+\documentclass[12pt,a4paper]{report}
+\usepackage[utf8]{inputenc}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{graphicx}
+\usepackage{color}
+\title{Reviewers' comments}
+
+\newcommand{\AG}[2][inline]{%
+ \todo[color=green!50,#1]{\sffamily\textbf{AG:} #2}\xspace}
+\newcommand{\JC}[2][inline]{%
+ \todo[color=red!10,#1]{\sffamily\textbf{JC:} #2}\xspace}
+
+\newcommand{\Xsub}[2]{{\ensuremath{#1_\mathit{#2}}}}
+
+%% used to put some subscripts lower, and make them more legible
+\newcommand{\fxheight}[1]{\ifx#1\relax\relax\else\rule{0pt}{1.52ex}#1\fi}
+
+\newcommand{\CL}{\Xsub{C}{L}}
+\newcommand{\Dist}{\mathit{Dist}}
+\newcommand{\EdNew}{\Xsub{E}{dNew}}
+\newcommand{\Eind}{\Xsub{E}{ind}}
+\newcommand{\Enorm}{\Xsub{E}{Norm}}
+\newcommand{\Eoriginal}{\Xsub{E}{Original}}
+\newcommand{\Ereduced}{\Xsub{E}{Reduced}}
+\newcommand{\Es}{\Xsub{E}{S}}
+\newcommand{\Fdiff}[1][]{\Xsub{F}{diff}_{\!#1}}
+\newcommand{\Fmax}[1][]{\Xsub{F}{max}_{\fxheight{#1}}}
+\newcommand{\Fnew}{\Xsub{F}{new}}
+\newcommand{\Ileak}{\Xsub{I}{leak}}
+\newcommand{\Kdesign}{\Xsub{K}{design}}
+\newcommand{\MaxDist}{\mathit{Max}\Dist}
+\newcommand{\MinTcm}{\mathit{Min}\Tcm}
+\newcommand{\Ntrans}{\Xsub{N}{trans}}
+\newcommand{\Pd}[1][]{\Xsub{P}{d}_{\fxheight{#1}}}
+\newcommand{\PdNew}{\Xsub{P}{dNew}}
+\newcommand{\PdOld}{\Xsub{P}{dOld}}
+\newcommand{\Pnorm}{\Xsub{P}{Norm}}
+\newcommand{\Ps}[1][]{\Xsub{P}{s}_{\fxheight{#1}}}
+\newcommand{\Scp}[1][]{\Xsub{S}{cp}_{#1}}
+\newcommand{\Sopt}[1][]{\Xsub{S}{opt}_{#1}}
+\newcommand{\Tcm}[1][]{\Xsub{T}{cm}_{\fxheight{#1}}}
+\newcommand{\Tcp}[1][]{\Xsub{T}{cp}_{#1}}
+\newcommand{\Pmax}[1][]{\Xsub{P}{max}_{\fxheight{#1}}}
+\newcommand{\Pidle}[1][]{\Xsub{P}{idle}_{\fxheight{#1}}}
+\newcommand{\TcpOld}[1][]{\Xsub{T}{cpOld}_{#1}}
+\newcommand{\Tnew}{\Xsub{T}{New}}
+\newcommand{\Told}{\Xsub{T}{Old}}
+
+
+
+\begin{document}
+
+
+
+\section{Reviewer 1}
+This work tries to reduce energy consumption of regular applications,
+with no dynamic load balancing, that execute in heterogeneous
+platforms with different machine configurations. A energy and
+execution time model are given for such configuration that allows the
+reader to easily understand the context. The proposed energy reduction
+strategy slows down (using DVFS) the faster processes, reducing their
+slack time. The technique could be seen as "load balancing" through
+de-acceleration. Of course the objective here is to reduce energy
+consumption, and the proposed technique is indeed interesting. I
+suggest you to read the following paper that has a similar strategy
+(slack time is called residual imbalances in this paper) applied in a
+slightly different scenario:
+
++ Padoin et. al. Saving energy by exploiting residual imbalances on
+ iterative applications. 21st International Conference on High
+ Performance Computing (HiPC), HIPC 2014.
+
+It is very hard to optimize energy consumption and performance. One
+affects the other, very few workarounds for that. I found the
+discussion in Sec. 4 very interesting since it details a possible
+workaround by exploring the fact that the application is distributed
+in the platform and we know that the overall execution time is
+dominated by the critical path.
+
+Remarks
+\begin{enumerate}
+
+
+
+\item In Sec. 5, I found intriguing the fact of executing Algorithm 1 only
+after the first iteration. I agree with you that your model finds the
+best trade-off given some data, but what about the variability? We
+know computer systems today always show some variability. You are
+measuring the computation time and energy consumption for one
+iteration only. Let's suppose something went bad in this first
+iteration. The scaling factors will not be the best tradeoff because
+variability has been ignored. What would be the solution for that?
+Consider variability in the model. Another point is that you mention
+in the abstract and introduction that your solution has low overhead,
+but it is a centralized solution. Probably it won't scale when we
+reach hundreds or thousands of computer nodes: take one of that large
+machines for example. In this paper experiments, only 16 and 32 nodes
+where considered.
+
+\textcolor{blue}{Answer: We plan to take the variability in the proposed algorithm as a future works in two steps. In the first step, the algorithm selects the best frequencies at the end of the first iterations and apply them to the system. In the second step, after some iterations (e.g. 5 iterations) the algorithm recomputes the frequencies depending on the average of the communication and computation times for all previous iterations. It will change the frequency of each node if the new frequency is different from the old one. Otherwise, it keeps the old frequency. We have added this to our perspectives at the paper.
+ The algorithm overhead is very small, for example in the simulation results [6], it takes 0.15 ms on average for 144 nodes to compute the best scaling factors vector for a heterogeneous cluster. On Grid'5000 it is very hard to book a lot of nodes that allow DVFS operations and have an energy measurement tools. }
+
+
+\item In Fig 6, you draw lines between the points. Lines here mean nothing
+since you are changing the benchmark. I would replot using for
+instance a non-stacked bar plot with four colors (one site/16, one
+site/32, two sites/16, two sites/32). I believe it would be much
+easier to compare and avoid the problem of lines.
+
+ \textcolor{blue}{Answer: we agree with reviewer. We have changed figures 6 and 8 in the paper.}
+
+
+
+
+\item About the discussion of results shown in Fig 7, one consideration
+draws my attention: "(...) the increase in the number of computing
+nodes can increase the communication times and thus produces less
+energy saving depending on the benchmarks being executed.". I agree
+with you that for very large applications, synchronous collective
+operations are very costly (take a very simple MPI-Allgather for
+instance). You say that on scale this would produce less energy
+savings, but your arguments for providing a solution for this was
+based that today's supercomputers are achieving massive scale.
+
+\textcolor{blue}{Answer: In grid, the cost of communications between distinct sites is the main factor. The NAS benchmarks are significantly affected by the number of nodes and the increase in the communications between them. So, the instance is too small to be executed over 32 nodes and the computation to communication ratio is very small. Therefore, bigger instances should be executed on
+much number of nodes. }
+
+\item In Sec 6.3, why did you choose to keep 32 processes for the evaluation
+with multi-core clusters? How did you configure MPI for the results
+
+\textcolor{blue}{Answer: We keep choosing 32 nodes in both scenarios
+to compare them while one core per node scenario has distributed communications (one network link for each node) and multi-core scenario uses shared network link communications and thus comparing their impact on the results.
+We configure MPI on one core per node scenario by choosing one core per nodes (e.g in machine file we did: node1, node2 ,node3, node4). While in multi-core scenario we choose one machine with four cores (e.g. node1 slots=4).}
+
+
+\item shown in Fig 8a? Some MPI implementations have an option to use shared
+memory when processes share the same processor. I agree with you in
+the explanation of the network card utilization, but this
+shared-memory optimization is possible (sometimes automatically
+detected by MPI if you pin processes to cores).
+
+\textcolor{blue}{Answer: We didn't manually pin processes to cores and since the communication times
+increased. We guess that the shared memory wasn't used.}
+
+\item In P33, Sec 6.5, you mention that the proposed algorithm outperforms
+EDP because the former considers both metrics (time, energy) and the
+same time. EDP does also, but using a single metric which you have
+defined: energy x execution time. I think this is only a matter of
+phrasing.
+
+\textcolor{blue}{Answer: we use the delay in execution time not the execution time. Then, the equation that we used is EDP= energy x (Tnew-Told). The experiments shows that our objective function
+is better than the EDP objective.}
+
+
+\item Other complementary points to consider:
+
++ P2, L51: there are three dots that looks like an error.
+
++ P4, L36: also unusual three dots at the end of paragraph.
+
++ P14 also has three dots in phrase endings. I consider this bad writing style.
+
++ Fig 2b is missing the X scale ticks. You could show some examples of vectors.
+
++ P23: "static power is assumed to be equal to 20\% of dynamic". Provide citation.
+
++ Fig 6 is referenced in P23, but appears only in P25. Hard to read.
+
++ Same for Fig 7.
+
+\item \textcolor{blue}{ Answer: We have considered these points in the paper.}
+
+\item From the design of experiments, did you consider using replications?
+There is no variability metric in your results. Have you run multiple
+times and got the average (execution time and energy consumption)? I
+feel that such variability needs to be accounted for, otherwise it is
+very hard to affirm anything about measurements.
+
+ \textcolor{blue}{Answer: Each experiment has been executed many times and the results presented in the
+ figures are the average values of many executions.}
+
+
+\item In summary, I think this is a very interesting work but the experimental evaluation lacks variability measurements, consider larger experiments (1K nodes for instance) to see how everything scales, and there is no overhead measurements although authors stress that in abstract/introduction.
+
+\textcolor{blue}{Answer: We will expand the experimental over a large number of nodes in the future work while increasing the problem size and considering the variability issues. We have discussed the algorithm overhead and its complexity in section 6.5.}
+\end{enumerate}
+
+
+\section{Reviewer 2}
+This paper presents detailed performance and energy model for iterative message passing applications. Further a method is proposed to select the frequencies of heterogeneous cpus online. The selection method itself is not difficult. But I like the systematic modeling for energy consumption and performance. This paper is well written in general. The technical contents are presented in a logical way overall. The experiments are conducted in real platform, which shows the practicality of this work and also makes the work have more impact on the field. However, I have the following comments and concerns for this paper. The authors should clarify them in the revised version.
+
+
+-move the contributions from related work to introduction
+
+\begin{enumerate}
+
+
+\item why emphasize it is a grid platform? the presentation of related work follows the logic of heterogeneous CPUs. Grid is only a type of platform with heterogeneous CPUs
+
+\textcolor{blue}{Answer: The proposed algorithm was adapted to the grid platform which is composed
+of homogeneous clusters and interconnected by a wide area network which is slower than the local
+network in each cluster. The algorithm can also work on other heterogeneous platforms.}
+
+
+\item Define what iterative message passing applications are and give exemplar applications of them targeted by this method.
+
+\textcolor{blue}{Answer: The message passing applications with iterations compute
+the same block of operations several times, starting from the initial solution until reaching
+the acceptable approximation of the exact solution (we have added this sentence to the paper page 21).
+There are many example for these applications
+such as JACOBI, GAUSS-SEIDE, Successive over-relaxation and conjugate gradient (CG) method and etc.
+Similarly, an offline method uses DVFS and applied to these applications is in \cite{1} }
+
+
+\item Figure 1 is not clearly explained. Where is the slack time in figure 1 and why slack time =0 for task 1?
+
+\textcolor{blue}{Answer: We agree with the reviewer, this figure was re-plotted to show the slack time.
+ In the figure, we assumed that task 1 is the slower task. So, there are no slack time (waiting time)
+ in the slower task because it is not wait for the others while other tasks wait for it.}
+
+\item define the parameters in eq. 1.
+
+\textcolor{blue}{Answer: We have defined Fmax and Fnew in the text.}
+
+\item eq. 2: are you assuming each cluster has the same number of nodes?
+
+
+
+
+\textcolor{blue}{Answer: No, we assume each cluster has different number of node, so in the equation we
+have replaced $M_i$ instead of $M$ and the same for $F$ replaced with $F_j$ in the all equations of the paper.}
+
+\item Eq.2 implicitly assumes that there is no overlapping between computation and communication. Is it reasonable?
+
+\textcolor{blue}{Answer: The communications between the computing nodes are synchronized, where each node
+need to wait for the others to finished their jobs before computing the next iteration. So, there is no
+overlapping between computations and communications for a node. The overlapping happens when the communications are asynchronous or the computations are not depend on the data sent by the neighbouring nodes. }
+
+\item eq. 2 is not clear:
+
+-how to define and determine the slowest cluster h? the one before scaling or after scaling?
+
+\textcolor{blue}{Answer: The slower task is the task which gives maximum execution time before scaling the frequency of the node. We have added this sentence to the paper (page 8).}
+
+
+- what is the communication time without slack time
+
+\textcolor{blue}{Answer: There is no synchronous communications with zero slack times, but if a node send a message to another node which is already waiting for that message. The latter will acknowledge the reception of the message from the sender without any delay. On the other hand, if the receiving node is still computing the sender has to wait for it to finish its computation to acknowledge the reception of the message. This time is called the slack time. }
+
+
+- in equation, min operation is used to get the communication time, but in text, it says to use the slowest communication time, which should use the max operation then.
+
+\textcolor{blue}{Answer: We agree with the reviewer and the sentence "slower communication time" changed to "communication time of the slower node" in the paper.}
+
+\item discuss the difference between eq. 2 and the prediction model in references [5] and [6]
+
+\textcolor{blue}{Answer: The prediction models in [5] and [6] are for homogeneous and heterogeneous clusters respectively, while eq. 2 is for a grid. where the homogeneous cluster predication model was used one scaling factor denoted as $S$, because all the nodes in the cluster have the same computing powers. Whereas, in heterogeneous cluster prediction model all the nodes have different scales and the scaling factors have denoted as one dimensional vector $(S_1, S_2, \dots, S_N)$. The execution time prediction model for a grid Equation (2) defines a two dimensional array of scales
+$(S_{11}, S_{12},\dots, S_{NM_i})$. We have added this to the paper (page 8).}
+
+\item Eq. 10: Can the authors comment on the energy consumed by communications?
+
+\textcolor{blue}{Answer: The CPU during communications consumed only the static power power. While
+in computations the CPU consumes both the dynamic and static communication, refer to \cite{3}. We have added this sentience to the paper, page 11.}
+
+\item This work assume homogeneous cpu in one cluster. Line 55 says: even if the distributed message
+passing iterative application is load balanced, the computation time of each cpu j in cluster i may be different Why?
+
+\textcolor{blue}{Answer: The computation times may be slightly different due to the delay caused
+by the scheduler of the operating system. We have added this in the paper.}
+
+\item Comment why the applications in NAS parallel benchmark are iterative application? These applications are normally run in one cluster. Describe in more detail how they are run across multiple clusters.
+
+\textcolor{blue}{Answer: The applications in NAS parallel benchmark are application with iterations because they iterate the same block of instructions (communications and computations) many times. All the benchmarks are MPI programs that allowed to be executed on any distributed memory platform such as clusters and grids with no required modifications. Since, we have deployed the same operating system on all the nodes, we just compile the source on one cluster and then copied the executable program on all the clusters. }
+
+\item broken sentence in line 28 on page 12
+
+\textcolor{blue}{Answer: The word "were" replaced with "where".}
+
+\item Why $T_{old}$ is computed using eq. 12, which applies MAX over computation time and communication time, while in $T_{new}$, max and min operations are applied over computation and communication separately?
+
+\textcolor{blue}{Answer: We agree with the reviewer, $T_{old}$ is the maximum execution time of the application before scaling the frequency and it is computed as in $T_{new}$ equation without scaling factors. So, we have changed the $T_{old}$ in the paper as as follows:
+\begin{equation}
+ \label{eq:told}
+ T_{old} = \mathop{\max_{i=1,2,\dots,N}}_{j=1,2,\dots,M_i} (\Tcp[ij]) +
+ \mathop{\min_{i=1,2,\dots,N}} (\Tcm[hj] )
+\end{equation}
+}
+
+\item Line 55 on page 16 is to define the slack time, which should be introduced at the beginning of the paper, such as in figure 1.
+
+\textcolor{blue}{Answer: We have changed it in the paper and added to page 6.}
+
+
+\item Authors comment whether (and how) the proposed methods can be applied/extended to other programming models and/or platform, such as mapreduce, heterogeneous cluster with CPU+GPU.
+Revision
+
+\textcolor{blue}{Answer: The proposed method can only be applied to parallel programming with iteration
+and with or without message passing. Indeed, the proposed method can be applied to the parallel application with mapreduce if it is a regular application with iterations. Therefore, the time of each map and reduce operations (communications) and the computation times in the program must be computed at the first iterations to predict the energy consumption and the execution time. After, the proposed algorithm can be used as it to select the best frequencies.
+The proposed method can be applied to a heterogeneous platform composed from GPUs and CPUs, since modern GPUs like CPUs allow the use of DVFS operation.}
+\end{enumerate}
+
+\section{Reviewer 3}
+In this paper, a new online frequency selecting algorithm for grids, composed of heterogeneous clusters, is presented. It selects the frequencies and tries to give the best trade-off between
+energy saving and performance degradation, for each node computing the message passing iterative application. The algorithm has a small overhead and works without training or profiling. It uses a new energy model for message
+passing iterative applications running on a grid. The proposed algorithm is evaluated on a real grid, the Grid'5000 platform, while running the NAS parallel benchmarks. The experiments on 16 nodes, distributed on three clusters, show
+that it reduces on average the energy consumption by 30\% while the performance is on average only degraded by 3.2\%. Finally, the algorithm is compared to an existing method. The comparison results show that it outperforms the
+latter in terms of energy consumption reduction and performance.
+
+this paper is quite interesting and solid. But before acceptance, I suggest to have the following major revisions:
+\begin{enumerate}
+
+\item suggest the authors to use much larger size of nodes, instead of on 16 nodes, distributed on three clusters, to see the scalability of the energy saving
+
+\textcolor{blue}{Answer: We have made the experiments not only on 16 nodes, but we have also made them over 32 nodes distributed over three clusters and in the near future we will apply the proposed method over a larger number of nodes.}
+
+\item the energy saving is actually calculated by the quantitative formula instead of the real measurements. Can you have any discussions on the real measurements?
+
+\textcolor{blue}{Answer: The scope of this paper is not mainly focuses on the energy measurements, but it focuses on modelling and optimizing the energy and performance of grid systems. The proposed energy model depends on the dynamic and static power values for each CPU. We have used a real power measurement tools allowed in Grid'5000 sites to measure the dynamic power consumption. Moreover, the real measurements are difficult for a grid platform when the nodes are geographically distributed. As a future work, it is interesting to compare the accuracy of the proposed energy model with a real instruments to measure the energy consumption for local clusters such as the measurement tools presented in \cite{2}.}
+
+\item the overhead is not measured, can you present something on this as well to demonstrate what the authors claimed "has a small overhead and works without training or profiling"?
+
+\textcolor{blue}{Answer: In the comparison section 6.5, we have presented the execution time of the algorithm when it is executed over 32 nodes distributed over three sites located at two different sites, it takes on average 0.01 $ms$. The algorithm works online without training which means it only uses the measured communication and computation times during the runtime and do not require any profiling or training executed before runtime.}
+\end{enumerate}
+\bibliographystyle{plain}
+\bibliography{ref.bib}
+
+
+\end{document}
+
