\end{align*}
In this case, processor $2$ can either sends load to processor $1$ or processor
$3$. If it sends load to processor $1$ it will not satisfy condition
-(\ref{eq.ping-pong}) because after the sending it will be less loaded that
+\eqref{eq.ping-pong} because after the sending it will be less loaded that
$x_3^2(t)$. So we consider that the \emph{ping-pong} condition is probably to
strong. Currently, we did not try to make another convergence proof without this
condition or with a weaker condition.
In this section, we present the concept of \emph{virtual load}. In order to
use this concept, load balancing messages must be sent using two different kinds
of messages: load information messages and load balancing messages. More
-precisely, a node wanting to send a part of its load to one of its neighbors,
-can first send a load information message containing the load it will send and
+precisely, a node wanting to send a part of its load to one of its neighbors
+can first send a load information message containing the load it will send, and
then it can send the load balancing message containing data to be transferred.
Load information message are really short, consequently they will be received
very quickly. In opposition, load balancing messages are often bigger and thus
balancing message.
Doing this, we can expect a faster convergence since nodes have a faster
-information of the load they will receive, so they can take in into account.
+information of the load they will receive, so they can take it into account.
\FIXME{Est ce qu'on donne l'algo avec virtual load?}
processor speeds were normalized, and we arbitrarily chose to fix them to
1~GFlop/s.
-Then we derived each sort of platform with four different number of computing
+Then we derived each kind of platform with four different numbers of computing
nodes: 16, 64, 256, and 1024 nodes.
\subsubsection{Configurations}
