-be noticed that in a homogeneous platform the search for the optimal scaling
-factor should start from the maximum frequency because the performance and the
-consumed energy decrease from the beginning of the plot. On the other hand,
-in the heterogeneous platform the performance is maintained at the beginning of
-the plot even if the frequencies of the faster nodes decrease until the
-computing power of scaled down nodes are lower than the slowest node. In other
-words, until they reach the higher bound. It can also be noticed that the higher
-the difference between the faster nodes and the slower nodes is, the bigger the
-maximum distance between the energy curve and the performance curve is while
- the scaling factors are varying which results in bigger energy savings.
-\begin{figure}[!t]
- \centering
- \includegraphics[scale=0.5]{fig/start_freq}
- \caption{Selecting the initial frequencies}
- \label{fig:st_freq}
-\end{figure}
-
-
-
-
-\begin{algorithm}
- \begin{algorithmic}[1]
- % \footnotesize
- \Require ~
- \begin{description}
- \item[$\Tcp_i$] array of all computation times for all nodes during one iteration and with highest frequency.
- \item[$\Tcm_i$] array of all communication times for all nodes during one iteration and with highest frequency.
- \item[$\Fmax_i$] array of the maximum frequencies for all nodes.
- \item[$\Pd_i$] array of the dynamic powers for all nodes.
- \item[$\Ps_i$] array of the static powers for all nodes.
- \item[$\Fdiff_i$] array of the difference between two successive frequencies for all nodes.
- \end{description}
- \Ensure $\Sopt_1,\Sopt_2 \dots, \Sopt_N$ is a vector of optimal scaling factors
-
- \State $\Scp_i \gets \frac{\max_{i=1,2,\dots,N}(\Tcp_i)}{\Tcp_i} $
- \State $F_{i} \gets \frac{\Fmax_i}{\Scp_i},~{i=1,2,\cdots,N}$
- \State Round the computed initial frequencies $F_i$ to the closest one available in each node.
- \If{(not the first frequency)}
- \State $F_i \gets F_i+\Fdiff_i,~i=1,\dots,N.$
- \EndIf
- \State $\Told \gets max_{~i=1,\dots,N } (\Tcp_i+\Tcm_i)$
- \State $\Eoriginal \gets \sum_{i=1}^{N}{( \Pd_i \cdot \Tcp_i)} +\sum_{i=1}^{N} {(\Ps_i \cdot \Told)}$
- \State $\Sopt_{i} \gets 1,~i=1,\dots,N. $
- \State $\Dist \gets 0 $
- \While {(all nodes not reach their minimum frequency)}
- \If{(not the last freq. \textbf{and} not the slowest node)}
- \State $F_i \gets F_i - \Fdiff_i,~i=1,\dots,N.$
- \State $S_i \gets \frac{\Fmax_i}{F_i},~i=1,\dots,N.$
- \EndIf
- \State $\Tnew \gets max_\textit{~i=1,\dots,N} (\Tcp_{i} \cdot S_{i}) + \MinTcm $
- \State $\Ereduced \gets \sum_{i=1}^{N}{(S_i^{-2} \cdot \Pd_i \cdot \Tcp_i)} + \sum_{i=1}^{N} {(\Ps_i \cdot \rlap{\Tnew)}} $
- \State $\Pnorm \gets \frac{\Told}{\Tnew}$
- \State $\Enorm\gets \frac{\Ereduced}{\Eoriginal}$
- \If{$(\Pnorm - \Enorm > \Dist)$}
- \State $\Sopt_{i} \gets S_{i},~i=1,\dots,N. $
- \State $\Dist \gets \Pnorm - \Enorm$
- \EndIf
- \EndWhile
- \State Return $\Sopt_1,\Sopt_2,\dots,\Sopt_N$
- \end{algorithmic}
- \caption{frequency scaling factors selection algorithm}
- \label{HSA}
-\end{algorithm}
-
-\begin{algorithm}
- \begin{algorithmic}[1]
- % \footnotesize
- \For {$k=1$ to \textit{some iterations}}
- \State Computations section.
- \State Communications section.
- \If {$(k=1)$}
- \State Gather all times of computation and\newline\hspace*{3em}%
- communication from each node.
- \State Call Algorithm \ref{HSA}.
- \State Compute the new frequencies from the\newline\hspace*{3em}%
- returned optimal scaling factors.
- \State Set the new frequencies to nodes.
- \EndIf
- \EndFor
- \end{algorithmic}
- \caption{DVFS algorithm}
- \label{dvfs}
-\end{algorithm}
+be noticed that in a homogeneous platform the search for the optimal scaling
+factor should start from the maximum frequency because the performance and the
+consumed energy decrease from the beginning of the plot. On the other hand, in
+the heterogeneous platform the performance is maintained at the beginning of the
+plot even if the frequencies of the faster nodes decrease until the computing
+power of scaled down nodes are lower than the slowest node. In other words,
+until they reach the higher bound. It can also be noticed that the higher the
+difference between the faster nodes and the slower nodes is, the bigger the
+maximum distance between the energy curve and the performance curve is while the
+scaling factors are varying which results in bigger energy savings.
+Finally, in a homogeneous platform the energy consumption is increased when the scaling factor is very high.
+Indeed, the dynamic energy saved by reducing the frequency of the processor is compensated by the significant increase of the execution time and thus the increased of the static energy. On the other hand, in a heterogeneous platform this is not the case.
