-\AG{Consider introducing the models (sec.~\ref{sec.ptasks},
- maybe~\ref{sec.energy}) before related works}
-
-In the this section some heuristics, to compute the scaling factor, are
-presented and classified in two parts : offline and online methods.
-
-\subsection{The offline DVFS orientations}
-
-The DVFS offline methods are static and are not executed during the runtime of
-the program. Some approaches used heuristics to select the best DVFS state
-during the compilation phases as an example in Azevedo et al.~\cite{40}. He used
-intra-task algorithm
-\AG{what is an ``intra-task algorithm''?}
-to choose the DVFS setting when there are dependency points
-between tasks. While in~\cite{29}, Xie et al. used breadth-first search
-algorithm to do that. Their goal is saving energy with time limits. Another
-approaches gathers and stores the runtime information for each DVFS state, then
-used their methods offline to select the suitable DVFS that optimize energy-time
-trade offs. As an example~\cite{8}, Rountree et al. used liner programming
-algorithm, while in~\cite{38,34}, Cochran et al. used multi logistic regression
-algorithm for the same goal. The offline study that shown the DVFS impact on the
-communication time of the MPI program is~\cite{17}, Freeh et al. show that these
-times not changed when the frequency is scaled down.
-
-\subsection{The online DVFS orientations}
-
-The objective of these works is to dynamically compute and set the frequency of
-the CPU during the runtime of the program for saving energy. Estimating and
-predicting approaches for the energy-time trade offs developed by
-~\cite{11,2,31}. These works select the best DVFS setting depending on the slack
-times. These times happen when the processors have to wait for data from other
-processors to compute their task. For example, during the synchronous
-communication time that take place in the MPI programs, the processors are
-idle. The optimal DVFS can be selected using the learning methods. Therefore, in
-~\cite{39,19} used machine learning to converge to the suitable DVFS
-configuration. Their learning algorithms have big time to converge when the
-number of available frequencies is high. Also, the communication time of the MPI
-program used online for saving energy as in~\cite{1}, Lim et al. developed an
-algorithm that detects the communication sections and changes the frequency
-during these sections only. This approach changes the frequency many times
-because an iteration may contain more than one communication section. The domain
-of analytical modeling used for choosing the optimal frequency as in~\cite{3},
-Rauber et al. developed an analytical mathematical model for determining the
-optimal frequency scaling factor for any number of concurrent tasks, without
-considering communication times. They set the slowest task to maximum frequency
-for maintaining performance. In this paper we compare our algorithm with
-Rauber's model~\cite{3}, because his model can be used for any number of
-concurrent tasks for homogeneous platform and this is the same direction of this
-paper. However, the primary contributions of this paper are:
-\begin{enumerate}
-\item Selecting the optimal frequency scaling factor for energy and performance
- simultaneously. While taking into account the communication time.
-\item Adapting our scale factor to taking into account the imbalanced tasks.
-\item The execution time of our algorithm is very small when compared to other
- methods (e.g.,~\cite{19}).
-\item The proposed algorithm works online without profiling or training as
- in~\cite{38,34}.
-\end{enumerate}
-
-\section{Parallel Tasks Execution on Homogeneous Platform}
-\label{sec.ptasks}
-
-A homogeneous cluster consists of identical nodes in terms of the hardware and
-the software. Each node has its own memory and at least one processor which can
-be a multi-core. The nodes are connected via a high bandwidth network. Tasks
-executed on this model can be either synchronous or asynchronous. In this paper
-we consider execution of the synchronous tasks on distributed homogeneous
-platform. These tasks can exchange the data via synchronous memory passing.
-\begin{figure*}[t]
- \centering
- \subfloat[Sync. Imbalanced Communications]{\includegraphics[scale=0.67]{synch_tasks}\label{fig:h1}}
- \subfloat[Sync. Imbalanced Computations]{\includegraphics[scale=0.67]{compt}\label{fig:h2}}
- \caption{Parallel Tasks on Homogeneous Platform}
- \label{fig:homo}
-\end{figure*}
-\AG{On fig.~\ref{fig:h1}, how can there be a synchronization point without communications just before ?\\
-Use ``Sync.'' to abbreviate ``Synchronization''}
-Therefore, the execution time of a task consists of the computation time and the
-communication time. Moreover, the synchronous communications between tasks can
-lead to idle time while tasks wait at the synchronous point for others tasks to
-finish their communications see figure~(\ref{fig:h1}). Another source for idle
-times is the imbalanced computations. This happen when processing different
-amounts of data on each processor as an example see figure~(\ref{fig:h2}). In
-this case the fastest tasks have to wait at the synchronous barrier for the
-slowest tasks to finish their job. In both two cases the overall execution time
-of the program is the execution time of the slowest task as :
-\begin{equation}
- \label{eq:T1}
- \textit{Program Time} = \max_{i=1,2,\dots,N} T_i
-\end{equation}
-where $T_i$ is the execution time of process $i$.
-
-\section{Energy Model for Homogeneous Platform}
-\label{sec.energy}
