Describe parameter k.

[loba-papers.git] / supercomp11 / supercomp11.tex

diff --git a/supercomp11/supercomp11.tex b/supercomp11/supercomp11.tex
index f41425c39afa1f7d7b3452e49f3cfd4905633c8d..2f2dd31bc46905d59c46caae3c0a96782fc50c34 100644 (file)
--- a/supercomp11/supercomp11.tex
+++ b/supercomp11/supercomp11.tex
@@ -195,11 +195,16 @@ condition or with a weaker condition.
 \section{Best effort strategy}
 \label{Best-effort}
 
 \section{Best effort strategy}
 \label{Best-effort}
 

-In this section we  describe  a new load-balancing strategy that we call
-\emph{best effort}.  The general idea behind this strategy is that each
-processor, that detects it has more load than some of its neighbors, 
-sends some load to the most of its less loaded neighbors, doing its
-best to reach the equilibrium between those neighbors and himself.
+In this section we describe a new load-balancing strategy that we call
+\emph{best effort}.  First, we explain the general idea behind this strategy,
+and then we describe some variants of this basic strategy.
+
+\subsection{Basic strategy}
+
+The general idea behind the \emph{best effort} strategy is that each processor,
+that detects it has more load than some of its neighbors, sends some load to the
+most of its less loaded neighbors, doing its best to reach the equilibrium
+between those neighbors and himself.

 
 More precisely, when a processor $i$ is in its load-balancing phase,
 he proceeds as following.
 
 More precisely, when a processor $i$ is in its load-balancing phase,
 he proceeds as following.


@@ -246,12 +251,28 @@ he proceeds as following.
   \end{equation*}
 \end{enumerate}
 
   \end{equation*}
 \end{enumerate}
 

-\FIXME{describe parameter $k$}
+\subsection{Leveling the amount to send}
+
+With the aforementioned basic strategy, each node does its best to reach the
+equilibrium with its neighbors.  Since each node may be taking the same kind of
+decision at the same moment, there is the risk that a node receives load from
+several of its neighbors, and then is temporary going off the equilibrium state.
+This is particularly true with strongly connected applications.
+
+In order to reduce this effect, we add the ability to level the amount to send.
+The idea, here, is to make smaller steps toward the equilibrium, such as a
+potentially wrong decision has a lower impact.
+
+Concretely, once $s_{ij}$ has been evaluated as before, it is simply divided by
+some configurable factor.  That's what we named the ``parameter $k$'' in
+Section~\ref{Results}.  The amount of data to send is then $s_{ij}(t) = (\bar{x}
+- x^i_j(t))/k$.
+\FIXME{check the name ($k$)}

 
 \section{Other strategies}
 \label{Other}
 
 
 \section{Other strategies}
 \label{Other}
 

-\FIXME{Réécrire en angliche.}
+\FIXME{Réécrire en anglais.}

 
 % \FIXME{faut-il décrire les stratégies makhoul et simple ?}
 
 
 % \FIXME{faut-il décrire les stratégies makhoul et simple ?}
 


@@ -497,8 +518,9 @@ an amount of load at less than 1\% of the load average, during an arbitrary
 number of computing iterations (2000 in our case).
 
 Note that this convergence detection was implemented in a centralized manner.
 number of computing iterations (2000 in our case).
 
 Note that this convergence detection was implemented in a centralized manner.

-This is easy to do within the simulator, but it's obviously not realistic.  In
-a real application we would have chosen a decentralized convergence detection algorithm, like the one described in \cite{10.1109/TPDS.2005.2}.
+This is easy to do within the simulator, but it's obviously not realistic.  In a
+real application we would have chosen a decentralized convergence detection
+algorithm, like the one described in \cite{10.1109/TPDS.2005.2}.

 
 \paragraph{Platforms}
 
 
 \paragraph{Platforms}
 


@@ -507,16 +529,21 @@ settings, we simulated the executions on two sorts of platforms.  These two
 sorts of platforms differ by their underlaid network topology.  On the one hand,
 we have homogeneous platforms, modeled as a cluster.  On the other hand, we have
 heterogeneous platforms, modeled as the interconnection of a number of clusters.
 sorts of platforms differ by their underlaid network topology.  On the one hand,
 we have homogeneous platforms, modeled as a cluster.  On the other hand, we have
 heterogeneous platforms, modeled as the interconnection of a number of clusters.

+
+The clusters were modeled by a fixed number of computing nodes interconnected
+through a backbone link.  Each computing node has a computing power of
+1~GFlop/s, and is connected to the backbone by a network link whose bandwidth is
+of 125~MB/s, with a latency of 50~$\mu$s.  The backbone has a network bandwidth
+of 2.25~GB/s, with a latency of 500~$\mu$s.
+

 The heterogeneous platform descriptions were created by taking a subset of the
 Grid'5000 infrastructure\footnote{Grid'5000 is a French large scale experimental
   Grid (see \url{https://www.grid5000.fr/}).}, as described in the platform file
 \texttt{g5k.xml} distributed with SimGrid.  Note that the heterogeneity of the
 The heterogeneous platform descriptions were created by taking a subset of the
 Grid'5000 infrastructure\footnote{Grid'5000 is a French large scale experimental
   Grid (see \url{https://www.grid5000.fr/}).}, as described in the platform file
 \texttt{g5k.xml} distributed with SimGrid.  Note that the heterogeneity of the

-platform only comes from the network topology.  The processor speeds, and
-network bandwidths were normalized since our algorithms currently are not aware
-of such heterogeneity.  We arbitrarily chose to fix the processor speed to
-1~GFlop/s, and the network bandwidth to 125~MB/s, with a latency of 50~$\mu$s,
-except for the links between geographically distant sites, where the network
-bandwidth was fixed to 2.25~GB/s, with a latency of 500~$\mu$s.
+platform here only comes from the network topology.  Indeed, since our
+algorithms currently do not handle heterogeneous computing resources, the
+processor speeds were normalized, and we arbitrarily chose to fix them to
+1~GFlop/s.

 
 Then we derived each sort of platform with four different number of computing
 nodes: 16, 64, 256, and 1024 nodes.
 
 Then we derived each sort of platform with four different number of computing
 nodes: 16, 64, 256, and 1024 nodes.


@@ -582,7 +609,7 @@ With these constraints in mind, we defined the following metrics:
   that can be compared between simulations of different sizes.
 
   This metric is expected to give an idea of the ability of the strategy to
   that can be compared between simulations of different sizes.
 
   This metric is expected to give an idea of the ability of the strategy to

-  diffuse the load quickly, lesser is better.
+  diffuse the load quickly.  A smaller value is better.

 
 \item[\textbf{average convergence date:}] that's the average of the dates when
   all nodes reached the convergence state.  The dates are measured as a number
 
 \item[\textbf{average convergence date:}] that's the average of the dates when
   all nodes reached the convergence state.  The dates are measured as a number


@@ -592,15 +619,15 @@ With these constraints in mind, we defined the following metrics:
   reached the convergence state.
 
   These two dates give an idea of the time needed by the strategy to reach the
   reached the convergence state.
 
   These two dates give an idea of the time needed by the strategy to reach the

-  equilibrium state, lesser is doubtlessly better.
+  equilibrium state.  A smaller value is better.

 
 

-\item[\textbf{data transfer amount:}] that's the sum of the amount of data of
-  all transfers during the simulation.  This sum is then normalized by dividing
-  it by the total amount of data present in the system.
+\item[\textbf{data transfer amount:}] that's the sum of the amount of all data
+  transfers during the simulation.  This sum is then normalized by dividing it
+  by the total amount of data present in the system.

 
   This metric is expected to give an idea of the efficiency of the strategy in
   terms of data movements, i.e. its ability to reach the equilibrium with fewer
 
   This metric is expected to give an idea of the efficiency of the strategy in
   terms of data movements, i.e. its ability to reach the equilibrium with fewer

-  transfers.
+  transfers.  Again, a smaller value is better.

 
 \end{description}
 
 
 \end{description}
 


@@ -657,4 +684,4 @@ Taille : 10 100 très gros
 
 % LocalWords:  Raphaël Couturier Arnaud Giersch Abderrahmane Sider Franche ij
 % LocalWords:  Bertsekas Tsitsiklis SimGrid DASUD Comté Béjaïa asynchronism ji
 
 % LocalWords:  Raphaël Couturier Arnaud Giersch Abderrahmane Sider Franche ij
 % LocalWords:  Bertsekas Tsitsiklis SimGrid DASUD Comté Béjaïa asynchronism ji

-% LocalWords:  ik isend irecv Cortés et al chan ctrl fifo Makhoul
+% LocalWords:  ik isend irecv Cortés et al chan ctrl fifo Makhoul GFlop xml