X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/loba-papers.git/blobdiff_plain/380e5cf3507605371bba52eb9a64a9e9c6bcdf24..59636878becb2087601db617b593fd3f35181655:/loba-besteffort/loba-besteffort.tex

diff --git a/loba-besteffort/loba-besteffort.tex b/loba-besteffort/loba-besteffort.tex
index e966c40..3ccb2b0 100644
--- a/loba-besteffort/loba-besteffort.tex
+++ b/loba-besteffort/loba-besteffort.tex
@@ -347,7 +347,7 @@ information of the load they will receive, so they can take in into account.
 
 In order to test and validate our approaches, we wrote a simulator
 using the SimGrid
-framework~\cite{casanova+legrand+quinson.2008.simgrid}.  This
+framework~\cite{simgrid.web,casanova+legrand+quinson.2008.simgrid}.  This
 simulator, which consists of about 2,700 lines of C++, allows to run
 the different load-balancing strategies under various parameters, such
 as the initial distribution of load, the interconnection topology, the
@@ -724,70 +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 will 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
-(with virtual load feature) are respectively labeled ``b'' and ``a''.
+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  is 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.  This can  be explained by the
-fact that the \besteffort{} strategy tries to distribute the load faitly between
+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. In this case, the \makhoul{} strategy which
-tries to give more load to few neighbors reaches the equilibrum faster.
+tries to give more load to few neighbors reaches the equilibrium faster.
 
 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.
+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.
 
 Globally   the  number  of   interconnection  is   very  important.    The  more
-interconnection links there are, the  faster the \makhoul{} strategy is because
-it distributes quickly significant amount of load even if this is unfair between
+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.
 
 
-\subsubsection{With the virtual load extension with the load initially on only
-  one node}
+\subsubsection{Virtual load}
 
-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.
+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.
 
-\subsubsection{The \besteffort{} strategy with an initial random load
-  distribution, and larger platforms}
+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}.
 
-MÃªmes conclusions pour line et hcube.
-Sur tore, BE se fait exploser quand les comms coutent cher.
+%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.
 
-\FIXME{virer les 1024 ?}
+%\subsubsection{The \besteffort{} strategy with an initial random load
+%  distribution, and larger platforms}
 
-\subsubsection{With the virtual load extension with an initial random load
-  distribution}
+%In 
+%MÃªmes conclusions pour line et hcube.
+%Sur tore, BE se fait exploser quand les comms coutent cher.
 
-Soit c'est Ã©quivalent, soit on gagne -> surtout quand les comms coutent cher et
-qu'il y a beaucoup de voisins.
+%\FIXME{virer les 1024 ?}
+
+%\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}
 
