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
-applications \textcolor{blue}{with iterations} running over homogeneous and heterogeneous clusters respectively.
+applications with iterations 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 describe homogeneous and heterogeneous platforms, and to simulate the execution of message passing parallel
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
- application \textcolor{blue}{with iterations} the vector of frequencies that simultaneously tries to
+ application with iterations 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.
sequential, parallel or distributed architecture, homogeneous or heterogeneous
platform, synchronous or asynchronous application.
-In this paper, we are interested in reducing energy for message passing
- synchronous applications \textcolor{blue}{with iterations} running over heterogeneous grid platforms. Some
+In this paper, we are interested in reducing the energy consumption of message passing
+ synchronous applications with iterations running over heterogeneous grid platforms. Some
works have already been done for such platforms and they can be classified into
two types of heterogeneous platforms:
\begin{itemize}
following contributions :
\begin{enumerate}
\item two new energy and performance models for message passing
- synchronous applications \textcolor{blue}{with iterations} running over a heterogeneous grid platform. Both models
+ synchronous applications with iterations running over a heterogeneous grid platform. Both models
take into account communication and slack times. The models can predict the
required energy and the execution time of the application.
platforms. The algorithm has a very small overhead and does not need any
training nor profiling. It uses a new optimization function which
simultaneously maximizes the performance and minimizes the energy consumption
- of a message passing synchronous application \textcolor{blue}{with iterations}.
+ of a message passing synchronous application with iterations.
\end{enumerate}
\label{sec.exe}
\subsection{The execution time of message passing distributed
- applications \textcolor{blue}{with iterations} on a heterogeneous platform}
+ applications with iterations on a heterogeneous platform}
In this paper, we are interested in reducing the energy consumption of message
-passing distributed synchronous applications \textcolor{blue}{with iterations} running over
+passing distributed synchronous applications with iterations running over
heterogeneous grid platforms. A heterogeneous grid platform could be defined as a collection of
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.
-The overall execution time of a distributed synchronous application \textcolor{blue}{with iterations}
+The overall execution time of a distributed synchronous application with iterations running
over a heterogeneous grid consists of the sum of the computation time and
the communication time for every iteration on a node.
-\textcolor{blue}{However, nodes from distinct clusters in a grid have different computing powers, thus
-while executing message passing \textcolor{blue}{with iterations} synchronous applications, fast nodes
+However, nodes from distinct clusters in a grid have different computing powers, thus
+while the application, 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. }
+periods are called idle or slack times.
Therefore, 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. \textcolor{blue}{For example, in Figure \ref{fig:heter} the task 1 is the slower task which has no slack time (not waits for the other nodes) and it is only has the communication times.}
+which has the highest computation time and almost no slack time. For example, in Figure \ref{fig:heter}, task 1 is the slower task and it does not have to wait for the other nodes to communicate with them because they all finish their computations before it.
\begin{figure}[!t]
\centering
\label{eq:s}
S = \frac{\Fmax}{\Fnew}
\end{equation}
-\textcolor{blue}{Where $\Fmax$ is the maximum frequency before applying DVFS and $\Fnew$ is the new frequency after applying DVFS.}
+where $\Fmax$ is the maximum frequency before applying any DVFS and $\Fnew$ is the new frequency after applying DVFS.
+
The execution time of a compute bound sequential program is linearly
proportional to the frequency scaling factor $S$. On the other hand, message
passing distributed applications consist of two parts: computation and
of these clusters, they may get different scaling factors represented by a scaling vector:
$(S_{11}, S_{12},\dots, S_{NM_i})$ where $S_{ij}$ is the scaling factor of processor $j$ in cluster $i$ . To
be able to predict the execution time of message passing synchronous
-applications \textcolor{blue}{with iterations} running over a heterogeneous grid, for different vectors of
+applications with iterations running over a heterogeneous grid, for different vectors of
scaling factors, the communication time and the computation time for all the
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
cluster $i$, $\TcpOld[ij]$ 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 \textcolor{blue}{the communication time of the slower node without slack time during one iteration.
-The slower node $h$ is the node that gives maximum execution time in all clusters befor scaling its frequency.}
+and the communication time of the slower node without slack time during one iteration.
+The slower node $h$ is the node that gives the maximum execution time in all the clusters before applying DVFS.
It means that only the communication time without any slack time is taken into account.
-Therefore, the execution time of the application \textcolor{blue}{with iterations} is equal to
+Therefore, the execution time of the application is equal to
the execution time of one iteration as in Equation (\ref{eq:perf}) multiplied by the
number of iterations of that application.
