X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/loba-papers.git/blobdiff_plain/1ccb8a3cdf8051ce59428e89b46322f8b6326db2..2216578e9740572a34f3064af72777d9fc281fe2:/supercomp11/supercomp11.tex?ds=inline diff --git a/supercomp11/supercomp11.tex b/supercomp11/supercomp11.tex index 2fc63f7..6a48cd3 100644 --- a/supercomp11/supercomp11.tex +++ b/supercomp11/supercomp11.tex @@ -1,5 +1,8 @@ - \documentclass[smallextended]{svjour3} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{mathptmx} +\usepackage{courier} \usepackage{graphicx} \begin{document} @@ -28,7 +31,8 @@ \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 @@ -40,7 +44,7 @@ balancing algorithm is implemented most of the time can dissociate messages 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. @@ -65,8 +69,9 @@ algorithm which is definitively a reference for many works. In their work, they 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 proposes a version working with -integer load. {\bf Rajouter des choses ici}. +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 @@ -117,7 +122,29 @@ 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. +In order prove the convergence of asynchronous iterative load balancing +Bertesekas and Tsitsiklis proposed a model +in~\cite{bertsekas+tsitsiklis.1997.parallel}. Here we recall some notations. +Consider that $N={1,...,n}$ processors are connected through a network. +Communication links are represented by a connected undirected graph $G=(N,V)$ +where $V$ is the set of links connecting differents processors. In this work, we +consider that processors are homogeneous for sake of simplicity. It is quite +easy to tackle the heterogeneous case~\cite{ElsMonPre02}. Load of processor $i$ +at time $t$ is represented by $x_i(t)\geq 0$. Let $V(i)$ be the set of +neighbors of processor $i$. Each processor $i$ has an estimate of the load of +each of its neighbors $j \in V(i)$ represented by $x_j^i(t)$. According to +asynchronism and communication delays, this estimate may be outdated. We also +consider that the load is described by a continuous variable. + +When a processor send a part of its load to one or some of its neighbors, the +transfer takes time to be completed. Let $s_{ij}(t)$ be the amount of load that +processor $i$ has transfered to processor $j$ at time $t$ and let $r_{ij}(t)$ be the +amount of load received by processor $j$ from processor $i$ at time $t$. Then +the amount of load of processor $i$ at time $t+1$ is given by: +\begin{equation} +x_i(t+1)=x_i(t)-\sum_{j\in V(i)} s_{ij}(t) + \sum_{j\in V(i)} r_{ji}(t) +\end{equation} + \section{Best effort strategy} \label{Best-effort} @@ -130,13 +157,59 @@ Comment on the problem in the convergence condition. \section{Simulations} \label{Simulations} +In order to test and validate our approaches, we wrote a simulator +using the SimGrid +framework~\cite{casanova+legrand+quinson.2008.simgrid}. The process +model is detailed in the next section (\ref{Sim model}), then the +results of the simulations are presented in section~\ref{Results}. + \subsection{Simulation model} +\label{Sim model} \subsection{Validation of our approaches} +\label{Results} + + +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} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% ispell-local-dictionary: "american" +%%% End: + +% LocalWords: Raphaël Couturier Arnaud Giersch Abderrahmane Sider +% LocalWords: Bertsekas Tsitsiklis SimGrid DASUD