+often much longer than the time to transfer a load information message. So,
+when a node is notified
+%receives the information
+that later it will receive a data message,
+it can take this information into account in its load's queue list for preventive purposes.
+%and it can consider that its new load is larger.
+Consequently, it can send a part of its predictive
+%real
+load to some of its
+neighbors if required. We call this trick the \emph{clairvoyant virtual load} transfer mechanism.
+
+\medskip
+The main contributions and novelties of our work are summarized in the following section.
+
+\section{Our contributions}
+\label{contributions}
+\begin{itemize}
+\item We propose a {\it best effort strategy} which proceeds greedily to achieve efficient local neighborhoods equilibrium. Upon local load imbalance detection, a {\it significant amount} of load is moved from a highly loaded node (initiator) to less loaded neighbors.
+
+\item Unlike earlier works, we use a new concept of virtual loads transfer which allows nodes to predict the future loads they will receive in the subsequent iterations.
+This leads to a noticeable speedup of the global convergence time of the load balancing process.
+
+\item We use SimGrid simulator which is known to be able to characterize and model realistic models of computation and communication in different types of platforms. We show that taking into account both loads transfers' costs and network contention is essential and has a real impact on the quality of the load balancing performances.
+
+\end{itemize}
+
+
+
+The reminder of the paper is organized as follows. Section~\ref{sec.related.works} offers a review of the relevant approaches in the literature. Section~\ref{sec.bt-algo} describes the
+Bertsekas and Tsitsiklis' asynchronous load balancing algorithm.
+Section~\ref{sec.besteffort} presents the best effort strategy which provides
+efficient local loads equilibrium.
+In Section~\ref{sec.virtual-load}, the clairvoyant virtual load scheme is proposed to speedup the convergence time of the load balancing process.
+In Section~\ref{sec.simulations}, a comprehensive set of numerical results that exhibit the usefulness of our proposal when dealing with realistic models of computation and communication is provided. Finally, some concluding remarks are made in Section~\ref{conclusions-remarks}.
+
+
+\section{Related works}
+\label{sec.related.works}
+In this section, the relevant techniques proposed in the literature to tackle the problem of load balancing in a general context of distributed systems are reviewed.
+
+As pointed above, the most interesting approach to this issue has been proposed by Bertsekas and Tsitsiklis~\cite{bertsekas+tsitsiklis.1997.parallel}. This algorithm which is outlined in Section~\ref{sec.bt-algo} for the sake of comparison, has been borrowed and adapted in many works. For instance, in~\cite{CortesRCSL02} a static load balancing (called DASUD) for non negative integer number of divisible loads in arbitrary networks topologies is investigated. The term {\it "static"} stems from the fact that no loads are added or consumed during the load balancing process. The theoretical correctness proofs of the convergence property are given. Some generalizations of the same authors' own work for partially asynchronous discrete load balancing model are presented in~\cite{cedo+cortes+ripoll+al.2007.convergence}. The authors prove that the algorithm's convergence is finite and bounded by the straightforward network's diameter of the global equilibrium threshold in the network. In~\cite{bahi+giersch+makhoul.2008.scalable}, a fault tolerant communication version is addressed to deal with average consensus in wireless sensor networks. The objective is to have all nodes converging to the average of their initial measurements based only on nodes' local information. A slight adaptation is also considered in~\cite{BahiCG10} for dynamic networks with bounded delays asynchronous diffusion. The dynamical aspect stands at the communication level as links between the network's resources may be intermittent.
+
+Cybenko~\cite{Cybenko89} proposes a {\it diffusion} approach for hypercube multiprocessor networks.
+The author targets both static and dynamic random models of work distribution.
+The convergence proof is derived based on the {\it eigenstructure} of the
+iteration matrices that arise in load balancing of equal amount of
+computational works. A static load balancing for both synchronous and asynchronous ring networks is addressed in~\cite{GehrkePR99}. The authors assume that at any time step, one token at the most (units of load) can be transmitted along any edge of the ring and no tokens are created during the balancing phase. They show that for every initial token distribution, the proposed algorithm converges to the stable equilibrium with tighter linear bounds of time step-complexity.
+
+In order to achieve the load balancing of cloud data centers, a LB technique based on Bayes theorem and Clustering is proposed in~\cite{zhao2016heuristic}. The main idea of this approach is that, the Bayes theorem is combined with the clustering process to obtain the optimal clustering set of physical target hosts leading to the overall load balancing equilibrium. Bidding is a market-technique for task scheduling and load balancing in distributed systems
+that characterize a set of negotiation rules for users' jobs. For instance, Izakian et al~\cite{IzakianAL10} formulate a double auction mechanism for tasks-resources matching in grid computing environments where resources are considered as provider agents and users as consumer ones. Each entity participates in the network independently and makes autonomous decisions. A provider agent determines its bid price based on its current workload and each consumer agent defines its bid value based on two main parameters: average remaining time and remaining resources for bidding. Based on JADE simulator, the proposed algorithm exhibits better performances in terms of successful execution rates, resource utilization rates and fair profit allocation.
