-\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 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 time for sparsely connected application 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 or 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.