\begin{abstract}
Most of the time, asynchronous load balancing algorithms have extensively been
-studied in a theoretical point of view. The Bertsekas and Tsitsiklis' algorithm
+studied in a theoretical point of view. The Bertsekas and Tsitsiklis'
+algorithm~\cite[section~7.4]{bertsekas+tsitsiklis.1997.parallel}
is certainly the most well known algorithm for which the convergence proof is
given. From a practical point of view, when a node wants to balance a part of
its load to some of its neighbors, the strategy is not described. In this
concerning load transfers and message concerning load information. In order to
increase the converge of a load balancing algorithm, we propose a simple
heuristic called \texttt{virtual load} which allows a node that receives an load
-information message to integrate the load that it will receive latter in its
+information message to integrate the load that it will receive later in its
load (virtually) and consequently sends a (real) part of its load to some of its
neighbors. In order to validate our approaches, we have defined a simulator
based on SimGrid which allowed us to conduct many experiments.
\end{abstract}
-
+\section{Introduction}
Load balancing algorithms are extensively used in parallel and distributed
applications in order to reduce the execution times. They can be applied in
proved that under classical hypotheses of asynchronous iterative algorithms and
a special constraint avoiding \texttt{ping-pong} effect, an asynchronous
iterative algorithm converge to the uniform load distribution. This work has
-been extended by many authors. For example, DASUD propose a version working with
-integer load.
+been extended by many authors. For example,
+DASUD~\cite{cortes+ripoll+cedo+al.2002.asynchronous} propose a version working
+with integer load. {\bf Rajouter des choses ici}.
+
+Although the Bertsekas and Tsitsiklis' algorithm describes the condition to
+ensure the convergence, there is no indication or strategy to really implement
+the load distribution. In other word, a node can send a part of its load to one
+or many of its neighbors while all the convergence conditions are
+followed. Consequently, we propose a new strategy called \texttt{best effort}
+that tries to balance the load of a node to all its less loaded neighbors while
+ensuring that all the nodes concerned by the load balancing phase have the same
+amount of load. Moreover, when real asynchronous applications are considered,
+using asynchronous load balancing algorithms can reduce the execution
+times. Most of the times, it is simpler to distinguish load information messages
+from data migration messages. Formers ones allows a node to inform its
+neighbors of its current load. These messages are very small, they can be sent
+quite often. For example, if an computing iteration takes a significant times
+(ranging from seconds to minutes), it is possible to send a new load information
+message at each neighbor at each iteration. Latter messages contains data that
+migrates from one node to another one. Depending on the application, it may have
+sense or not that nodes try to balance a part of their load at each computing
+iteration. But the time to transfer a load message from a node to another one is
+often much nore longer that to time to transfer a load information message. So,
+when a node receives the information that later it will receive a data message,
+it can take this information into account and it can consider that its new load
+is larger. Consequently, it can send a part of it real load to some of its
+neighbors if required. We call this trick the \texttt{virtual load} mecanism.
+
+
+
+So, in this work, we propose a new strategy for improving the distribution of
+the load and a simple but efficient trick that also improves the load
+balacing. Moreover, we have conducted many simulations with simgrid in order to
+validate our improvements are really efficient. Our simulations consider that in
+order to send a message, a latency delays the sending and according to the
+network performance and the message size, the time of the reception of the
+message also varies.
+
+In the following of this paper, Section~\ref{BT algo} describes the Bertsekas
+and Tsitsiklis' asynchronous load balancing algorithm. Moreover, we present a
+possible problem in the convergence conditions. Section~\ref{Best-effort}
+presents the best effort strategy which provides an efficient way to reduce the
+execution times. In Section~\ref{Virtual load}, the virtual load mecanism is
+proposed. Simulations allowed to show that both our approaches are valid using a
+quite realistic model detailed in Section~\ref{Simulations}. Finally we give a
+conclusion and some perspectives to this work.
+
+
+
+
+\section{Bertsekas and Tsitsiklis' asynchronous load balancing algorithm}
+\label{BT algo}
+
+Comment on the problem in the convergence condition.
+
+\section{Best effort strategy}
+\label{Best-effort}
+
+
+
+\section{Virtual load}
+\label{Virtual load}
+
+\section{Simulations}
+\label{Simulations}
+
+\subsection{Simulation model}
+
+\subsection{Validation of our approaches}
+
+
+On veut montrer quoi ? :
+
+1) best plus rapide que les autres (simple, makhoul)
+2) avantage virtual load
+
+Est ce qu'on peut trouver des contre exemple?
+Topologies variées
+
+
+Simulation avec temps définies assez long et on mesure la qualité avec : volume de calcul effectué, volume de données échangées
+Mais aussi simulation avec temps court qui montre que seul best converge
+
+
+Expés avec ratio calcul/comm rapide et lent
+
+Quelques expés avec charge initiale aléatoire plutot que sur le premier proc
+
+Cadre processeurs homogènes
+
+Topologies statiques
+
+On ne tient pas compte de la vitesse des liens donc on la considère homogène
+
+Prendre un réseau hétérogène et rendre processeur homogène
+
+Taille : 10 100 très gros
+
+\section{Conclusion and perspectives}
+\bibliographystyle{spmpsci}
+\bibliography{biblio}
\end{document}
