début du travail sur a patie async

[hpcc2014.git] / hpcc.tex

diff --git a/hpcc.tex b/hpcc.tex
index 207c56083c6e498dadd6fd3b166a6662938615b0..5ab9faf540739761cb6c88495eb6688aa0841ad7 100644 (file)
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -4,7 +4,7 @@
 \usepackage[utf8]{inputenc}
 \usepackage{amsfonts,amssymb}
 \usepackage{amsmath}
 \usepackage[utf8]{inputenc}
 \usepackage{amsfonts,amssymb}
 \usepackage{amsmath}

-\usepackage{algorithm}
+%\usepackage{algorithm}

 \usepackage{algpseudocode}
 %\usepackage{amsthm}
 \usepackage{graphicx}
 \usepackage{algpseudocode}
 %\usepackage{amsthm}
 \usepackage{graphicx}


@@ -25,10 +25,12 @@
 \usepackage[textsize=footnotesize]{todonotes}
 \newcommand{\AG}[2][inline]{%
   \todo[color=green!50,#1]{\sffamily\textbf{AG:} #2}\xspace}
 \usepackage[textsize=footnotesize]{todonotes}
 \newcommand{\AG}[2][inline]{%
   \todo[color=green!50,#1]{\sffamily\textbf{AG:} #2}\xspace}

-\newcommand{\RC}[2][inline]{%
-  \todo[color=red!10,#1]{\sffamily\textbf{RC:} #2}\xspace}
+\newcommand{\DL}[2][inline]{%
+  \todo[color=yellow!50,#1]{\sffamily\textbf{DL:} #2}\xspace}

 \newcommand{\LZK}[2][inline]{%
   \todo[color=blue!10,#1]{\sffamily\textbf{LZK:} #2}\xspace}
 \newcommand{\LZK}[2][inline]{%
   \todo[color=blue!10,#1]{\sffamily\textbf{LZK:} #2}\xspace}

+\newcommand{\RC}[2][inline]{%
+  \todo[color=red!10,#1]{\sffamily\textbf{RC:} #2}\xspace}

 
 \algnewcommand\algorithmicinput{\textbf{Input:}}
 \algnewcommand\Input{\item[\algorithmicinput]}
 
 \algnewcommand\algorithmicinput{\textbf{Input:}}
 \algnewcommand\Input{\item[\algorithmicinput]}


@@ -45,27 +47,30 @@
 
 \author{%
   \IEEEauthorblockN{%
 
 \author{%
   \IEEEauthorblockN{%

-    Charles Emile Ramamonjisoa and
-    David Laiymani and
-    Arnaud Giersch and
-    Lilia Ziane Khodja and
-    Raphaël Couturier
+    Charles Emile Ramamonjisoa\IEEEauthorrefmark{1},
+    David Laiymani\IEEEauthorrefmark{1},
+    Arnaud Giersch\IEEEauthorrefmark{1},
+    Lilia Ziane Khodja\IEEEauthorrefmark{2} and
+    Raphaël Couturier\IEEEauthorrefmark{1}
+  }
+  \IEEEauthorblockA{\IEEEauthorrefmark{1}%
+    Femto-ST Institute -- DISC Department\\
+    Université de Franche-Comté,
+    IUT de Belfort-Montbéliard\\
+    19 avenue du Maréchal Juin, BP 527, 90016 Belfort cedex, France\\
+    Email: \email{{charles.ramamonjisoa,david.laiymani,arnaud.giersch,raphael.couturier}@univ-fcomte.fr}

   }
   }

-  \IEEEauthorblockA{%
-    Femto-ST Institute - DISC Department\\
-    Université de Franche-Comté\\
-    Belfort\\
-    Email: \email{{raphael.couturier,arnaud.giersch,david.laiymani,charles.ramamonjisoa}@univ-fcomte.fr}
+  \IEEEauthorblockA{\IEEEauthorrefmark{2}%
+    Inria Bordeaux Sud-Ouest\\
+    200 avenue de la Vieille Tour, 33405 Talence cedex, France \\
+    Email: \email{lilia.ziane@inria.fr}

   }
 }
 
 \maketitle
 
 \RC{Ordre des autheurs pas définitif.}
   }
 }
 
 \maketitle
 
 \RC{Ordre des autheurs pas définitif.}

-\LZK{Adresse de Lilia: Inria Bordeaux Sud-Ouest, 200 Avenue de la Vieille Tour, 33405 Talence Cedex, France \\ Email: lilia.ziane@inria.fr}

 \begin{abstract}
 \begin{abstract}

-ABSTRACT
-

 In recent years, the scalability of large-scale implementation in a 
 distributed environment of algorithms becoming more and more complex has 
 always been hampered by the limits of physical computing resources 
 In recent years, the scalability of large-scale implementation in a 
 distributed environment of algorithms becoming more and more complex has 
 always been hampered by the limits of physical computing resources 


@@ -80,19 +85,18 @@ balance and a compromise between computation and communication time
 during the execution. Two important factors determine the success of the 
 experimentation: the convergence of the iterative algorithm on a large 
 scale and the execution time reduction in asynchronous mode. Once again, 
 during the execution. Two important factors determine the success of the 
 experimentation: the convergence of the iterative algorithm on a large 
 scale and the execution time reduction in asynchronous mode. Once again, 

-from the current work, a simulated environment like Simgrid provides 
+from the current work, a simulated environment like SimGrid provides

 accurate results which are difficult or even impossible to obtain in a 
 physical platform by exploiting the flexibility of the simulator on the 
 computing units clusters and the network structure design. Our 
 accurate results which are difficult or even impossible to obtain in a 
 physical platform by exploiting the flexibility of the simulator on the 
 computing units clusters and the network structure design. Our 

-experimental outputs showed a saving of up to 40 \% for the algorithm 
+experimental outputs showed a saving of up to \np[\%]{40} for the algorithm

 execution time in asynchronous mode compared to the synchronous one with 
 execution time in asynchronous mode compared to the synchronous one with 

-a residual precision up to E-11. Such successful results open 
+a residual precision up to \np{E-11}. Such successful results open

 perspectives on experimentations for running the algorithm on a 
 simulated large scale growing environment and with larger problem size. 
 
 perspectives on experimentations for running the algorithm on a 
 simulated large scale growing environment and with larger problem size. 
 

-Keywords : Algorithm distributed iterative asynchronous simulation 
-simgrid
-
+% no keywords for IEEE conferences
+% Keywords: Algorithm distributed iterative asynchronous simulation SimGrid

 \end{abstract}
 
 \section{Introduction}
 \end{abstract}
 
 \section{Introduction}


@@ -103,11 +107,11 @@ researchers on various scientific disciplines but also by industrial in
 the field. Indeed, the increasing complexity of these requested 
 applications combined with a continuous increase of their sizes lead to 
 write distributed and parallel algorithms requiring significant hardware 
 the field. Indeed, the increasing complexity of these requested 
 applications combined with a continuous increase of their sizes lead to 
 write distributed and parallel algorithms requiring significant hardware 

-resources (grid computing, clusters, broadband network, etc\dots{}) but
+resources (grid computing, clusters, broadband network, etc.) but

 also a non-negligible CPU execution time. We consider in this paper a
 class of highly efficient parallel algorithms called iterative executed 
 in a distributed environment. As their name suggests, these algorithm 
 also a non-negligible CPU execution time. We consider in this paper a
 class of highly efficient parallel algorithms called iterative executed 
 in a distributed environment. As their name suggests, these algorithm 

-solves a given problem that might be NP- complete complex by successive 
+solves a given problem that might be NP-complete complex by successive

 iterations ($X_{n +1} = f(X_{n})$) from an initial value $X_{0}$ to find
 an approximate value $X^*$ of the solution with a very low
 residual error. Several well-known methods demonstrate the convergence 
 iterations ($X_{n +1} = f(X_{n})$) from an initial value $X_{0}$ to find
 an approximate value $X^*$ of the solution with a very low
 residual error. Several well-known methods demonstrate the convergence 


@@ -157,7 +161,7 @@ This article is structured as follows: after this introduction, the next
 section will give a brief description of iterative asynchronous model. 
 Then, the simulation framework SimGrid will be presented with the
 settings to create various distributed architectures. The algorithm of 
 section will give a brief description of iterative asynchronous model. 
 Then, the simulation framework SimGrid will be presented with the
 settings to create various distributed architectures. The algorithm of 

-the multi -splitting method used by GMRES written with MPI primitives 
+the multi-splitting method used by GMRES written with MPI primitives

 and its adaptation to SimGrid with SMPI (Simulated MPI) will be in the
 next section. At last, the experiments results carried out will be
 presented before the conclusion which we will announce the opening of 
 and its adaptation to SimGrid with SMPI (Simulated MPI) will be in the
 next section. At last, the experiments results carried out will be
 presented before the conclusion which we will announce the opening of 


@@ -165,17 +169,75 @@ our future work after the results.
  
 \section{The asynchronous iteration model}
 
  
 \section{The asynchronous iteration model}
 

-Décrire le modèle asynchrone. Je m'en charge (DL)
-
-\section{SimGrid}
-
-Décrire SimGrid~\cite{casanova+legrand+quinson.2008.simgrid} (Arnaud)
-
+As exposed in the introduction, parallel iterative methods are now
+widely used in many scientific domains. They can be classified in three main classes
+depending on how iterations and communications are managed (for more
+details readers can refer to \cite{bcvc02:ip}). In the
+\textit{Synchronous Iterations - Synchronous Communications (SISC)}
+model data are exchanged at the end of each iteration. All the
+processors must begin the same iteration at the same time and
+important idle times on processors are generated. The
+\textit{Synchronous Iterations - Asynchronous Communications (SIAC)}
+model can be compared to the previous one except that data required on
+another processor are sent asynchronously i.e.  without stopping
+current computations. This technique allows to partially overlap
+communications by computations but unfortunately, the overlapping is
+only partial and important idle times remain.  It is clear that, in a
+grid computing context, where the number of computational nodes is large,
+heterogeneous and widely distributed, the idle times generated by
+synchronizations are very penalizing. One way to overcome this problem
+is to use the \textit{Asynchronous Iterations - Asynchronous
+  Communications (AIAC)} model. Here, local computations do not need
+to wait for required data. Processors can then perform their
+iterations with the data present at that time. Figure \ref{fig:aiac}
+illustrates this model where the grey blocks represent the computation
+phases, the white spaces the idle times and the arrows the
+communications. With this algorithmic model, the number of iterations
+required before the convergence is generally greater than for the two
+former classes. But, and as detailed in \cite{bcvc06:ij}, AIAC
+algorithms can significantly reduce overall execution times by
+suppressing idle times due to synchronizations especially in a grid
+computing context.
+
+\begin{figure}[htbp]
+  \centering
+    \includegraphics[width=8cm]{AIAC.pdf}
+  \caption{The Asynchronous Iterations - Asynchronous Communications model } 
+  \label{fig:aiac}
+\end{figure}

 
 
 
 
 
 
 
 

+\section{SimGrid}

 
 

+SimGrid~\cite{casanova+legrand+quinson.2008.simgrid,SimGrid} is a simulation
+framework to sudy the behavior of large-scale distributed systems.  As its name
+says, it emanates from the grid computing community, but is nowadays used to
+study grids, clouds, HPC or peer-to-peer systems.
+%- open source, developped since 1999, one of the major solution in the field
+%
+SimGrid provides several programming interfaces: MSG to simulate Concurrent
+Sequential Processes, SimDAG to simulate DAGs of (parallel) tasks, and SMPI to
+run real applications written in MPI~\cite{MPI}.  Apart from the native C
+interface, SimGrid provides bindings for the C++, Java, Lua and Ruby programming
+languages.  The SMPI interface supports applications written in C or Fortran,
+with little or no modifications.
+%- implements most of MPI-2 \cite{ref} standard [CHECK]
+
+%%% explain simulation
+%- simulated processes folded in one real process
+%- simulates interactions on the network, fluid model
+%- able to skip long-lasting computations
+%- traces + visu?
+
+%%% platforms
+%- describe resources and their interconnection, with their properties
+%- XML files
+
+%%% validation + refs
+
+\AG{Décrire SimGrid~\cite{casanova+legrand+quinson.2008.simgrid,SimGrid} (Arnaud)}

 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Simulation of the multisplitting method}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Simulation of the multisplitting method}


@@ -199,7 +261,7 @@ B_1 \\
 \vdots\\
 B_L
 \end{array} \right)\] 
 \vdots\\
 B_L
 \end{array} \right)\] 

-in such a way that successive rows of matrix $A$ and both vectors $x$ and $b$ are assigned to one cluster, where for all $l,m\in\{1,\ldots,L\}$ $A_{lm}$ is a rectangular block of $A$ of size $n_l\times n_m$, $X_l$ and $B_l$ are sub-vectors of $x$ and $b$, respectively, each of size $n_l$ and $\sum_{l} n_l=\sum_{m} n_m=n$.
+in such a way that successive rows of matrix $A$ and both vectors $x$ and $b$ are assigned to one cluster, where for all $l,m\in\{1,\ldots,L\}$ $A_{lm}$ is a rectangular block of $A$ of size $n_l\times n_m$, $X_l$ and $B_l$ are sub-vectors of $x$ and $b$, respectively, of size $n_l$ each and $\sum_{l} n_l=\sum_{m} n_m=n$.

 
 The multisplitting method proceeds by iteration to solve in parallel the linear system on $L$ clusters of processors, in such a way each sub-system
 \begin{equation}
 
 The multisplitting method proceeds by iteration to solve in parallel the linear system on $L$ clusters of processors, in such a way each sub-system
 \begin{equation}


@@ -213,8 +275,9 @@ Y_l = B_l - \displaystyle\sum_{\substack{m=1\\ m\neq l}}^{L}A_{lm}X_m
 \end{equation}
 is solved independently by a cluster and communications are required to update the right-hand side sub-vector $Y_l$, such that the sub-vectors $X_m$ represent the data dependencies between the clusters. As each sub-system (\ref{eq:4.1}) is solved in parallel by a cluster of processors, our multisplitting method uses an iterative method as an inner solver which is easier to parallelize and more scalable than a direct method. In this work, we use the parallel algorithm of GMRES method~\cite{ref1} which is one of the most used iterative method by many researchers. 
 
 \end{equation}
 is solved independently by a cluster and communications are required to update the right-hand side sub-vector $Y_l$, such that the sub-vectors $X_m$ represent the data dependencies between the clusters. As each sub-system (\ref{eq:4.1}) is solved in parallel by a cluster of processors, our multisplitting method uses an iterative method as an inner solver which is easier to parallelize and more scalable than a direct method. In this work, we use the parallel algorithm of GMRES method~\cite{ref1} which is one of the most used iterative method by many researchers. 
 

-\begin{algorithm}
-\caption{A multisplitting solver with GMRES method}
+\begin{figure}
+  %%% IEEE instructions forbid to use an algorithm environment here, use figure
+  %%% instead

 \begin{algorithmic}[1]
 \Input $A_l$ (sparse sub-matrix), $B_l$ (right-hand side sub-vector)
 \Output $X_l$ (solution sub-vector)\vspace{0.2cm}
 \begin{algorithmic}[1]
 \Input $A_l$ (sparse sub-matrix), $B_l$ (right-hand side sub-vector)
 \Output $X_l$ (solution sub-vector)\vspace{0.2cm}


@@ -235,10 +298,23 @@ is solved independently by a cluster and communications are required to update t
 \State \Return $X_l^k$
 \EndFunction
 \end{algorithmic}
 \State \Return $X_l^k$
 \EndFunction
 \end{algorithmic}

+\caption{A multisplitting solver with GMRES method}

 \label{algo:01}
 \label{algo:01}

-\end{algorithm}
+\end{figure}

 
 

-Algorithm~\ref{algo:01} shows the main key points of the multisplitting method to solve a large sparse linear system. This algorithm is based on an outer-inner iteration method where the parallel synchronous GMRES method is used to solve the inner iteration. It is executed in parallel by each cluster of processors. For all $l,m\in\{1,\ldots,L\}$, the matrices and vectors with the subscript $l$ represent the local data for cluster $l$, while $\{A_{lm}\}_{m\neq l}$ are off-diagonal matrices of sparse matrix $A$ and $\{X_m\}_{m\neq l}$ contain vector elements of solution $x$ shared with neighboring clusters. At every outer iteration $k$, asynchronous communications are performed between processors of the local cluster and those of distant clusters (lines $6$ and $7$ in Algorithm~\ref{algo:01}). The shared vector elements of the solution $x$ are exchanged by message passing using MPI non-blocking communication routines. 
+Algorithm on Figure~\ref{algo:01} shows the main key points of the
+multisplitting method to solve a large sparse linear system. This algorithm is
+based on an outer-inner iteration method where the parallel synchronous GMRES
+method is used to solve the inner iteration. It is executed in parallel by each
+cluster of processors. For all $l,m\in\{1,\ldots,L\}$, the matrices and vectors
+with the subscript $l$ represent the local data for cluster $l$, while
+$\{A_{lm}\}_{m\neq l}$ are off-diagonal matrices of sparse matrix $A$ and
+$\{X_m\}_{m\neq l}$ contain vector elements of solution $x$ shared with
+neighboring clusters. At every outer iteration $k$, asynchronous communications
+are performed between processors of the local cluster and those of distant
+clusters (lines $6$ and $7$ in Figure~\ref{algo:01}). The shared vector
+elements of the solution $x$ are exchanged by message passing using MPI
+non-blocking communication routines.

 
 \begin{figure}
 \centering
 
 \begin{figure}
 \centering


@@ -263,7 +339,7 @@ where $\MI$ is the maximum number of outer iterations and $\epsilon$ is the tole
 
 \section{Experimental results}
 
 
 \section{Experimental results}
 

-When the ``real'' application runs in the simulation environment and produces
+When the \emph{real} application runs in the simulation environment and produces

 the expected results, varying the input parameters and the program arguments
 allows us to compare outputs from the code execution. We have noticed from this
 study that the results depend on the following parameters: (1) at the network
 the expected results, varying the input parameters and the program arguments
 allows us to compare outputs from the code execution. We have noticed from this
 study that the results depend on the following parameters: (1) at the network


@@ -271,11 +347,12 @@ level, we found that the most critical values are the bandwidth (bw) and the
 network latency (lat). (2) Hosts power (GFlops) can also influence on the
 results. And finally, (3) when submitting job batches for execution, the
 arguments values passed to the program like the maximum number of iterations or
 network latency (lat). (2) Hosts power (GFlops) can also influence on the
 results. And finally, (3) when submitting job batches for execution, the
 arguments values passed to the program like the maximum number of iterations or

-the ``external'' precision are critical to ensure not only the convergence of the
+the \emph{external} precision are critical to ensure not only the convergence of the

 algorithm but also to get the main objective of the experimentation of the
 simulation in having an execution time in asynchronous less than in synchronous
 algorithm but also to get the main objective of the experimentation of the
 simulation in having an execution time in asynchronous less than in synchronous

-mode, in others words, in having a ``speedup'' less than 1 (Speedup = Execution
-time in synchronous mode / Execution time in asynchronous mode).
+mode, in others words, in having a \emph{speedup} less than 1
+({speedup}${}={}${execution time in synchronous mode}${}/{}${execution time in
+asynchronous mode}).

 
 A priori, obtaining a speedup less than 1 would be difficult in a local area
 network configuration where the synchronous mode will take advantage on the rapid
 
 A priori, obtaining a speedup less than 1 would be difficult in a local area
 network configuration where the synchronous mode will take advantage on the rapid


@@ -288,7 +365,7 @@ clusters linked with long distance network like Internet.
 As a first step, the algorithm was run on a network consisting of two clusters
 containing fifty hosts each, totaling one hundred hosts. Various combinations of
 the above factors have providing the results shown in Table~\ref{tab.cluster.2x50} with a matrix size
 As a first step, the algorithm was run on a network consisting of two clusters
 containing fifty hosts each, totaling one hundred hosts. Various combinations of
 the above factors have providing the results shown in Table~\ref{tab.cluster.2x50} with a matrix size

-ranging from Nx = Ny = Nz = 62 to 171 elements or from $62^{3} = \np{238328}$ to
+ranging from $N_x = N_y = N_z = 62 \text{ to } 171$ elements or from $62^{3} = \np{238328}$ to

 $171^{3} = \np{5211000}$ entries.
 
 Then we have changed the network configuration using three clusters containing
 $171^{3} = \np{5211000}$ entries.
 
 Then we have changed the network configuration using three clusters containing


@@ -318,8 +395,8 @@ lat latency, \dots{}).
        \item Description of the cluster architecture;
        \item Maximum number of internal and external iterations;
        \item Internal and external precisions;
        \item Description of the cluster architecture;
        \item Maximum number of internal and external iterations;
        \item Internal and external precisions;

-       \item Matrix size NX, NY and NZ;
-       \item Matrix diagonal value = 6.0;
+       \item Matrix size $N_x$, $N_y$ and $N_z$;
+       \item Matrix diagonal value: \np{6.0};

        \item Execution Mode: synchronous or asynchronous.
 \end{itemize}
 
        \item Execution Mode: synchronous or asynchronous.
 \end{itemize}
 


@@ -327,7 +404,10 @@ lat latency, \dots{}).
   \centering
   \caption{2 clusters X 50 nodes}
   \label{tab.cluster.2x50}
   \centering
   \caption{2 clusters X 50 nodes}
   \label{tab.cluster.2x50}

-  \AG{Les images manquent dans le dépôt Git. Si ce sont vraiment des tableaux, utiliser un format vectoriel (eps ou pdf), et surtout pas de jpeg!}
+  \AG{Ces tableaux (\ref{tab.cluster.2x50}, \ref{tab.cluster.3x33} et
+    \ref{tab.cluster.3x67}) sont affreux. Utiliser un format vectoriel (eps ou
+    pdf) ou, mieux, les réécrire en \LaTeX{}. Réécrire les légendes proprement
+    également (\texttt{\textbackslash{}times} au lieu de \texttt{X} par ex.)}

   \includegraphics[width=209pt]{img1.jpg}
 \end{table}
 
   \includegraphics[width=209pt]{img1.jpg}
 \end{table}
 


@@ -335,7 +415,7 @@ lat latency, \dots{}).
   \centering
   \caption{3 clusters X 33 nodes}
   \label{tab.cluster.3x33}
   \centering
   \caption{3 clusters X 33 nodes}
   \label{tab.cluster.3x33}

-  \AG{Le fichier manque.}
+  \AG{Refaire le tableau.}

   \includegraphics[width=209pt]{img2.jpg}
 \end{table}
 
   \includegraphics[width=209pt]{img2.jpg}
 \end{table}
 


@@ -343,7 +423,7 @@ lat latency, \dots{}).
   \centering
   \caption{3 clusters X 67 nodes}
   \label{tab.cluster.3x67}
   \centering
   \caption{3 clusters X 67 nodes}
   \label{tab.cluster.3x67}

-  \AG{Le fichier manque.}
+  \AG{Refaire le tableau.}

 %  \includegraphics[width=160pt]{img3.jpg}
   \includegraphics[scale=0.5]{img3.jpg}
 \end{table}
 %  \includegraphics[width=160pt]{img3.jpg}
   \includegraphics[scale=0.5]{img3.jpg}
 \end{table}


@@ -373,7 +453,7 @@ For the 3 clusters architecture including a total of 100 hosts, Table~\ref{tab.c
 that it was difficult to have a combination which gives an efficiency of
 asynchronous below \np[\%]{80}. Indeed, for a matrix size of 62 elements, equality
 between the performance of the two modes (synchronous and asynchronous) is
 that it was difficult to have a combination which gives an efficiency of
 asynchronous below \np[\%]{80}. Indeed, for a matrix size of 62 elements, equality
 between the performance of the two modes (synchronous and asynchronous) is

-achieved with an inter cluster of \np[Mbits/s]{10} and a latency of \np{E-1} ms. To
+achieved with an inter cluster of \np[Mbits/s]{10} and a latency of \np[ms]{E-1}. To

 challenge an efficiency by \np[\%]{78} with a matrix size of 100 points, it was
 necessary to degrade the inter cluster network bandwidth from 5 to 2 Mbit/s.
 
 challenge an efficiency by \np[\%]{78} with a matrix size of 100 points, it was
 necessary to degrade the inter cluster network bandwidth from 5 to 2 Mbit/s.
 


@@ -382,8 +462,6 @@ with 200 nodes in total. The convergence with a speedup of \np[\%]{90} was obtai
 with a bandwidth of \np[Mbits/s]{1} as shown in Table~\ref{tab.cluster.3x67}.
 
 \section{Conclusion}
 with a bandwidth of \np[Mbits/s]{1} as shown in Table~\ref{tab.cluster.3x67}.
 
 \section{Conclusion}

-CONCLUSION
-

 The experimental results on executing a parallel iterative algorithm in 
 asynchronous mode on an environment simulating a large scale of virtual 
 computers organized with interconnected clusters have been presented. 
 The experimental results on executing a parallel iterative algorithm in 
 asynchronous mode on an environment simulating a large scale of virtual 
 computers organized with interconnected clusters have been presented. 


@@ -403,7 +481,7 @@ executing the algorithm in asynchronous mode.
 \setcounter{numberedCntD}{\theenumi}
 \end{enumerate}
 Our results have shown that in certain conditions, asynchronous mode is 
 \setcounter{numberedCntD}{\theenumi}
 \end{enumerate}
 Our results have shown that in certain conditions, asynchronous mode is 

-speeder up to 40 \% than executing the algorithm in synchronous mode 
+speeder up to \np[\%]{40} than executing the algorithm in synchronous mode

 which is not negligible for solving complex practical problems with more 
 and more increasing size.
 
 which is not negligible for solving complex practical problems with more 
 and more increasing size.
 


@@ -424,7 +502,7 @@ The authors would like to thank\dots{}
 % adjust value as needed - may need to be readjusted if
 % the document is modified later
 \bibliographystyle{IEEEtran}
 % adjust value as needed - may need to be readjusted if
 % the document is modified later
 \bibliographystyle{IEEEtran}

-\bibliography{hpccBib}
+\bibliography{IEEEabrv,hpccBib}

 
 \end{document}
 
 
 \end{document}