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8 %\title{Reviewers' comments}
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55 \title{Answers to the questions of the reviewers}
58 We would like to thank the reviewers for taking time to review our paper. Their remarks were very constructive and allowed us to improve our paper and clarify some ambiguous points. We took in consideration all the remarks of the reviewers and modified the paper accordingly. In the following sections, the reviewers can find our answers to their questions:
60 \section{Questions and remarks of the first reviewer}
66 \item In Sec. 5, I found intriguing the fact of executing Algorithm 1 only
67 after the first iteration. I agree with you that your model finds the
68 best trade-off given some data, but what about the variability? We
69 know computer systems today always show some variability. You are
70 measuring the computation time and energy consumption for one
71 iteration only. Let's suppose something went bad in this first
72 iteration. The scaling factors will not be the best tradeoff because
73 variability has been ignored. What would be the solution for that?
74 Consider variability in the model.
76 \textbf{Answer:} In this paper we have considered that the application executes regular iterations over stable computers computing only this application. Therefore, we have assumed that the execution times of all the iterations of the application executed on the same computing node should be almost the same. For this reason we did not take into consideration the variability of the computer system. Moreover, applying the frequency scaling algorithm after many iterations would reduce its impact on the energy consumption especially for applications executing a relatively low number of iterations.
78 However, the variability of the computing system can be taken into consideration in a future work. For example, the proposed algorithm can be executed twice: after the first iteration the frequencies are scaled down according to the execution times measured in the first iteration, then after a fixed number of iterations, the frequencies are adjusted according to the execution times measured during the fixed number of iterations. If the computing power of the system is constantly changing, it would be interesting to implement a mechanism that detects this change and adjusts the frequencies according to the variability of the system.
80 Taking account of the variability of the system has been added as a perspective at the end of the paper.
83 \item Another point is that you mention
84 in the abstract and introduction that your solution has low overhead,
85 but it is a centralized solution. Probably it won't scale when we
86 reach hundreds or thousands of computer nodes: take one of that large
87 machines for example. In this paper experiments, only 16 and 32 nodes
91 We agree with the reviewer that the algorithm is centralized and might be a bottleneck if it was applied to an application running on many thousands of nodes. However, up to 144 nodes in a heterogeneous cluster, the overhead of the algorithm was very small, 0.15 ms, as presented in the simulation results of \cite{5}. We did not execute experiments with more than 32 nodes on Grid'5000 because it does not have many nodes that allow DVFS operations and have energy measurement tools.
93 On the other hand, the scalability of the proposed algorithm can be improved if we use asynchronous computations or if the algorithm was distributed in a hierarchical manner where a leader is chosen for each cluster or a group of nodes to compute their scaled frequencies. Improving the scalability of the algorithm is beyond the scope of this paper.
97 \item In Fig 6, you draw lines between the points. Lines here mean nothing
98 since you are changing the benchmark. I would replot using for
99 instance a non-stacked bar plot with four colors (one site/16, one
100 site/32, two sites/16, two sites/32). I believe it would be much
101 easier to compare and avoid the problem of lines.
103 \textbf{Answer:} We agree with the reviewer. The curves in Figures 6 and 8 in the paper were replaced by histograms.
108 \item About the discussion of results shown in Fig 7, one consideration
109 draws my attention: "(...) the increase in the number of computing
110 nodes can increase the communication times and thus produces less
111 energy saving depending on the benchmarks being executed.". I agree
112 with you that for very large applications, synchronous collective
113 operations are very costly (take a very simple MPI-Allgather for
114 instance). You say that on scale this would produce less energy
115 savings, but your arguments for providing a solution for this was
116 based that today's supercomputers are achieving massive scale.
118 \textbf{Answer:} In Figure 7, the energy consumption of the benchmarks solving the class D and running on many scenarios are presented. The number of used nodes varies between 16 and 32 in the scenarios while the size of the problem is not modified. Therefore, the computations to communications times ratio is lower when 32 nodes are used instead of 16. When this ratio is small, it means there are not enough computations when compared to the communications times and the impact of scaling down the frequency of the CPU on its energy consumption is reduced. To solve this problem, the problem
119 should be solved on a number of nodes adequate to its size. For example, for the NAS benchmarks, the class E should have been solved on 32 nodes to have a good computations to communications times ratio.
122 \item In Sec 6.3, why did you choose to keep 32 processes for the evaluation
123 with multi-core clusters? How did you configure MPI for the results
125 \textbf{Answer:} In section 6.3, we wanted to evaluate how much energy can be saved when applying the proposed algorithm to message passing applications with iterations running over a grid composed of multi-core nodes. Therefore, the same experiments as in section 6.2 were conducted on the new multi-core platform. Instead of running one process per node as in the previous section, 3 or 4 processes were executed on each multi-core node. The total number of processes, 32 processes, was not modified in order to fairly compare the single core and the multi-core versions.
127 Only the architecture file was modified between the single and the multi-core architectures. For the single core architecture, the architecture file contains the name of 32 different nodes. For the multi-core architecture, the architecture file contains less nodes and for every node 3 or 4 slots (cores) are used. The total number of slots is equal to 32.
131 \item shown in Fig 8a? Some MPI implementations have an option to use shared
132 memory when processes share the same processor. I agree with you in
133 the explanation of the network card utilization, but this
134 shared-memory optimization is possible (sometimes automatically
135 detected by MPI if you pin processes to cores).
137 \textbf{Answer:} We did not manually pin processes to cores. Since the communication times
138 increased, we think that the shared memory was not used when two processes, running on the same node, exchange data.
140 \item In P33, Sec 6.5, you mention that the proposed algorithm outperforms
141 EDP because the former considers both metrics (time, energy) and the
142 same time. EDP does also, but using a single metric which you have
143 defined: energy x execution time. I think this is only a matter of
146 \textbf{Answer:} We agree with the reviewer, EDP also uses two metrics in the objective function: energy and delay. The sentence in the paper was modified to clarify this misunderstanding. The main difference between our algorithm and the EDP method is the used objective function. For EDP, the product of energy and delay must be minimized, while for our algorithm, the difference between the normalized performance and the normalized energy should be maximized. This new formulation of the objective function allows our algorithm to select the set of frequencies that gives the best tradeoff between the energy consumption and the performance. The objective function of EDP does not give the same frequencies as our algorithm and thus it is outperformed by our method. The results of the experiments confirm that the objective function used by our algorithm is more efficient than the one used by EDP.
149 \item Other complementary points to consider:
151 + P2, L51: there are three dots that looks like an error.
153 + P4, L36: also unusual three dots at the end of paragraph.
155 + P14 also has three dots in phrase endings. I consider this bad writing style.
157 + Fig 2b is missing the X scale ticks. You could show some examples of vectors.
159 + P23: "static power is assumed to be equal to 20\% of dynamic". Provide citation.
161 + Fig 6 is referenced in P23, but appears only in P25. Hard to read.
165 \textbf{Answer:} Answer: We have taken in consideration all these remarks and the paper was modified accordingly.
167 \item From the design of experiments, did you consider using replications?
168 There is no variability metric in your results. Have you run multiple
169 times and got the average (execution time and energy consumption)? I
170 feel that such variability needs to be accounted for, otherwise it is
171 very hard to affirm anything about measurements.
173 \textbf{Answer:} Each experiment has been executed many times and the results presented in the
174 figures are the average values of many executions. Since we have deployed the same operating system on the booked machines and we were the only users executing processes on them during the experiments, no significant variability in the execution time of the applications was noticed.
177 \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.
179 \textbf{Answer:} For the time being, we do not have the resources nor the time to evaluate the proposed algorithm over large platforms composed of more than 1K nodes. However, as said in the perspectives of the paper, the evaluation of the scalability of the algorithm will be in a conducted in a future work as soon as we have access to larger resources. We have discussed the overhead of the algorithm and its complexity in section 6.5 and given in the answer to question 2 some solutions to improve its scalability and reduce its overhead.
181 For the variability issue, please refer to the answer to question 1.
187 \section{Questions and remarks of the second reviewer}
190 \item Move the contributions from related work to introduction.
192 \textbf{Answer:} The contributions were moved to the introduction section.
194 \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.
196 \textbf{Answer:} We agree with the reviewer that a grid is a type of heterogeneous architecture and the proposed algorithm can also work on any heterogeneous architecture.
198 In \cite{5}, we have proposed a frequency selection algorithm for distributed applications running on heterogeneous clusters, while in this work, the proposed algorithm was adapted to the grid architecture which is composed
199 of homogeneous clusters interconnected by a wide area network which is slower than the local
200 network in each cluster.
202 \item Define what iterative message passing applications are and give exemplar applications of them targeted by this method.
204 \textbf{Answer:} In order to clarify things, we have replaced in the paper the sentence ``the iterative message passing applications'' with ``the message passing applications with iterations''. Therefore, the proposed algorithm can be applied to any application that executes the same block of instructions many times and it is not limited to iterative methods that repeat the same block of instructions until convergence.
206 Many problems are solved by methods with iterations such as solving a linear system of equations with Jacobi and Gauss-Seidel methods, Image processing with methods that apply the same instructions for each pixel or block of pixels, etc.
209 \item Figure 1 is not clearly explained. Where is the slack time in figure 1 and why slack time =0 for task 1?
212 \textbf{Answer:} Figure 1 was redrawn, the white space before the barrier is the slack time. Slack times occur when a node has to wait for another node to finish its computation to synchronously communicate with it. In Figure 1, task 1 was assumed to be the slowest task. All the other tasks will finish their computations before the slowest task and wait until it finishes its computation before being able to synchronously communicate with it. This waiting time is the slack time and since the slowest task do not have to wait for the other tasks it has almost no slack time.
214 \item Define the parameters in eq. 1.
216 \textbf{Answer:} Fmax and Fnew have been defined as follows in the paper: ``$\Fmax$ is the maximum frequency before applying any DVFS and $\Fnew$ is the new frequency after applying DVFS''.
218 \item Eq. 2: are you assuming each cluster has the same number of nodes?
220 \textbf{Answer:} No, each cluster can have a different number of nodes. Therefore, in the paper, $M$, the number of nodes in a cluster, was replaced by $M_i$, the number of nodes in cluster $i$, in all the equations.
222 \item Eq.2 implicitly assumes that there is no overlapping between computation and communication. Is it reasonable?
224 \textbf{Answer:} In this paper, only message passing applications with synchronous and blocking communications were considered. In such applications, there is no overlapping between computations and communications on a node.
226 Asynchronous applications are beyond the scope of this paper and will be considered in a future work.
228 \item Eq. 2 is not clear:
230 \item How to define and determine the slowest cluster h? the one before scaling or after scaling?
232 \textbf{Answer:} The slowest node $h$ is the node which takes the maximum execution time to execute an iteration before scaling down its frequency. The previous sentence has been added to the paper.
235 \item What is the communication time without slack time?
237 \textbf{Answer:} There is no synchronous communications with zero slack times, but if a node sends a message to another node who 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.
240 \item 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.
242 \textbf{Answer:} We agree with the reviewer and the sentence "the slowest communication time" has been changed to "the communication time of the slowest node" in the paper.
247 \item Discuss the difference between eq. 2 and the prediction model in references \cite{4} and \cite{5}.
249 \textbf{Answer:} The prediction models in \cite{4} and \cite{5} are for homogeneous and heterogeneous clusters respectively, while the model in Equation 2 is adapted for grids. We have adapted the prediction models to the used architecture. Each architecture has its own characteristics. For example, in a homogeneous cluster all the nodes have the same specifications and only one scaling factor is computed by the algorithm to all the nodes of the cluster.
250 On the other hand, in a heterogeneous cluster, the nodes may have different specifications and a scaling factor should be computed to each node. The prediction models of a heterogeneous cluster can be used for a homogeneous cluster. In the same the models in this paper take more characteristics into considerations such as different networks to be adapted for grids and they can also be applied to a heterogeneous cluster. Therefore, the models presented in this paper are more complete than those presented in \cite{4} and \cite{5} and take more characteristics into consideration.
253 \item Eq. 10: Can the authors comment on the energy consumed by communications?
255 \textbf{Answer:} During communications, the CPU only consumes the static power power and during computations it consumes both dynamic and static power. For more information the reviewer can refer to \cite{3}.
257 \item This work assume homogeneous cpu in one cluster. Line 55 says: even if the distributed message
258 passing iterative application is load balanced, the computation time of each cpu j in cluster i may be different Why?
260 \textbf{Answer:} In a homogeneous cluster executing a load balanced distributed application, the computation time of each node might be slightly different than the others due to some delay caused
261 by the scheduler of the operating system of the node.
263 \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.
265 \textbf{Answer:} The sentence ``iterative applications'' was replaced by ``applications with iterations'' because the proposed algorithm can be applied to any application that executes the same block of instructions many times and it is not limited to iterative methods that terminate when they converge. The NAS parallel benchmarks are application with iterations because they iterate the same block of instructions until convergence or for fixed number of iterations. These benchmarks can be executed on any distributed memory platform such as clusters or grids with no required modifications. Since, we have deployed the same operating system on all the nodes, we just compile the source on one node and then copy the executable program on all the nodes. The application can then be executed with an ``mpirun'' command that takes three arguments:
267 \item the name of the application to execute
268 \item the number of processes required to execute the application
269 \item the architecture file that contains the names of the nodes that will execute the application. They could be from different clusters.
272 \item Broken sentence in line 28 on page 12.
274 \textbf{Answer:} The sentence was corrected.
276 \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?
278 \textbf{Answer:} Both forms can be used for computing $T_{old}$ and $T_{new}$. To avoid this confusion, the same form was used for both equations in the paper.
282 T_{old} = \mathop{\max_{i=1,2,\dots,N}}_{j=1,2,\dots,M_i} (\Tcp[ij]) +
283 \mathop{\min_{j=1,2,\dots,M_h}} (\Tcm[hj] )
285 where $h$ is the index of the slowest cluster.
289 \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.
291 \textbf{Answer:} We agree with the reviewer and the slack time is now presented at the beginning of the paper.
294 \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.
296 \textbf{Answer:} The proposed method can only be applied to parallel models with iterations
297 and with or without message passing. If only a few map and reduce operations are executed in the application and these operations are not iterative, the proposed algorithm cannot be adapted to that type of applications. On the other hand, if the map or reduce operations are iterative, the proposed algorithm can be applied when executing these operations. Finally, if in the application, the same map and reduce operations are executed many times iteratively, the proposed algorithm can then be applied to the whole application while considering that an iteration consists of a map operation followed by a reduce operation.
299 The proposed method with some adaptations can be applied to applications with iterations running on heterogeneous platforms composed of GPUs and CPUs because modern GPUs like CPUs allow the use of DVFS.
302 \section{Questions and remarks of the third reviewer}
305 \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
307 \textbf{Answer:} The experiments were not only conducted over 16 nodes, but they were also executed over 32 nodes distributed over three clusters.
308 In \cite{5} the algorithm was evaluated on a simulated heterogeneous cluster composed of up to 144 nodes. The overhead of the algorithm was very small, just 0.15 ms.
310 The experiments were not conducted on more than 32 nodes of Grid'5000 because it does not have many nodes that allow DVFS operations and have energy measurement tools. We agree with the reviewer that experiments using much more nodes should be conducted to evaluate the scalability of the proposed algorithm and when we will have access to such platforms, we will evaluate the proposed method over a larger number of nodes.
312 \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?
314 \textbf{Answer:} This paper does not focus on measuring the energy consumption of CPUs in a grid. It presents models to predict the energy consumption and the performance of an application with iterations running on a grid. These models use the given dynamic and static powers to predict the energy consumption of each CPU with different scaling factors. Moreover, since we do not have physical access to the nodes of the grid which are geographically distributed on many sites in France, we cannot use hardware tools to measure the consumption of CPUs. Therefore, we used Grid'5000's tool which measures the overall power consumption of a node in real-time. These values were used to deduce the dynamic power of the node when computing with the maximum frequency.
316 As a future work, it would be interesting to compare the accuracy of the results of the proposed energy model to the values given by instruments that measure the energy consumptions of CPUs during the execution time, as in \cite{2}.
318 \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"?
320 \textbf{Answer:} In the comparison section 6.5, we have presented the execution time of the algorithm when it is executed over 32 nodes from three clusters and located in two different sites. It takes on average 0.01 $ms$. In \cite{5} the algorithm was evaluated on a simulated heterogeneous cluster composed of up to 144 nodes. The overhead of the algorithm was just 0.15 ms.
323 The algorithm works online without profiling means it only uses the measured communication and computation times during the run-time and do not require to profile the application before run-time. Some methods use profilers before executing the application to gather a lot of information about the application such as computations to communication ratios and dependencies between tasks. The gathered information is used to scale the frequency of each node before executing the application.
325 The algorithm works without training because it does not require the partial or the total execution of the application before run-time. Indeed, some applications run parts of the application while using various frequencies to measure in advance their energy consumption. Then, using these values they select the the frequency of each node before executing the application.
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