execution time of a distributed iterative synchronous application
over a heterogeneous grid consists of the sum of the computation time and
the communication time for every iteration on a node. However, due to the
overall execution time of the program is the execution time of the slowest task
which has the highest computation time and no slack time.
+\begin{figure}[!t]
+ \centering
+ \includegraphics[scale=0.6]{fig/commtasks}
+ \caption{Parallel tasks on a heterogeneous platform}
+ \label{fig:heter}
+\end{figure}
+
Dynamic Voltage and Frequency Scaling (DVFS) is a process, implemented in
modern processors, that reduces the energy consumption of a CPU by scaling
down its voltage and frequency. Since DVFS lowers the frequency of a CPU
tasks must be measured during the first iteration before applying any DVFS
operation. Then the execution time for one iteration of the application with any
vector of scaling factors can be predicted using (\ref{eq:perf}).
+%
\begin{equation}
\label{eq:perf}
\Tnew = \mathop{\max_{i=1,\dots N}}_{j=1,\dots,M}({\TcpOld[ij]} \cdot S_{ij})
+\mathop{\min_{j=1,\dots,M}} (\Tcm[hj])
\end{equation}
-
+%
where $N$ is the number of clusters in the grid, $M$ is the number of nodes in
each cluster, $\TcpOld[ij]$ is the computation time of processor $j$ in the cluster $i$
and $\Tcm[hj]$ is the communication time of processor $j$ in the cluster $h$ during the
-first iteration. the execution time for one iteration is equal to the sum of the maximum computation time for all nodes with the new scaling factors
- and the slowest communication time without slack time during one iteration.
+first iteration. The execution time for one iteration is equal to the sum of the maximum computation time for all nodes with the new scaling factors
+and the slowest communication time without slack time during one iteration.
The latter is equal to the communication time of the slowest node in the slowest cluster $h$.
-It means only the communication time without any slack time is taken into account.
+It means\AG[]{It means that\dots} only the communication time without any slack time is taken into account.
Therefore, the execution time of the iterative application is equal to
the execution time of one iteration as in (\ref{eq:perf}) multiplied by the
number of iterations of that application.
time is normalized by computing the ratio between the new execution time (after
scaling down the frequencies of some processors) and the initial one (with
maximum frequency for all nodes) as follows:
+%
\begin{equation}
\label{eq:pnorm}
\Pnorm = \frac{\Tnew}{\Told}
\end{equation}
-
-
-Where $Tnew$ is computed as in (\ref{eq:perf}) and $Told$ is computed as in (\ref{eq:told})
+%
+where $Tnew$ is computed as in (\ref{eq:perf}) and $Told$ is computed as in (\ref{eq:told}).
+%
\begin{equation}
\label{eq:told}
\Told = \mathop{\max_{i=1,2,\dots,N}}_{j=1,2,\dots,M} (\Tcp[ij]+\Tcm[ij])
\end{equation}
+%
In the same way, the energy is normalized by computing the ratio between the
consumed energy while scaling down the frequency and the consumed energy with
maximum frequency for all nodes:
+%
\begin{equation}
\label{eq:enorm}
\Enorm = \frac{\Ereduced}{\Eoriginal}
\end{equation}
-
-Where $\Ereduced$ is computed using (\ref{eq:energy}) and $\Eoriginal$ is
+%
+where $\Ereduced$ is computed using (\ref{eq:energy}) and $\Eoriginal$ is
computed as in (\ref{eq:eorginal}).
-
-
+%
\begin{equation}
\label{eq:eorginal}
\Eoriginal = \sum_{i=1}^{N} \sum_{j=1}^{M} ( \Pd[ij] \cdot \Tcp[ij]) +
While the main goal is to optimize the energy and execution time at the same
time, the normalized energy and execution time curves do not evolve (increase/decrease) in the same way.
-According to Equations~\ref{eq:pnorm} and \ref{eq:enorm}, the
-vector of frequency scaling factors $S_1,S_2,\dots,S_N$ reduce both the energy
-and the execution time simultaneously. But the main objective is to produce
+According to (\ref{eq:pnorm}) and (\ref{eq:enorm}), the
+vector of frequency scaling factors $S_1,S_2,\dots,S_N$ reduces both the energy
+and the execution time, but the main objective is to produce
maximum energy reduction with minimum execution time reduction.
This problem can be solved by making the optimization process for energy and
distance between the energy curve (\ref{eq:enorm}) and the performance curve
(\ref{eq:pnorm_inv}) over all available sets of scaling factors. This
represents the minimum energy consumption with minimum execution time (maximum
-performance) at the same time, see Figure~\ref{fig:r1} or
+performance) at the same time, see Figure~\ref{fig:r1} and
Figure~\ref{fig:r2}. Then the objective function has the following form:
\begin{equation}
\label{eq:max}
\end{algorithm}
-In this section, the scaling factors selection algorithm for grids, algorithm~\ref{HSA},
+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
energy consumption and maximizing the performance of a message passing
bound until all nodes reach their minimum frequencies or their lower bounds, to compute the overall
energy consumption and performance and selects the optimal vector of the frequency scaling
factors. At each iteration the algorithm determines the slowest node
-according to Equation~\ref{eq:perf} and keeps its frequency unchanged,
+according to Equation~\ref{eq:perf}
+%\AG[]{Be consistent: remove word ``Equation'' and add parentheses around equation number, here and all along the rest of the text.}
+and keeps its frequency unchanged,
while it lowers the frequency of all other nodes by one gear. The new overall
energy consumption and execution time are computed according to the new scaling
factors. The optimal set of frequency scaling factors is the set that gives the
the grid platform the performance is maintained at the beginning of the
plot even if the frequencies of the faster nodes decrease until the computing
power of scaled down nodes are lower than the slowest node. In other words,
+\AG[]{That's not a sentence.}
until they reach the higher bound. It can also be noticed that the higher the
difference between the faster nodes and the slower nodes is, the bigger the
maximum distance between the energy curve and the performance curve is, which results in bigger energy savings.
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 to 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 all the components of a node at a given instant, such as CPU, hard drive, main-board, memory, ... For more details refer to
+the power consumption for each node in those sites. The measured power is the overall consumed power by all the components of a node at a given instant, such as CPU, hard drive, main-board, memory, \dots{} For more details refer to
\cite{Energy_measurement}. In order to correctly 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 consumptions represents the
dynamic power consumption of that core with the maximum frequency, see Figure~\ref{fig:power_cons}.
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 shown on Figure~\ref{fig:grid5000}.
Four clusters from the two sites were selected in the experiments: one cluster from
Lyon's site, Taurus, and three clusters from Nancy's site, Graphene,
\begin{figure}[!t]
\centering
\includegraphics[scale=0.6]{fig/power_consumption.pdf}
+ \AG{I don't understand the labels on the horizontal axis: 10:30:37, 10:30:38,
+ etc.}
\caption{The power consumption by one core from the Taurus cluster}
\label{fig:power_cons}
\end{figure}
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 Plots~\ref{fig:eng_sen} and \ref{fig:time_sen} respectively.
+presented in Figures~\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 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. Moreover, 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).
+scenario. Moreover, 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).\AG{Parse error (cannot understand the previous sentence).}
-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.
+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\AG[]{the communication time?} of the rest of the benchmarks increases when
+using long distance communications between two sites or increasing the number of
+computing nodes.
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 bigger than the communication times which
+than in the second one. Moreover, the frequency selecting algorithm selects smaller frequencies when the computation 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 hand, the increase in the number of computing nodes can
increase the communication times and thus produces less energy saving depending on the
The performance degradation percentages of the NAS benchmarks are presented in
-Figure\ref{fig:per-d-mc}. It shows that the performance degradation percentages are higher for the NAS benchmarks over the one core per node scenario (on average equal to 10.6\%) than over the multi-cores scenario (on average equal to 7.5\%). The performance degradation percentages over the multi-cores scenario are lower because the computations to communications ratios are smaller than the ratios of the other scenario.
+Figure~\ref{fig:per-d-mc}. It shows that the performance degradation percentages are higher for the NAS benchmarks over the one core per node scenario (on average equal to 10.6\%) than over the multi-cores scenario (on average equal to 7.5\%). The performance degradation percentages over the multi-cores scenario are lower because the computations to communications ratios are smaller than the ratios of the other scenario.
The trade-off distances percentages of the NAS benchmarks over the two scenarios are presented
in ~Figure~\ref{fig:dist-mc}. These trade-off distances between energy consumption reduction and performance are used to verify which scenario is the best in both terms at the same time. The figure shows that the trade-off distance percentages are on average bigger over the multi-cores scenario (17.6\%) than over the one core per node scenario (15.3\%).
\end{figure}
The energy saving percentages of the NAS benchmarks with the three static power scenarios are presented
-in Figure\ref{fig:eng_sen}. This figure shows that the 10\% of static power scenario
+in Figure~\ref{fig:eng_sen}. This figure shows that the 10\% of static power scenario
gives the biggest energy saving percentages in comparison to the 20\% and 30\% static power
scenarios. The small value of the static power consumption makes the proposed
scaling algorithm select smaller frequencies for the CPUs.
These smaller frequencies reduce the dynamic energy consumption more than increasing the consumed static energy which gives less overall energy consumption.
The energy saving percentages of the 30\% static power scenario is the smallest between the other scenarios, because the scaling algorithm selects bigger frequencies for the CPUs which increases the energy consumption. Figure \ref{fig:fre-pow} demonstrates that the proposed scaling algorithm selects the best frequency scaling factors according to the static power consumption ratio being used.
-The performance degradation percentages are presented in Figure\ref{fig:per-pow}.
+The performance degradation percentages are presented in Figure~\ref{fig:per-pow}.
The 30\% static power scenario had less performance degradation percentage because the scaling algorithm
had selected big frequencies for the CPUs. While,
the inverse happens in the 10\% and 20\% scenarios because the scaling algorithm had selected CPUs' frequencies smaller than those of the 30\% scenario. The trade-off distance percentage for the NAS benchmarks with these three static power scenarios
