\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
\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
$x_3^2(t)$. 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.
$x_3^2(t)$. 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
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
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
simulator, which consists of about 2,700 lines of C++, allows to run
the different load-balancing strategies under various parameters, such
as the initial distribution of load, the interconnection topology, the
simulator, which consists of about 2,700 lines of C++, allows to run
the different load-balancing strategies under various parameters, such
as the initial distribution of load, the interconnection topology, the
these descriptions. For an exhaustive presentation, we refer to the
actual source code that was used for the experiments%
\footnote{As mentioned before, our simulator relies on the SimGrid
these descriptions. For an exhaustive presentation, we refer to the
actual source code that was used for the experiments%
\footnote{As mentioned before, our simulator relies on the SimGrid
experiments, we used a pre-release of SimGrid 3.7 (Git commit
67d62fca5bdee96f590c942b50021cdde5ce0c07, available from
\url{https://gforge.inria.fr/scm/?group_id=12})}, and which is
experiments, we used a pre-release of SimGrid 3.7 (Git commit
67d62fca5bdee96f590c942b50021cdde5ce0c07, available from
\url{https://gforge.inria.fr/scm/?group_id=12})}, and which is
nodes: 16, 64, 256, and 1024 nodes.
\subsubsection{Configurations}
nodes: 16, 64, 256, and 1024 nodes.
\subsubsection{Configurations}