+often much more longer that 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.
+
+\subsection{Our 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 transfers 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 modelize 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.
+
+%\item We improve the straightforward network's diameter bound of the global equilibrium threshold in the network. % not sure, it depends on the remaining time before the paper submission ...
+\end{itemize}
+
+
+%{\bf The contributions of this paper are the following:}
+%\begin{itemize}
+%\item We propose a new strategy to improve the distribution of the
+%load and a simple but efficient trick that also improves the load
+%balancing.
+%\item we have conducted many simulations with SimGrid in order to
+%validate that 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.
+%\end{itemize}
+
+The reminder of the paper is organized as follows.
+In Section~\ref{sec.related.works}, we review the relevant related works in load balancing. Section~\ref{sec.bt-algo} describes the
+Bertsekas and Tsitsiklis' asynchronous load balancing algorithm. %Moreover, we present a possible problem in the convergence conditions.
+Section~\ref{sec.besteffort} presents the best effort strategy which provides
+efficient local loads equilibrium. This strategy will be compared with other existing competitor ones, presented in Section~\ref{sec.other}. In
+Section~\ref{sec.virtual-load}, the clairvoyant virtual load scheme is proposed to speedup the convergence time of the load balancing process.
+We provide in Section~\ref{sec.simulations}, a comprehensive set of numerical results that exhibit the usefulness of our proposals when we deal with realistic models of computation and communication. Finally, we give some concluding remarks in Section~\ref{conclusions-remarks}.
+
+
+\section{Related works}
+\label{sec.related.works}
+In this section, we fairly review the relevant techniques proposed in the literature to tackle the problem of load balancing in a general context of distributed systems.
+
+
+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.
+
+
+Choi et al.~\cite{ChoiBH09} address the problem of robust task allocation in arbitrary networks. The proposed
+approaches combine bidding approach for task selection and consensus procedure scheme for
+decentralized conflict resolution. The developed algorithms are proven to converge to a conflict-free assignment in
+both single and multiple task assignment problem.
+
+
+An online stochastic dual gradient LB algorithm which is called DGLB is proposed in~\cite{chen2017dglb}. The authors deal with both workload and energy management for cloud networks consisting of multiple geo-distributed mapping nodes and data Centers. To enable online distributed implementation, tasks are decomposed both across time and space by leveraging a dual decomposition approach. Experimental results corroborate the merits of the proposed algorithm.
