\maketitle
\begin{abstract}
-
+Green computing emphasizes the importance of energy conservation, minimizing the negative impact
+on the environment while achieving high performance and minimizing operating costs. So, energy reduction
+process in a high performance clusters it can be archived using dynamic voltage and frequency
+scaling (DVFS) technique, through reducing the frequency of a CPU. Using DVFS to lower levels
+result in a high increase in performance degradation ratio. Therefore selecting the best frequencies
+must give the best possible tradeoff between the energy and the performance of parallel program.
+
+In this paper we present a new online heterogeneous scaling algorithm that selects the best vector
+of frequency scaling factors. These factors give the best tradeoff between the energy saving and the
+performance degradation. The algorithm has small overhead and works without training and profiling.
+We developed a new energy model for distributed iterative application running on heterogeneous cluster.
+The proposed algorithm experimented on Simgrid simulator that applying the NAS parallel benchmarks.
+It reduces the energy consumption up to 35\% while limits the performance degradation as much as possible.
\end{abstract}
\section{Introduction}
\label{sec.intro}
-Modern processors continue increasing in a performance.
-The CPUs constructors are competing to achieve maximum number
+Modern processors continue increasing in performance,
+the CPUs constructors are competing to achieve maximum number
of floating point operations per second (FLOPS).
Thus, the energy consumption and the heat dissipation are increased
drastically according to this increase. Because the number of FLOPS
-is linearly related to the power consumption of a CPU
+is more related to the power consumption of a CPU
~\cite{Luley_Energy.efficiency.evaluation.and.benchmarking}.
-As an example of the more power hungry cluster, Tianhe-2 became in
+As an example of the most power hungry cluster, Tianhe-2 became in
the top of the Top500 list in June 2014 \cite{TOP500_Supercomputers_Sites}.
It has more than 3 millions of cores and consumed more than 17.8 megawatts.
Moreover, according to the U.S. annual energy outlook 2014
influences. Therefore, a green computing clusters with maximum number of
FLOPS per watt are required nowadays. For example, the GSIC center of Tokyo,
became the top of the Green500 list in June 2014 \cite{Green500_List}.
-This platform has more than four thousand of MFLOPS per watt. Dynamic
+This heterogeneous platform has more than four thousand of MFLOPS per watt. Dynamic
voltage and frequency scaling (DVFS) is a process used widely to reduce the energy
-consumption of the processor. In a heterogeneous clusters enabled DVFS, many researchers
+consumption of the processor. In heterogeneous clusters enabled DVFS, many researchers
used DVFS in a different ways. DVFS can be minimized the energy consumption
-but it leads to a disadvantage due to increase in performance degradation.
+but it leads to a disadvantage due to the increase in performance degradation.
Therefore, researchers used different optimization strategies to overcame
this problem. The best tradeoff relation between the energy reduction and
performance degradation ratio is became a key challenges in a heterogeneous
\section{Related works}
\label{sec.relwork}
-Energy reduction process for a high performance clusters recently performed using
+Energy reduction process for high performance clusters recently performed using
dynamic voltage and frequency scaling (DVFS) technique. DVFS is a technique enabled
-in a modern processors to scaled down both of the voltage and the frequency of
+in modern processors to scaled down both of the voltage and the frequency of
the CPU while it is in the computing mode to reduce the energy consumption. DVFS is
also allowed in the graphical processors GPUs, to achieved the same goal. Applying
DVFS has a dramatical side effect if it is applied to minimum levels to gain more
-energy reduction, producing a high percentage of performance degradations for the
+energy reduction, producing a high percentage of performance degradations for the
parallel applications. Many researchers used different strategies to solve this
nonlinear problem for example in
~\cite{Hao_Learning.based.DVFS,Dhiman_Online.Learning.Power.Management}, their methods
add big overheads to the algorithm to select the suitable frequency.
In this paper we present a method
-to find the optimal set of frequency scaling factors for a heterogeneous cluster to
-simultaneously optimize both the energy and the execution time without adding a big
-overhead. This work is developed from our previous work of a homogeneous cluster~\cite{Our_first_paper}.
+to find the optimal set of frequency scaling factors for heterogeneous cluster to
+simultaneously optimize both the energy and the execution time without adding big
+overhead. This work is developed from our previous work of homogeneous cluster~\cite{Our_first_paper}.
Therefore we are interested to present some works that concerned the heterogeneous clusters
enabled DVFS. In general, the heterogeneous cluster works fall into two categorizes:
GPUs-CPUs heterogeneous clusters and CPUs-CPUs heterogeneous clusters. In GPUs-CPUs
-heterogeneous clusters some parallel tasks executed on a GPUs and the others executed
-on a CPUs. As an example of this works, Luley et al.
+heterogeneous clusters some parallel tasks executed on GPUs and the others executed
+on CPUs. As an example of this works, Luley et al.
~\cite{Luley_Energy.efficiency.evaluation.and.benchmarking}, proposed a heterogeneous
cluster composed of Intel Xeon CPUs and NVIDIA GPUs. Their main goal is to determined the
energy efficiency as a function of performance per watt, the best tradeoff is done when the
performance per watt function is maximized. In the work of Kia Ma et al.
-~\cite{KaiMa_Holistic.Approach.to.Energy.Efficiency.in.GPU-CPU}, They developed a scheduling
+~\cite{KaiMa_Holistic.Approach.to.Energy.Efficiency.in.GPU-CPU}, they developed a scheduling
algorithm to distributed different workloads proportional to the computing power of the node
-to be executed on a CPU or a GPU, emphasize all tasks must be finished in the same time.
+to be executed on CPU or GPU, emphasize all tasks must be finished in the same time.
Recently, Rong et al.~\cite{Rong_Effects.of.DVFS.on.K20.GPU}, Their study explain that
a heterogeneous clusters enabled DVFS using GPUs and CPUs gave better energy and performance
efficiency than other clusters composed of only CPUs.
The CPUs-CPUs heterogeneous clusters consist of number of computing nodes all of the type CPU.
Our work in this paper can be classified to this type of the clusters.
-As an example of this works see Naveen et al.~\cite{Naveen_Power.Efficient.Resource.Scaling} work,
+As an example of these works see Naveen et al.~\cite{Naveen_Power.Efficient.Resource.Scaling} work,
They developed a policy to dynamically assigned the frequency to a heterogeneous cluster.
The goal is to minimizing a fixed metric of $energy*delay^2$. Where our proposed method is automatically
optimized the relation between the energy and the delay of the iterative applications.
their algorithm divided the executed tasks into two types: the critical and
non critical tasks. The algorithm scaled down the frequency of the non critical tasks
as function to the amount of the slack and communication times that
-have with maximum of performance degradation percentage of 10\%. In our method there is no
+have with maximum of performance degradation percentage less than 10\%. In our method there is no
fixed bounds for performance degradation percentage and the bound is dynamically computed
according to the energy and the performance tradeoff relation of the executed application.
There are some approaches used a heterogeneous cluster composed from two different types
iterative application. Greedy dynamic approach used by Chen et al.~\cite{Chen_DVFS.under.quality.of.service.requirements},
minimized the power consumption of a heterogeneous severs with time/space complexity, this approach
had considerable overhead. In our proposed scaling algorithm has very small overhead and
-it is works without any previous analysis for the application time complexity.
+it is works without any previous analysis for the application time complexity. The primary
+contributions of our paper are :
+\begin{enumerate}
+\item It is presents a new online heterogeneous scaling algorithm which has very small
+ overhead and not need for any training and profiling.
+\item It is develops a new energy model for iterative distributed applications running over
+ a heterogeneous clusters, taking into account the communication and slack times.
+\item The proposed scaling algorithm predicts both the energy and the execution time
+ of the iterative application.
+\item It demonstrates a new optimization function which maximize the performance and
+ minimize the energy consumption simultaneously.
+
+\end{enumerate}
\section{The performance and energy consumption measurements on heterogeneous architecture}
\label{sec.exe}
power (FLOPS), energy consumption, CPU's frequency range, \dots{} but they all
have the same network bandwidth and latency.
-The overall execution time of a distributed iterative synchronous application
+The overall execution time of a distributed iterative synchronous application
over a heterogeneous platform consists of the sum of the computation time and
the communication time for every iteration on a node. However, due to the
heterogeneous computation power of the computing nodes, slack times might occur
when fast nodes have to wait, during synchronous communications, for the slower
-nodes to finish their computations (see Figure~(\ref{fig:heter}).
+nodes to finish their computations (see Figure~(\ref{fig:heter})).
Therefore, the overall execution time of the program is the execution time of the slowest
task which have the highest computation time and no slack time.
equal to the execution time of one iteration as in EQ(\ref{eq:perf}) multiplied
by the number of iterations of that application.
-This prediction model is based on our model for predicting the execution time of
+This prediction model is developed from our model for predicting the execution time of
message passing distributed applications for homogeneous architectures~\cite{Our_first_paper}.
The execution time prediction model is used in our method for optimizing both
energy consumption and performance of iterative methods, which is presented in the
Rizvandi_Some.Observations.on.Optimal.Frequency} divide the power consumed by a processor into
two power metrics: the static and the dynamic power. While the first one is
consumed as long as the computing unit is turned on, the latter is only consumed during
-computation times. The dynamic power $P_{d}$ is related to the switching
+computation times. The dynamic power $Pd$ is related to the switching
activity $\alpha$, load capacitance $C_L$, the supply voltage $V$ and
operational frequency $F$, as shown in EQ(\ref{eq:pd}).
\begin{equation}
\label{eq:pd}
- P_\textit{d} = \alpha \cdot C_L \cdot V^2 \cdot F
+ Pd = \alpha \cdot C_L \cdot V^2 \cdot F
\end{equation}
-The static power $P_{s}$ captures the leakage power as follows:
+The static power $Ps$ captures the leakage power as follows:
\begin{equation}
\label{eq:ps}
- P_\textit{s} = V \cdot N_{trans} \cdot K_{design} \cdot I_{leak}
+ Ps = V \cdot N_{trans} \cdot K_{design} \cdot I_{leak}
\end{equation}
where V is the supply voltage, $N_{trans}$ is the number of transistors,
$K_{design}$ is a design dependent parameter and $I_{leak}$ is a
to execute a given program can be computed as:
\begin{equation}
\label{eq:eind}
- E_\textit{ind} = P_\textit{d} \cdot Tcp + P_\textit{s} \cdot T
+ E_\textit{ind} = Pd \cdot Tcp + Ps \cdot T
\end{equation}
-where $T$ is the execution time of the program, $T_{cp}$ is the computation
-time and $T_{cp} \leq T$. $T_{cp}$ may be equal to $T$ if there is no
+where $T$ is the execution time of the program, $Tcp$ is the computation
+time and $Tcp \leq T$. $Tcp$ may be equal to $T$ if there is no
communication and no slack time.
The main objective of DVFS operation is to reduce the overall energy consumption~\cite{Le_DVFS.Laws.of.Diminishing.Returns}.
constant $\beta$. This equation is used to study the change of the dynamic
voltage with respect to various frequency values in~\cite{Rauber_Analytical.Modeling.for.Energy}. The reduction
process of the frequency can be expressed by the scaling factor $S$ which is the
-ratio between the maximum and the new frequency as in EQ~(\ref{eq:s}).
+ratio between the maximum and the new frequency as in EQ(\ref{eq:s}).
The CPU governors are power schemes supplied by the operating
system's kernel to lower a core's frequency. we can calculate the new frequency
$F_{new}$ from EQ(\ref{eq:s}) as follow:
The static energy of a processor after scaling its frequency is computed as follows:
\begin{equation}
\label{eq:Estatic}
- E_\textit{s} = P_\textit{s} \cdot (Tcp \cdot S + Tcm)
+ E_\textit{s} = Ps \cdot (Tcp \cdot S + Tcm)
\end{equation}
In the considered heterogeneous platform, each processor $i$ might have different dynamic and
The heterogeneous platform had up to 144 nodes and had nodes from the four types in equal proportions,
for example if a benchmark was executed on 8 nodes, 2 nodes from each type were used. Since the constructors
of CPUs do not specify the dynamic and the static power of their CPUs, for each type of node they were
-chosen proportionally to its computing power (FLOPS). In the initial heterogeneous platform, while computing
+chosen proportionally to its computing power (FLOPS). In the initial heterogeneous platform, while computing
with highest frequency, each node consumed power proportional to its computing power which 80\% of it was
dynamic power and the rest was 20\% for the static power, the same assumption was made in \cite{Our_first_paper,Rauber_Analytical.Modeling.for.Energy}.
Finally, These nodes were connected via an ethernet network with 1 Gbit/s bandwidth.
respectively for all the benchmarks according to the number of used nodes. As shown in the first plot,
the energy saving percentages of the benchmarks MG, LU, BT and FT are decreased linearly when the the
number of nodes is increased. While for the EP and SP benchmarks, the energy saving percentage is not
-affected by the increase of the number of computing nodes, because in these benchmarks there are no
-communications. Finally, the energy saving of the GC benchmark is significantly decreased when the number
+affected by the increase of the number of computing nodes, because in these benchmarks there are little or
+no communications. Finally, the energy saving of the GC benchmark is significantly decreased when the number
of nodes is increased because this benchmark has more communications than the others. The second plot
shows that the performance degradation percentages of most of the benchmarks are decreased when they
run on a big number of nodes because they spend more time communicating than computing, thus, scaling
\subsection{The results for different power consumption scenarios}
-
+\label{sec.compare}
The results of the previous section were obtained while using processors that consume during computation
an overall power which is 80\% composed of dynamic power and 20\% of static power. In this section,
these ratios are changed and two new power scenarios are considered in order to evaluate how the proposed
the work presented in this paper is based on the execution time model. To verify this model, the predicted
execution time was compared to the real execution time over Simgrid for all the NAS parallel benchmarks
running class B on 8 or 9 nodes. The comparison showed that the proposed execution time model is very precise,
-the maximum normalized difference between the predicted execution time and the real execution time is equal
+the maximum normalized difference between the predicted execution time and the real execution time is equal
to 0.03 for all the NAS benchmarks.
Since the proposed algorithm is not an exact method and do not test all the possible solutions (vectors of scaling factors)
table~(\ref{table:platform}), it takes on average \np[ms]{0.04} for 4 nodes and \np[ms]{0.15} on average for 144 nodes
to compute the best scaling factors vector. The algorithm complexity is $O(F\cdot (N \cdot4) )$, where $F$ is the number
of iterations and $N$ is the number of computing nodes. The algorithm needs from 12 to 20 iterations to select the best
-vector of frequency scaling factors that gives the results of the section (\ref{sec.res}).
+vector of frequency scaling factors that gives the results of the sections (\ref{sec.res}) and (\ref{sec.compare}).
\section{Conclusion}
\label{sec.concl}
-
+In this paper, we have presented a new online heterogeneous scaling algorithm
+that selects the best possible vector of frequency scaling factors. This vector
+gives the maximum distance (optimal tradeoff) between the predicted energy and
+the predicted performance curves. In addition, we developed a new energy model for measuring
+and predicting the energy of distributed iterative applications running over heterogeneous
+cluster. The proposed method evaluated on Simgrid/SMPI simulator to built a heterogeneous
+platform to executes NAS parallel benchmarks. The results of the experiments showed the ability of
+the proposed algorithm to changes its behaviour to selects different scaling factors when
+the number of computing nodes and both of the static and the dynamic powers are changed.
+
+In the future, we plan to improve this method to apply on asynchronous iterative applications
+where each task does not wait the others tasks to finish there works. This leads us to develop a new
+energy model to an asynchronous iterative applications, where the number of iterations is not
+known in advance and depends on the global convergence of the iterative system.
\section*{Acknowledgment}
+
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