From: Arnaud Giersch Date: Thu, 15 May 2014 15:26:41 +0000 (+0200) Subject: Misc. X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/loba-papers.git/commitdiff_plain/f1aa5b9dfdd4ecd85ea65ea01584c8c452d8acec Misc. --- diff --git a/loba-besteffort/loba-besteffort.tex b/loba-besteffort/loba-besteffort.tex index 3ccb2b0..2d37f5f 100644 --- a/loba-besteffort/loba-besteffort.tex +++ b/loba-besteffort/loba-besteffort.tex @@ -87,7 +87,8 @@ Load balancing algorithms are extensively used in parallel and distributed applications in order to reduce the execution times. They can be applied in different scientific fields from high performance computation to micro sensor -networks. They are iterative by nature. In literature many kinds of load +networks. They are iterative by nature.\FIXME{really?} +In literature many kinds of load balancing algorithms have been studied. They can be classified according different criteria: centralized or decentralized, in static or dynamic environment, with homogeneous or heterogeneous load, using synchronous or @@ -115,11 +116,11 @@ 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. Former ones allows a node to inform its +from data migration messages. Former ones allow 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 +quite often. For example, if a 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 +message to each neighbor at each iteration. Latter messages contain 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 @@ -129,14 +130,12 @@ 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 \emph{virtual load} mechanism. - - -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 -balancing. 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 +So, in this work, we propose a new strategy to improve the distribution of the +load and a simple but efficient trick that also improves the load +balancing. Moreover, 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. In the following of this paper, Section~\ref{sec.bt-algo} describes the @@ -159,8 +158,8 @@ In order prove the convergence of asynchronous iterative load balancing Bertsekas 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 different processors. In this work, we +Communication links are represented by a connected undirected graph $G=(N,A)$ +where $A$ is the set of links connecting different 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 @@ -193,12 +192,12 @@ Nevertheless, we think that this condition may lead to deadlocks in some cases. For example, if we consider only three processors and that processor $1$ is linked to processor $2$ which is also linked to processor $3$ (i.e. a simple chain which 3 processors). Now consider we have the following values at time $t$: -\begin{eqnarray*} -x_1(t)=10 \\ -x_2(t)=100 \\ -x_3(t)=99.99\\ - x_3^2(t)=99.99\\ -\end{eqnarray*} +\begin{align*} + x_1(t) &= 10 \\ + x_2(t) &= 100 \\ + x_3(t) &= 99.99 \\ + x_3^2(t) &= 99.99 \\ +\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 (\ref{eq.ping-pong}) because after the sending it will be less loaded that @@ -307,7 +306,7 @@ a load balancing decision, it starts by sorting its neighbors by increasing order of their load. Then, it computes the difference between its own load, and the load of each of its neighbors. Finally, taking the neighbors following the order defined before, the amount of load to send $s_{ij}$ is computed as -$1/(N+1)$ of the load difference, with $N$ being the number of neighbors. This +$1/(n+1)$ of the load difference, with $n$ being the number of neighbors. This process continues as long as the node is more loaded than the considered neighbor.