From e25948dd52ceacdc4dc6175e899ae810ea4cc134 Mon Sep 17 00:00:00 2001 From: jean-claude Date: Mon, 24 Nov 2014 14:04:48 +0100 Subject: [PATCH] reduced the we --- Heter_paper.tex | 39 +++++++++++++++++++-------------------- 1 file changed, 19 insertions(+), 20 deletions(-) diff --git a/Heter_paper.tex b/Heter_paper.tex index ec89460..90793bf 100644 --- a/Heter_paper.tex +++ b/Heter_paper.tex @@ -132,7 +132,7 @@ Section~\ref{sec.optim} details the proposed frequency selecting algorithm then Section~\ref{sec.expe} presents the results of applying the algorithm on the NAS parallel benchmarks and executing them on a heterogeneous platform. It also shows the results of running three different power scenarios and comparing them. -Finally, we conclude in Section~\ref{sec.concl} with a summary and some future works. +Finally, in Section~\ref{sec.concl} the paper is ended with a summary and some future works. \section{Related works} \label{sec.relwork} @@ -196,7 +196,7 @@ In contrast to the above described papers, this paper presents the following con In this paper, we are interested in reducing the energy consumption of message passing distributed iterative synchronous applications running over -heterogeneous platforms. We define a heterogeneous platform as a collection of +heterogeneous platforms. A heterogeneous platform is defined as a collection of heterogeneous computing nodes interconnected via a high speed homogeneous network. Therefore, each node has different characteristics such as computing power (FLOPS), energy consumption, CPU's frequency range, \dots{} but they all @@ -282,7 +282,7 @@ to compute the best scaling factors vector. The algorithm complexity is $O(F\cd 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 sections (\ref{sec.res}) and (\ref{sec.compare}). slowest node, it means only the communication time without any slack time. -Therefore, we can consider the execution time of the iterative application is +Therefore, 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. @@ -330,8 +330,8 @@ voltage with respect to various frequency values in~\cite{Rauber_Analytical.Mode 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}). 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: +system's kernel to lower a core's frequency. The new frequency +$F_{new}$ from EQ(\ref{eq:s}) can be calculated as follows: \begin{equation} \label{eq:fnew} F_\textit{new} = S^{-1} \cdot F_\textit{max} @@ -357,7 +357,7 @@ and is given by the following equation: \end{equation} The static power is related to the power leakage of the CPU and is consumed during computation and even when idle. As in~\cite{Rauber_Analytical.Modeling.for.Energy,Zhuo_Energy.efficient.Dynamic.Task.Scheduling}, -we assume that the static power of a processor is constant + the static power of a processor is considered as constant during idle and computation periods, and for all its available frequencies. The static energy is the static power multiplied by the execution time of the program. According to the execution time model in EQ(\ref{eq:perf}), the execution time of the program @@ -392,8 +392,8 @@ for each processor. It is computed as follows: 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{Kim_Leakage.Current.Moore.Law}. We can measure the overall energy consumption for the iterative -application by measuring the energy consumption for one iteration as in EQ(\ref{eq:energy}) +increased~\cite{Kim_Leakage.Current.Moore.Law}. The overall energy consumption for the iterative +application can be measured by measuring the energy consumption for one iteration as in EQ(\ref{eq:energy}) multiplied by the number of iterations of that application. @@ -422,8 +422,8 @@ The relation between the energy consumption and the execution time for an applic complex and nonlinear, Thus, unlike the relation between the execution time and the scaling factor, the relation of the energy with the frequency scaling factors is nonlinear, for more details refer to~\cite{Freeh_Exploring.the.Energy.Time.Tradeoff}. -Moreover, they are not measured using the same metric. To solve this problem, we normalize the -execution time by computing the ratio between the new execution time (after +Moreover, they are not measured using the same metric. To solve this problem, the +execution time is normalized by computing the ratio between the new execution time (after scaling down the frequencies of some processors) and the initial one (with maximum frequency for all nodes,) as follows: \begin{multline} @@ -434,7 +434,7 @@ frequency for all nodes,) as follows: \end{multline} -In the same way, we normalize the energy by computing the ratio between the consumed energy +In the same way, the energy is normalized by computing the ratio between the consumed energy while scaling down the frequency and the consumed energy with maximum frequency for all nodes: \begin{multline} \label{eq:enorm} @@ -455,9 +455,9 @@ reduction with minimum execution time reduction. -Our solution for this problem is to make the optimization process for energy and -execution time follow the same direction. Therefore, we inverse the equation of the -normalized execution time which gives the normalized performance equation, as follows: +This problem can be solved by making the optimization process for energy and +execution time follow the same direction. Therefore, the equation of the +normalized execution time is inverted which gives the normalized performance equation, as follows: \begin{multline} \label{eq:pnorm_inv} P_\textit{Norm} = \frac{T_\textit{Old}}{T_\textit{New}}\\ @@ -477,7 +477,7 @@ normalized execution time which gives the normalized performance equation, as fo \caption{The energy and performance relation} \end{figure} -Then, we can model our objective function as finding the maximum distance +Then, the objective function can be modeled as finding the maximum distance between the energy curve EQ~(\ref{eq:enorm}) and the performance curve EQ~(\ref{eq:pnorm_inv}) over all available sets of scaling factors. This represents the minimum energy consumption with minimum execution time (maximum @@ -491,8 +491,8 @@ function has the following form: \overbrace{E_\textit{Norm}(S_{ij})}^{\text{Minimize}} ) \end{equation} where $N$ is the number of nodes and $F$ is the number of available frequencies for each nodes. -Then we can select the optimal set of scaling factors that satisfies EQ~(\ref{eq:max}). -Our objective function can work with any energy model or any power values for each node +Then, the optimal set of scaling factors that satisfies EQ~(\ref{eq:max}) can be selected. +The objective function can 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{Zhuo_Energy.efficient.Dynamic.Task.Scheduling,Rauber_Analytical.Modeling.for.Energy,Hao_Learning.based.DVFS}. @@ -500,7 +500,7 @@ the energy curve has a convex form as shown in~\cite{Zhuo_Energy.efficient.Dynam \label{sec.optim} \subsection{The algorithm details} -In this section we propose algorithm~(\ref{HSA}) which selects the frequency scaling factors +In this section algorithm~(\ref{HSA}) is presented. It 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. @@ -1055,8 +1055,7 @@ results in less energy saving but less performance degradation. \section{Conclusion} \label{sec.concl} -In this paper, we have presented a new online selecting frequency scaling factors algorithm -that selects the best possible vector of frequency scaling factors for a heterogeneous platform. +In this paper, a new online frequency selecting algorithm have been presented. It selects the best possible vector of frequency scaling factors for a heterogeneous platform. 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 -- 2.39.5