\textbf{We agree with the reviewer that it would be interesting to compare the algorithm's performances with other relevant existing works in the literature.
-As reported in the paper, the Bertsekas and Tsitsiklis' algorithm is, to our knowledge, the closest work to the one we propose. The focus and the load balancing models addressed in [7, 9, 24] are different: The reference [7] consider partially asynchronous and static integer load balancing in homogeneous networks. The authors' work is more on the theoretical side of the spectrum, and no experimental results
-are presented to validate their approach. In [9], the authors deal with dynamic networks where communication links between the resources of the network are intermittent. The work in [24] investigate the problem of allocating non divisible load applications on heterogeneous platforms with the goal of response time minimization of users' jobs.}
+As reported in the paper, the Bertsekas and Tsitsiklis' algorithm is, to our knowledge, the closest work to the one we propose. The focus and the load balancing models addressed in [7, 9, 24] are different: Reference [7] considers partially asynchronous and static integer load balancing in homogeneous networks. The authors' work is more on the theoretical side of the spectrum, and no experimental results
+are presented to validate their approach. In [9], the authors deal with dynamic networks where communication links between the resources of the network are intermittent. The work in [24] investigates the problem of allocating non divisible load applications on heterogeneous platforms and it also aims at minimizing the response time of users' jobs.}
\textbf{
-We tried to perform a second reading and check our paper as well as we could.
+We have tried to perform a second reading and check our paper as well as we could.
}
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To avoid the ping-pong effect they use a k-factor to reduce the amount of load. They also distinguish between control message (metadata about the load that is going to be exchanged) and data message (actual exchanged load) that allows to have a more precise and fast estimation of the load at a given time.\\
The experiments are convincing and I like very much the discussion about the data and the conclusion drawn from them. I think the authors did a very good job in that aspect. }
-\subsection*{Request 1: My only concern is the section 5.2. I did not understand clearly what is this k-factor. The authors say, "Roughly speaking...", I do not what a fuzzy explanation but I need a correct, precise and operational description of that aspect of the work. I think the authors should present a clear explanation of what they do.
+\textit{My only concern is the section 5.2. I did not understand clearly what is this k-factor. The authors say, "Roughly speaking...", I do not what a fuzzy explanation but I need a correct, precise and operational description of that aspect of the work. I think the authors should present a clear explanation of what they do.
}
-\textbf{The weighting system parameter k is introduced to orchestrate the right balance between the topology structure and the CCR values of the deployed application. Indeed, to speedup the convergence time of the load balancing process, we face a difficult trade-off for choosing an appropriate amount of load to send between node neighbors upon load imbalance detection. On the one hand, if k is small, we expect faster convergence time for sparse connected application and large CCR values. On the other hand, for strong connected applications and small CCR values, a large value of k will enable us to better balance the load locally and therefore minimize the number of iterations toward the global equilibrium. In the experiments section, we observe that choosing k in [1..4], leads to good results for the considered CCR values and the targeted topology structures: a line, a torus, and an hypercube.
+\textbf{This point is now clarified in the revised version.
+\\
+The weighting system parameter k is introduced to orchestrate the right balance between the topology structure and the CCR values of the deployed application. Indeed, to speedup the convergence time of the load balancing process, we face a difficult trade-off to choose an appropriate amount of load to send between node neighbors upon load imbalance detection. On the one hand, if k is small, we expect faster convergence times for sparsely connected applications and large CCR values. On the other hand, for strongly connected applications and small CCR values, a large value of k will enable us to better balance the load locally and therefore minimize the number of iterations toward the global equilibrium. In the experiments section, we observe that choosing k in $\{1, 2, 4\}$ leads to good results for the considered CCR values and the targeted topology structures: a line, a torus, and an hypercube.
}
