X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/loba-papers.git/blobdiff_plain/af32e62a6cd1228c1efbdad6d120bc81ea240282..a63036f3425d8303146d21053b097d533b3a6521:/loba-besteffort/loba-besteffort.tex

diff --git a/loba-besteffort/loba-besteffort.tex b/loba-besteffort/loba-besteffort.tex
index 5570b35..03cb38c 100644
--- a/loba-besteffort/loba-besteffort.tex
+++ b/loba-besteffort/loba-besteffort.tex
@@ -653,7 +653,7 @@ With these constraints in mind, we defined the following metrics:
 \label{sec.results}
 
 In this section, the results for the different simulations will be presented,
-and we'll try to explain our observations.
+and we will try to explain our observations.
 
 \subsubsection{Cluster vs grid platforms}
 
@@ -724,65 +724,103 @@ allocated time, or because we simply decided not to run it.
 
 \FIXME{annoncer le plan de la suite}
 
-\subsubsection{The \besteffort{} strategy with the load initially on only one
-  node}
+\subsubsection{The \besteffort{} and  \makhoul{} strategies without virtual load}
 
-Before looking at the different variations, we'll first show that the plain
-\besteffort{} strategy is valuable, and may be as good as the \makhoul{}
-strategy.  On the graphs from the figure~\ref{fig.results1}, these strategies
-are respectively labeled ``b'' and ``a''.
+Before looking  at the different variations,  we will first show  that the plain
+\besteffort{}  strategy  is valuable,  and  may be  as  good  as the  \makhoul{}
+strategy.  On  Figures~\ref{fig.results1} and~\ref{fig.resultsN},
+these strategies are respectively labeled ``b'' and ``a''.
 
-We can see that the relative performance of these strategies is mainly
-influenced by the application topology.  It's for the line topology that the
-difference is the more important.  In this case, the \besteffort{} strategy is
-nearly twice as fast as the \makhoul{} strategy.
+We  can  see  that  the  relative  performance of  these  strategies  is  mainly
+influenced by  the application topology.  It  is for the line  topology that the
+difference is the  more important.  In this case,  the \besteffort{} strategy is
+nearly faster than the \makhoul{} strategy.  This can  be explained by the
+fact that the \besteffort{} strategy tries to distribute the load fairly between
+all the nodes  and with the line topology,  it is easy to load  balance the load
+fairly.
 
 On the contrary, for the hypercube topology, the \besteffort{} strategy performs
-worse than the \makhoul{} strategy.
+worse than the \makhoul{} strategy. In this case, the \makhoul{} strategy which
+tries to give more load to few neighbors reaches the equilibrium faster.
 
-Finally, the results are more nuanced for the torus topology.
+For the torus  topology, for which the  number of links is between  the line and
+the hypercube, the \makhoul{} strategy  is slightly better but the difference is
+more nuanced when the initial load is  only on one node. The only case where the
+\makhoul{} strategy is really faster than the \besteffort{} strategy is with the
+random initial distribution when the communication are slow.
 
-This can be explained by ...
+Globally   the  number  of   interconnection  is   very  important.    The  more
+the interconnection links are, the  faster the \makhoul{} strategy is because
+it distributes quickly significant amount of load, even if this is unfair, between
+all the  neighbors.  In opposition,  the \besteffort{} strategy  distributes the
+load fairly so this strategy is better for low connected strategy.
 
--> interconnection
 
-plus c'est connectÃ©, moins bon est BE car Ã  vouloir trop bien Ã©quilibrer
-localement, le processeurs se perturbent mutuellement.  Du coup, makhoul qui
-Ã©quilibre moins bien localement est moins perturbÃ© par ces interfÃ©rences.
+\subsubsection{Virtual load}
 
-\subsubsection{With the virtual load extension with the load initially on only
-  one node}
+The influence of virtual load is most of the time really significant compared to
+the  same configuration  without  it. Sometimes  it  has no  effect  but {\bf  A
+  VERIFIER} it has never a negative effect on the load balancing we tested.
 
-Dans ce cas lÃ©gÃ¨re amÃ©lioration de la cvg. max.  Temps moyen de cvg. amÃ©liorÃ©,
-mais plus de temps passÃ© en idle, surtout quand les comms coutent cher.
+On Figure~\ref{fig.results1}, when the load is  initially on one node, it can be
+noticed that the  average idle times are generally longer  with the virtual load
+than without  it. This  can be explained  by the  fact that, with  virtual load,
+processors  will exchange all  the load  they need  to exchange  as soon  as the
+virtual load has been balanced  between all the processors. So consequently they
+cannot  compute  at  the  beginning.  This is  especially  noticeable  when  the
+communication are slow (on the left part of Figure ~\ref{fig.results1}.
 
-\subsubsection{The \besteffort{} strategy with an initial random load
-  distribution, and larger platforms}
+%Dans ce cas  lÃ©gÃ¨re amÃ©lioration de la cvg. max.  Temps  moyen de cvg. amÃ©liorÃ©,
+%mais plus de temps passÃ© en idle, surtout quand les comms coutent cher.
 
-MÃªmes conclusions pour line et hcube.
-Sur tore, BE se fait exploser quand les comms coutent cher.
+%\subsubsection{The \besteffort{} strategy with an initial random load
+%  distribution, and larger platforms}
 
-\FIXME{virer les 1024 ?}
+%In 
+%MÃªmes conclusions pour line et hcube.
+%Sur tore, BE se fait exploser quand les comms coutent cher.
 
-\subsubsection{With the virtual load extension with an initial random load
-  distribution}
+%\FIXME{virer les 1024 ?}
 
-Soit c'est Ã©quivalent, soit on gagne -> surtout quand les comms coutent cher et
-qu'il y a beaucoup de voisins.
+%\subsubsection{With the virtual load extension with an initial random load
+%  distribution}
+
+%Soit c'est Ã©quivalent, soit on gagne -> surtout quand les comms coutent cher et
+%qu'il y a beaucoup de voisins.
 
 \subsubsection{The $k$ parameter}
 \label{results-k}
 
-Dans le cas oÃ¹ les comms coutent cher et ou BE se fait avoir, on peut ameliorer
-les perfs avec le param k.
+As  explained  previously when  the  communication  are  slow the  \besteffort{}
+strategy is efficient. This is due to the fact that it tries to balance the load
+fairly and consequently  a significant amount of the  load is transfered between
+processors.  In this situation, it is possible to reduce the convergence time by
+using  the leveler  parameter  (parameter  $k$).  The  advantage  of using  this
+solution is particularly efficient when the initial load is randomly distributed
+on  the nodes with  torus and  hypercube topology  and slow  communication. When
+virtual load  mechanism is used,  the effect of  this parameter is  also visible
+with the same condition.
+
+
+
+\subsubsection{With integer load}
+
+We also performed  some experiments with integer load instead  of load with real
+value.  In  this case, the  results have globally  the same behavior.   The most
+intereting  result, from  our point  of view,  is that  the virtual  mode allows
+processors in a line topology to converge to the uniform load balancing. Without
+the virtual  load, most  of the time,  processors converge  to what we  call the
+``stairway effect'', that  is to say that  there is only a difference  of one in
+the load of each processor and its neighbors (for example with 10 processors, we
+obtain 10 9 8 7 6 6 7 8 9 10 instead of 8 8 8 8 8 8 8 8 8 8).
 
-\subsubsection{With integer load, 1 ou N}
+%Cas normal, ligne -> converge pas (effet d'escalier).
+%Avec vload, Ã§a converge.
 
-Cas normal, ligne -> converge pas (effet d'escalier).
-Avec vload, Ã§a converge.
+%Dans les autres cas, rÃ©sultats similaires au cas rÃ©el: redire que vload est
+%intÃ©ressant.
 
-Dans les autres cas, rÃ©sultats similaires au cas rÃ©el: redire que vload est
-intÃ©ressant.
+\FIXME{ajouter une courbe avec l'Ã©quilibrage en entier}
 
 \FIXME{virer la metrique volume de comms}
 
