overhead and works without training or profiling. It uses a new energy model
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
- energy consumption on average by \np[\%]{30} while the performance is only degraded
- on average by \np[\%]{3.2}. Finally, the algorithm is
+ running the NAS parallel benchmarks. The experiments on 16 nodes, distributed on three clusters, show that it reduces on average the
+ energy consumption by \np[\%]{30} while the performance is on average only degraded
+ by \np[\%]{3.2}. Finally, the algorithm is
compared to an existing method. The comparison results show that it outperforms the
latter in terms of energy consumption reduction and performance.
\end{abstract}
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 frequencies selecting algorithm was proposed to reduce
+\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
-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,
+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
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 model computes the maximum computation time with scaling factor
-from each node added to the communication time of the slowest node in the slowest cluster $h$.
+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.
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
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}
+\subsection{Grid'5000 architecture and power consumption}
\label{sec.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,
+Grid'5000~\cite{grid5000} is a large-scale testbed that consists of ten sites distributed all over 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
+Each site of the grid is composed of a 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 $\Pmax[jx]$. The difference between the two measured power consumption represents the
+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
+\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}).
Therefore, the dynamic power of one core is computed as the difference between the maximum
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 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}).
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,
+Lyon's site, Taurus, 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
+the detailed characteristics of these four clusters. Moreover, the dynamic powers were computed using equation (\ref{eq:pdyn}) for all the nodes in the
selected clusters and are presented in table \ref{table:grid5000}.
\end{figure}
-The energy model and the scaling factors selection algorithm were applied to the NAS parallel benchmarks v3.3 \cite{NAS.Parallel.Benchmarks} and evaluated over grid'5000.
+The energy model and the scaling factors selection algorithm were applied to the NAS parallel benchmarks v3.3 \cite{NAS.Parallel.Benchmarks} and evaluated over Grid'5000.
The benchmark suite contains seven applications: CG, MG, EP, LU, BT, SP and FT. These applications have different computations and communications ratios and strategies which make them good testbed applications to evaluate the proposed algorithm and energy model.
-The benchmarks have seven different classes, S, W, A, B, C, D and E, that represent the size of the problem that the method solves. In this work, the class D was used for all benchmarks in all the experiments presented in the next sections.
+The benchmarks have seven different classes, S, W, A, B, C, D and E, that represent the size of the problem that the method solves. In this work, class D was used for all benchmarks in all the experiments presented in the next sections.
to the NAS parallel benchmarks are presented.
As mentioned previously, the experiments
-were conducted over two sites of grid'5000, Lyon and Nancy sites.
+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
via a long distance network.
-\item In the second scenario nodes from three clusters that are located in one site, Nancy site.
+\item In the second scenario nodes from three clusters located in one site, Nancy site, were selected.
\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
+for 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.
+is very low due to the higher communication times which reduce 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 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.
+16 and 32 nodes for each scenario. The number of participating computing nodes from each cluster
+is 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]
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.
+presented in 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.
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
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
+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
-benchmarks being executed. The results of the benchmarks CG, MG, BT and FT show more
+benchmarks being executed. The results of 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 their computations to communications ratio is not affected by the increase of the number of local communications.
\begin{figure}
\centering
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
+scenario, except for the EP benchmark which has no communication. 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 which is more powerful.
-Therefore, the energy saving of EP benchmarks are bigger in the two sites scenario due
+in the one site scenario, the graphite cluster is selected but in the two sites scenario
+this cluster is replaced with the Taurus cluster which is more powerful.
+Therefore, the energy savings of the EP benchmark are bigger in the two sites scenario due
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
The performance degradation percentage for the benchmarks running on two sites with
16 or 32 nodes is on average equal to 8.3\% or 4.7\% respectively.
For this scenario, the proposed scaling algorithm selects smaller frequencies for the executions with 32 nodes without significantly degrading their performance because the communication times are higher with 32 nodes which results in smaller computations to communications ratio. On the other hand, the performance degradation percentage for the benchmarks running on one site with
-16 or 32 nodes is on average equal to 3.2\% or 10.6\% respectively. In opposition to the two sites scenario, when the number of computing nodes is increased in the one site scenario, the performance degradation percentage is increased. Therefore, doubling the number of computing
+16 or 32 nodes is on average equal to 3.2\% or 10.6\% respectively. In contrary to the two sites scenario, when the number of computing nodes is increased in the one site scenario, the performance degradation percentage is increased. Therefore, doubling the number of computing
nodes when the communications occur in high speed network does not decrease the computations to
communication ratio.
core per node and multi-cores nodes are shown in Table \ref{table:sen-mc}.
The energy consumptions and execution times of running the class D of the NAS parallel
benchmarks over these four different scenarios are presented
-in the figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.
+in figures \ref{fig:eng-cons-mc} and \ref{fig:time-mc} respectively.
\begin{table}[]
\centering
scenarios because there are no or small communications. 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 two scenarios are presented in the figure \ref{fig:eng-s-mc}.
+The energy saving percentages of all NAS benchmarks running over these two scenarios are presented in figure \ref{fig:eng-s-mc}.
The figure shows that the energy saving percentages in the one
core and the multi-cores scenarios
are approximately equivalent, on average they are equal to 25.9\% and 25.1\% respectively.
figure \ref{fig:per-d-mc}. It shows that the performance degradation percentages is 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 is lower because the computations to communications ratio is smaller than the ratio of the other scenario.
The tradeoff distance percentages of the NAS benchmarks over the two scenarios are presented
-in the figure \ref{fig:dist-mc}. These tradeoff distance 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 tradeoff distance percentages are on average bigger over the multi-cores scenario (17.6\%) than over the one core per node scenario (15.3\%).
+in figure \ref{fig:dist-mc}. These tradeoff distance 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 tradeoff distance percentages are on average bigger over the multi-cores scenario (17.6\%) than over the one core per node scenario (15.3\%).
The aim of this section is to evaluate the scaling algorithm while assuming different values of static powers.
In addition to the previously used percentage of static power, two new static power ratios, 10\% and 30\% of the measured dynamic power of the core, are used in this section.
The experiments have been executed with these two new static power scenarios over the one site one core per node scenario.
-In these experiments, the class D of the NAS parallel benchmarks are executed over Nancy's site. 16 computing nodes from the three clusters, Graphite, Graphene and Griffon, where used in this experiment.
+In these experiments, class D of the NAS parallel benchmarks are executed over the Nancy site. 16 computing nodes from the three clusters, Graphite, Graphene and Griffon, where used in this experiment.
\begin{figure}
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 the 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 tradeoff distance percentage for the NAS benchmarks with these three static power scenarios
-are presented in the figure \ref{fig:dist}.
+are presented in figure \ref{fig:dist}.
It shows that the best tradeoff
distance percentage is obtained with the 10\% static power scenario and this percentage
is decreased for the other two scenarios because the scaling algorithm had selected different frequencies according to the static power values.
In the EP benchmark, the energy saving, performance degradation and tradeoff
-distance percentages for the these static power scenarios are not significantly different because there is no communication in this benchmark. Therefore, the static power is only consumed during computation and the proposed scaling algorithm selects similar frequencies for the three scenarios. On the other hand, for the rest of the benchmarks, the scaling algorithm selects the values of the frequencies according to the communication times of each benchmark because the static energy consumption increases proportionally to the communication times.
+distance percentages for these static power scenarios are not significantly different because there is no communication in this benchmark. Therefore, the static power is only consumed during computation and the proposed scaling algorithm selects similar frequencies for the three scenarios. On the other hand, for the rest of the benchmarks, the scaling algorithm selects the values of the frequencies according to the communication times of each benchmark because the static energy consumption increases proportionally to the communication times.
-\subsection{The comparison of the proposed frequencies selecting algorithm }
+\subsection{Comparison of the proposed frequencies selecting algorithm }
\label{sec.compare_EDP}
-Finding the frequencies that gives the best tradeoff between the energy consumption and the performance for a parallel
+Finding the frequencies that give the best tradeoff between the energy consumption and the performance for a parallel
application is not a trivial task. Many algorithms have been proposed to tackle this problem.
In this section, the proposed frequencies selecting algorithm is compared to a method that uses the well known energy and delay product objective function, $EDP=energy \times delay$, that has been used by many researchers \cite{EDP_for_multi_processors,Energy_aware_application_scheduling,Exploring_Energy_Performance_TradeOffs}.
This objective function was also used by Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS} where they select the frequencies that minimize the EDP product and apply them with DVFS operations to the multi-cores
Finally, the resulting EDP algorithm is an exhaustive search algorithm that tests all the possible frequencies, starting from the initial frequencies (upper bound),
and selects the vector of frequencies that minimize the EDP product.
-Both algorithms were applied to the class D of the NAS benchmarks over 16 nodes.
+Both algorithms were applied to class D of the NAS benchmarks over 16 nodes.
The participating computing nodes are distributed according to the two scenarios described in section \ref{sec.res}.
The experimental results, the energy saving, performance degradation and tradeoff distance percentages, are
presented in the figures \ref{fig:edp-eng}, \ref{fig:edp-perf} and \ref{fig:edp-dist} respectively.
maximizes the energy saving and the performance at the same time.
Moreover, the proposed scaling algorithm gives the same weight for these two metrics.
Whereas, the EDP algorithm gives sometimes negative tradeoff values for some benchmarks in the two sites scenarios.
-These negative tradeoff values mean that the performance degradation percentage is higher than energy saving percentage.
+These negative tradeoff values mean that the performance degradation percentage is higher than the energy saving percentage.
The high positive values of the tradeoff distance percentage mean that the energy saving percentage is much higher than the performance degradation percentage.
The time complexity of both Maxdist and EDP algorithms are $O(N \cdot M \cdot F)$ and
$O(N \cdot M \cdot F^2)$ respectively, where $N$ is the number of the clusters, $M$ is the number of nodes and $F$ is the
\section{Conclusion}
\label{sec.concl}
-This paper has presented a new online frequencies selection algorithm.
+This paper presents a new online frequencies selection algorithm.
The algorithm selects the best vector of
frequencies that maximizes the tradeoff distance
between the predicted energy consumption and the predicted execution time of the distributed
is used by the proposed algorithm to predict the energy consumption
of the distributed iterative message passing application running over a grid architecture.
To evaluate the proposed method on a real heterogeneous grid platform, it was applied on the
- 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 3.2\% 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 or use multi-cores per node architecture or consume different static power values. The algorithm selects different vector of frequencies according to the
+ NAS parallel benchmarks and the class D instance was executed over the Grid'5000 testbed platform.
+ The experiments on 16 nodes, distributed over three clusters, showed that the algorithm on average reduces by 30\% the energy consumption
+for all the NAS benchmarks while on average only degrading by 3.2\% the performance.
+The Maxdist algorithm was also evaluated in different scenarios that vary in the distribution of the computing nodes between different clusters' sites or use multi-cores per node architecture or consume different static power values. The algorithm selects different vectors 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
