X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/mpi-energy2.git/blobdiff_plain/300741fe3069be22399dd00ac07a1b213375a604..fd1e7fdfccf97deb22fc8f1c1cbc8979908d5b80:/Heter_paper.tex?ds=inline

diff --git a/Heter_paper.tex b/Heter_paper.tex
index 31a476a..7bd1de4 100644
--- a/Heter_paper.tex
+++ b/Heter_paper.tex
@@ -5,6 +5,7 @@
 \usepackage[english]{babel}
 \usepackage{algpseudocode}
 \usepackage{graphicx}
+\usepackage{algorithm}
 \usepackage{subfig}
 \usepackage{amsmath}
 
@@ -144,7 +145,7 @@ vector of scaling factors can be predicted using EQ (\ref{eq:perf}).
 \end{equation}
 where $TcpOld_i$ is the computation time  of processor $i$ during the first iteration and $MinTcm$ is the communication time of the slowest processor from 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, it means  only the
- communication time without any slack time. Therefore, we can consider the execution time of the iterative application is the execution time of one iteration as in EQ(\ref{eq:perf}) multiply by the number of iterations of the application.
+ communication time without any slack time. Therefore, we can consider the execution time of the iterative application is 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 message passing distributed applications for homogeneous architectures~\cite{45}. 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 following sections.
 
@@ -229,8 +230,8 @@ Reducing the frequencies of the processors according to the vector of
 scaling factors $(S_1, S_2,\dots, S_N)$ may degrade the performance of the
 application and thus, increase the static energy because the execution time is
 increased~\cite{36}. We can measure the overall energy consumption for the iterative 
-application by measuring  the energy consumption from one iteration as in EQ(\ref{eq:energy}) multiply by 
-the number of iterations of the iterative application.
+application by measuring  the energy consumption for one iteration as in EQ(\ref{eq:energy}) multiplied by 
+the number of iterations of that application.
 
 
 \section{Optimization of both energy consumption and performance}
@@ -319,28 +320,42 @@ Then we can select the optimal set of scaling factors that satisfies EQ~(\ref{eq
 work with any energy model or any power values for each node (static and dynamic powers).
 However, the most energy reduction gain can be achieved when the energy curve has a convex form as shown in~\cite{15,3,19}.
 
-\section{The heterogeneous scaling algorithm }
+\section{The scaling factors selection algorithm for heterogeneous platforms }
 \label{sec.optim}
 
-In this section we are proposed a heterogeneous scaling algorithm,
-(figure~\ref{HSA}), that selects the optimal vector of the frequency scaling factors from each
-node.  The algorithm is numerates the suitable range of available vectors of the frequency scaling
-factors for all node in a heterogeneous cluster, returns a vector of optimal
-frequency scaling factors define as $Sopt_1,Sopt_2,\dots,Sopt_N$. Using heterogeneous cluster 
-has different computing powers is produces different workloads for each node. Therefore, the fastest nodes waiting at the
-synchronous barrier for the slowest nodes to finish there work as in figure 
-(\ref{fig:heter}). Our algorithm is takes into account these imbalanced workloads
-when is starts to search for selecting the best vector of the frequency scaling factors. So, the
-algorithm is selects the initial frequencies values for each node proportional
-to the times of computations that gathered from the first iteration. As an
-example in figure (\ref{fig:st_freq}), the algorithm don't tests the first
-frequencies of the computing nodes until  their frequencies  is converge to the
-frequency of the slowest node. The operational frequency gear not surly related to computing power, therefore the algorithm 
-rapprochement the frequencies according to the computing power of each frequency. Moreover, If the algorithm is starts to test change the
-frequency of the slowest node from the first gear, we are loosing the performance and
-then the best trade-off relation (the maximum distance) be not reachable. This case will be similar
-to a homogeneous cluster when all nodes scale down their frequencies together from
-the first gears. Therefore, there is a small distance between the energy and
+In this section we  propose algorithm~\ref{HSA}) which selects the frequency scaling factors vector that gives the best trade-off between minimizing the energy consumption  and maximizing the performance of a message passing synchronous iterative application executed on a heterogeneous platform.  
+IT works online during the execution time of the iterative message passing program.  It uses information gathered during the first iteration such as the computation time and the communication time in one iteration for each node. The algorithm is executed  after the first iteration and returns a vector of optimal frequency scaling factors   that satisfies the objective function EQ(\ref{eq:max}). The program apply DVFS operations to change the frequencies of the CPUs according to the computed scaling factors.  This algorithm is called just once during the execution of the program. Algorithm~(\ref{dvfs}) shows where and when the proposed scaling algorithm is called in the iterative MPI program.
+
+
+The nodes in a heterogeneous platform have different computing powers, thus while executing message passing iterative synchronous applications, fast nodes have to wait for the slower ones to finish their computations before being able to synchronously communicate with them as in figure (\ref{fig:heter}). These periods are called idle or slack times.
+Our algorithm takes into account this problem and tries to reduce these slack times when selecting the frequency scaling factors vector. At first, it selects initial frequency scaling factors that increase the execution times of fast nodes and  minimize the  differences between  the  computation times of fast and slow nodes. The value of the initial frequency scaling factor  for each node is inversely proportional to its computation time that was gathered from the first iteration. These initial frequency scaling factors are computed as   a ratio between the computation time of the slowest node and the computation time of the node $i$ as follows:
+\begin{equation}
+  \label{eq:Scp}
+ Scp_{i} = \frac{\max_{i=1,2,\dots,N}(Tcp_i)}{Tcp_i}
+\end{equation}
+Using the initial  frequency scaling factors computed in EQ(\ref{eq:Scp}), the algorithm computes the initial frequencies for all nodes as a ratio between the 
+maximum frequency of node $i$  and the computation scaling factor $Scp_i$ as follows:
+\begin{equation}
+  \label{eq:Fint}
+ F_{i} = \frac{Fmax_i}{Scp_i},~{i=1,2,\cdots,N}
+\end{equation}
+If the computed initial frequency for a node is not available in the gears of that node, the computed initial frequency is replaced by the nearest available frequency.
+In  figure (\ref{fig:st_freq}), the nodes are  sorted by their computing powers in ascending order and the frequencies of the faster nodes are scaled down according to the computed initial frequency scaling factors. The resulting new frequencies are colored in blue in  figure (\ref{fig:st_freq}). This set of frequencies can be considered as a higher bound for the search space of the optimal set of frequencies because selecting frequency scaling factors higher than the higher bound will not improve the performance of the application and it will increase its overall energy consumption. Therefore the frequency selecting factors algorithm starts its search method from these initial frequencies and takes a downward search direction. The algorithm iterates on all left frequencies, from the higher bound until all nodes reach their minimum frequencies, to compute their overall energy consumption and performance, and select the optimal frequency scaling factors vector. At each iteration the algorithm determines the slowest node according to EQ(\ref{eq:perf}) 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 highest distance according to  the objective function EQ(\ref{eq:max}).
+
+  
+
+
+
+This algorithm has a small
+execution time: for a heterogeneous cluster composed of four different types of
+nodes having the characteristics presented in table~(\ref{table:platform}), it  
+takes \np[ms]{0.04} on average for 4 nodes and \np[ms]{0.15} on average for 144
+nodes.  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 on average from 12 to 20 iterations to selects the best vector of frequency scaling factors that give the results of the next section. 
+
+
+Therefore, there is a small distance between the energy and
 the performance curves in a homogeneous cluster compare to heterogeneous one, for example see the figure(\ref{fig:r1}) and figure(\ref{fig:r2}) .  Then the
 algorithm starts to search for the optimal vector of the frequency scaling factors from the selected initial 
 frequencies until all node reach their minimum frequencies.
@@ -352,18 +367,8 @@ frequencies until all node reach their minimum frequencies.
 \end{figure}
 
 
-To compute the initial frequencies in each node, the algorithm firstly needs to compute the computation scaling factors $Scp_i$ of the node $i$. Each one of these factors is represents a ratio between the computation time of the slowest node and the computation time of the node $i$ as follow:
-\begin{equation}
-  \label{eq:Scp}
- Scp_{i} = \frac{\max_{i=1,2,\dots,N}(Tcp_i)}{Tcp_i}
-\end{equation}
-Depending on the initial computation scaling factors EQ(\ref{eq:Scp}), the algorithm computes the initial frequencies for all nodes as a ratio between the 
-maximum frequency of node $i$  and the computation scaling factor $Scp_i$ as follow:
-\begin{equation}
-  \label{eq:Fint}
- F_{i} = \frac{Fmax_i}{Scp_i},~{i=1,2,\cdots,N}
-\end{equation}
-\begin{figure}[tp]
+
+\begin{algorithm}
   \begin{algorithmic}[1]
     % \footnotesize
     \Require ~
@@ -406,24 +411,9 @@ maximum frequency of node $i$  and the computation scaling factor $Scp_i$ as fol
   \end{algorithmic}
   \caption{Heterogeneous scaling algorithm}
   \label{HSA}
-\end{figure}
-When the initial frequencies are computed, the algorithm numerates all available
-frequency scaling factors starting from the initial frequencies until all nodes reach their
-minimum frequencies. At each iteration the algorithm determine the slowest node according to EQ(\ref{eq:perf}). 
-It is remains the frequency of the slowest node without change, while it is scales down the frequency of the other
-nodes. This is improved the execution time degradation and energy saving in the same time.  
-The proposed algorithm works online during the execution time of the iterative MPI program.  It is 
-returns a vector of optimal frequency scaling factors  depending on the
-objective function EQ(\ref{eq:max}). The program changes the new frequencies of
-the CPUs according to the computed scaling factors.  This algorithm has a small
-execution time: for a heterogeneous cluster composed of four different types of
-nodes having the characteristics presented in table~(\ref{table:platform}), it  
-takes \np[ms]{0.04} on average for 4 nodes and \np[ms]{0.15} on average for 144
-nodes.  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 on average from 12 to 20 iterations to selects the best vector of frequency scaling factors that give the results of the next section. It is called just once during the execution of the program.  The DVFS algorithm in figure~(\ref{dvfs}) shows where
-and when the proposed scaling algorithm is called in the iterative MPI program.
-\begin{figure}[tp]
+\end{algorithm}
+
+\begin{algorithm}
   \begin{algorithmic}[1]
     % \footnotesize
     \For {$k=1$ to \textit{some iterations}}
@@ -441,29 +431,18 @@ and when the proposed scaling algorithm is called in the iterative MPI program.
   \end{algorithmic}
   \caption{DVFS algorithm}
   \label{dvfs}
-\end{figure}
+\end{algorithm}
 
 \section{Experimental results}
 \label{sec.expe}
+To evaluate the efficiency and the overall energy consumption reduction of algorithm~\ref{HSA}), it was applied to the NAS parallel benchmarks NPB v3.3 
+\cite{44}. The experiments were executed on the simulator SimGrid/SMPI
+v3.10~\cite{casanova+giersch+legrand+al.2014.versatile} which offers easy tools to create a heterogeneous platform and run message passing applications over it. The heterogeneous platform that was used in the experiments, had one core per node because just one process was executed per node. The heterogeneous platform  was composed of four types of nodes. Each type of nodes had different characteristics such as the maximum CPU frequency, the number of
+available frequencies and the computational power, see table
+(\ref{table:platform}). The characteristics of these different types of  nodes are inspired   from the specifications of real Intel processors. 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 with highest frequency, each node  consumed power proportional to its computing power which 80\% of it was dynamic power and the rest was 20\% was static power, the same assumption  was made in \cite{45,3}. Finally, These nodes were connected via an ethernet network with 1 Gbit/s bandwidth.
+
 
-The experiments of this work are executed on the simulator SimGrid/SMPI
-v3.10~\cite{casanova+giersch+legrand+al.2014.versatile}. We are configure the
-simulator to use a heterogeneous cluster with one core per node. The proposed
-heterogeneous cluster has four different types of nodes. Each node in the cluster
-has different characteristics such as the maximum frequency speed, the number of
-available frequencies and dynamic and static powers values, see table
-(\ref{table:platform}). These different types of processing nodes are simulate some
-real Intel processors. The maximum number of nodes that supported by the cluster
-is 144 nodes according to characteristics of some MPI programs of the NAS
-benchmarks that used. We are use the same number from each type of nodes when we
-run the iterative MPI programs, for example if  we are execute the program on 8 node, there
-are 2 nodes from each type participating in the computation. The dynamic and
-static power values is different from one type to other. Each node has a dynamic
-and static power values proportional to their computing power (FLOPS), for more
-details see the Intel data sheets in \cite{47}.  Each node has a percentage of
-80\% for dynamic power and 20\% for static power of the total power
-consumption of a CPU, the same assumption is made in \cite{45,3}. These nodes are
-connected via an ethernet network with 1 Gbit/s bandwidth.
+\textbf{modify the characteristics table by replacing the similar column with the computing power of the different types of nodes in flops}
 \begin{table}[htb]
   \caption{Heterogeneous nodes characteristics}
   % title of Table
@@ -496,11 +475,9 @@ connected via an ethernet network with 1 Gbit/s bandwidth.
 \subsection{The experimental results of the scaling algorithm}
 \label{sec.res}
 
-The proposed algorithm was applied to seven MPI programs of the NAS benchmarks (EP, CG, MG, FT, BT, LU and SP) NPB v3.3 
-\cite{44},  which were run with three classes (A, B and C).
-In this experiments we are interested to run the class C, the biggest class compared to A and B, on different number of 
-nodes, from 4 to 128 or 144 nodes according to the type of the iterative MPI program.  Depending on the proposed energy consumption model EQ(\ref{eq:energy}),
- we are measure the energy consumption for all NAS MPI programs. The dynamic and static power values are used under the same assumption used by \cite{45,3}, we are used a percentage of 80\% for dynamic power and 20\% for static of the total power consumption of a CPU. The heterogeneous nodes in table (\ref{table:platform}) have different  simulated computing power (FLOPS), ranked from the node of type 1 with smaller computing power (FLOPS) to the highest computing power (FLOPS) for node of type 4. Therefore, the power values are used proportionally increased from nodes of type 1 to nodes of type 4 that with highest computing power. Then, we are used an assumption that the power consumption is increased linearly when the computing power (FLOPS) of the processor is increased, see \cite{48}.   
+The proposed algorithm was applied to the seven parallel NAS benchmarks (EP, CG, MG, FT, BT, LU and SP) and the benchmarks were executed with the three classes: A,B and C. However, due to the lack of space in this paper, only the results of the biggest class, C, are presented while being run on different number of nodes, ranging  from 4 to 128 or 144 nodes depending on the benchmark being executed. 
+
+ 
  
 \begin{table}[htb]
   \caption{Running NAS benchmarks on 4 nodes }
@@ -664,9 +641,12 @@ nodes, from 4 to 128 or 144 nodes according to the type of the iterative MPI pro
   \end{tabular}
   \label{table:res_128n}
 \end{table}
+The overall energy consumption was computed for each instance according to the energy consumption  model EQ(\ref{eq:energy}), with and without applying the algorithm. The execution time was also measured for all these experiments. Then, the energy saving and performance degradation percentages were computed for each instance. The results are presented in tables (\ref{table:res_4n}, \ref{table:res_8n}, \ref{table:res_16n}, \ref{table:res_32n}, \ref{table:res_64n} and \ref{table:res_128n}).
+These tables  show the experimental results for running the NAS parallel benchmarks on different number of nodes. The experiments show that the algorithm reduce significantly the energy consumption (up to 35\%) and tries to limit the performance degradation. They also show that the  energy saving percentage is decreased  when the number of the computing nodes is increased. This reduction is due to the increase of the communication times compared to the execution times when the benchmarks are run over a high number of nodes. Indeed, the benchmarks with the same class, C, are executed on different number of nodes, so the computation required for each iteration is divided by the number of computing nodes.   On the other hand, more communications are required when increasing the number of nodes so the static energy is increased linearly according to the communication time and the dynamic power is less relevant in the overall energy consumption. Therefore, reducing the frequency with algorithm~\ref{HSA}) have less effect in reducing the overall energy savings. It can also be noticed that for the benchmarks EP and SP that contain little or no communications,  the energy savings are not significantly affected with the high number of nodes. No experiments were conducted using bigger classes such as D, because they require a lot of memory(more than 64GB) when being executed by the simulator on one machine.
+The maximum distance between the normalized energy curve and the normalized performance for each instance is also shown in the result tables. It is decreased in the same way as the energy saving percentage. The tables also show that the performance degradation percentage is not significantly increased when the number of computing nodes is increased because the computation times are small when compared to the communication times.  
 
-The results of applying the proposed scaling algorithm to the NAS benchmarks is demonstrated in tables (\ref{table:res_4n}, \ref{table:res_8n}, \ref{table:res_16n}, \ref{table:res_32n}, \ref{table:res_64n} and \ref{table:res_128n}). These tables are show the experimental results for running the NAS benchmarks on different number of nodes. In general the energy saving percent is decreased  when the number of the computing nodes is increased. Also the distance is decreased by the same direction of the energy saving. This because when we are run the iterative MPI programs on a big number of nodes the communications times is increased, so the static energy is increased linearly to these times. The tables also show that the performance degradation percent still approximately the same ratio or decreased in a very small present when the number of computing nodes is increased. This is gives a good prove that the proposed algorithm keeping the performance degradation as mush as possible is the same. 
 
+ 
 \begin{figure}
   \centering
   \subfloat[CG, MG, LU and FT benchmarks]{%
