%% Lilia Ziane Khodja: Department of Aerospace \& Mechanical Engineering\\ Non Linear Computational Mechanics\\ University of Liege\\ Liege, Belgium. Email: l.zianekhodja@ulg.ac.be
\begin{abstract}
-ABSTRACT
+ The behavior of multicore applications is always a challenge to predict, especially with a new architecture for which no experiment has been performed. With some applications, it is difficult, if not impossible, to build accurate performance models. That is why another solution is to use a simulation tools that allows us to change many parameters of the architecture (network bandwidth, latency, number of processors) and to simulate the execution of such applications.
+
+ In this paper, we focus our attention on two parallel iterative algorithms: one with synchronoous iterations and another one with asynchronous iterations.
+
+
\end{abstract}
\keywords{Algorithm; distributed; iterative; asynchronous; simulation; simgrid; performance}
\maketitle
-\section{Introduction}
+\section{Introduction}
\section{The asynchronous iteration model}
%\end{algorithm}
\end{figure}
+\subsection{Simulation of two-stage methods using SimGrid framework}
+\label{sec:04.02}
+One of our objectives when simulating the application in SIMGRID is, as in real life, to get accurate results (solutions of the problem) but also ensure the test reproducibility under the same conditions.According our experience, very few modifications are required to adapt a MPI program to run in SIMGRID simulator using SMPI (Simulator MPI).The first modification is to include SMPI libraries and related header files (smpi.h). The second and important modification is to eliminate all global variables in moving them to local subroutine or using a Simgrid selector called "runtime automatic switching" (smpi/privatize\_global\_variables). Indeed, global variables can generate side effects on runtime between the threads running in the same process, generated by the Simgrid to simulate the grid environment.The last modification on the MPI program pointed out for some cases, the review of the sequence of the MPI\_Isend, MPI\_Irecv and MPI\_Waitall instructions which might cause an infinite loop.
+\paragraph{SIMGRID Simulator parameters}
+\begin{itemize}
+ \item HOSTFILE: Hosts description file.
+ \item PLATFORM: File describing the platform architecture : clusters (CPU power,
+\dots{}), intra cluster network description, inter cluster network (bandwidth bw,
+lat latency, \dots{}).
+ \item ARCHI : Grid computational description (Number of clusters, Number of
+nodes/processors for each cluster).
+\end{itemize}
+In addition, the following arguments are given to the programs at runtime:
+\begin{itemize}
+ \item Maximum number of inner and outer iterations;
+ \item Inner and outer precisions;
+ \item Matrix size (NX, NY and NZ);
+ \item Matrix diagonal value = 6.0;
+ \item Execution Mode: synchronous or asynchronous.
+\end{itemize}
-
-\subsection{Simulation of two-stage methods using SimGrid framework}
+At last, note that the two solver algorithms have been executed with the Simgrid selector --cfg=smpi/running\_power which determine the computational power (here 19GFlops) of the simulator host machine.
%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Experimental, Results and Comments}
-\textbf{V.1. Setup study and Methodology}
+\subsection{Setup study and Methodology}
To conduct our study, we have put in place the following methodology
which can be reused with any grid-enabled applications.
enhanced version of the multisplitting method as Algo-3. In addition,
SIMGRID simulator has been chosen to simulate the behaviors of the
distributed applications. SIMGRID is running on the Mesocentre
-datacenter in Franche-Comte University $[$10$]$ but also in a virtual
+datacenter in Franche-Comte University but also in a virtual
machine on a laptop.
\textbf{Step 3} : Fix the criteria which will be used for the future
input matrix. Note that some parameters should be invariant to allow the
comparison like some program input arguments.
-\textbf{Step 6} : Collect and analyze the output results.
+{Step 6} : Collect and analyze the output results.
-\textbf{ V.2. Factors impacting distributed applications performance in
+\subsection{Factors impacting distributed applications performance in
a grid environment}
From our previous experience on running distributed application in a
application is the network configuration. Two main network parameters
can modify drastically the program output results : (i) the network
bandwidth (bw=bits/s) also known as "the data-carrying capacity"
-$[$13$]$ of the network is defined as the maximum of data that can pass
+of the network is defined as the maximum of data that can pass
from one point to another in a unit of time. (ii) the network latency
(lat : microsecond) defined as the delay from the start time to send the
data from a source and the final time the destination have finished to
between distant clusters might be a bottleneck for the global
performance of the application.
-\textbf{V.3 Comparing GMRES and Multisplitting algorithms in
+\subsection{Comparing GMRES and Multisplitting algorithms in
synchronous mode}
In the scope of this paper, our first objective is to demonstrate the
should figure out that, for various grid parameters values, the
simulator will confirm the targeted outcomes, particularly for poor and
slow networks, focusing on the impact on the communication performance
-on the chosen class of algorithm $[$12$]$.
+on the chosen class of algorithm.
The following paragraphs present the test conditions, the output results
and our comments.
Input matrix size & N$_{x}$ =150 x 150 x 150 and\\ %\hline
- & N$_{x}$ =170 x 170 x 170 \\ \hline
\end{tabular}
-\end{footnotesize}
+Table 1 : Clusters x Nodes with NX=150 or NX=170 \\
+\end{footnotesize}
- Table 1 : Clusters x Nodes with NX=150 or NX=170
-\RCE{J'ai voulu mettre les tableaux des données mais je pense que c'est inutile et ça va surcharger}
+
+%\RCE{J'ai voulu mettre les tableaux des données mais je pense que c'est inutile et ça va surcharger}
The results in figure 1 show the non-variation of the number of
iterations of classical GMRES for a given input matrix size; it is not
the case for the multisplitting method.
-%\begin{wrapfigure}{l}{60mm}
+%\begin{wrapfigure}{l}{100mm}
\begin{figure} [ht!]
\centering
-\includegraphics[width=60mm]{cluster_x_nodes_nx_150_and_nx_170.pdf}
+\includegraphics[width=100mm]{cluster_x_nodes_nx_150_and_nx_170.pdf}
\caption{Cluster x Nodes NX=150 and NX=170}
%\label{overflow}}
\end{figure}
(compared with the classical GMRES) when scaling up to higher input
matrix size.
-\textit{3.b Running on various computational grid architecture}
+\textit{\\3.b Running on various computational grid architecture\\}
% environment
\begin{footnotesize}
- & N2 : bw=1Gbs-lat=5E-05 \\
Input matrix size & N$_{x}$ =150 x 150 x 150\\ \hline \\
\end{tabular}
-\end{footnotesize}
+Table 2 : Clusters x Nodes - Networks N1 x N2 \\
+
+ \end{footnotesize}
-%Table 2 : Clusters x Nodes - Networks N1 x N2
-%\RCE{idem pour tous les tableaux de donnees}
-%\begin{wrapfigure}{l}{60mm}
+%\begin{wrapfigure}{l}{100mm}
\begin{figure} [ht!]
\centering
-\includegraphics[width=60mm]{cluster_x_nodes_n1_x_n2.pdf}
+\includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}
\caption{Cluster x Nodes N1 x N2}
%\label{overflow}}
\end{figure}
when the network speed drops down, the difference between the execution
times can reach more than 25\%.
-\textit{\\\\\\\\\\\\\\\\\\3.c Network latency impacts on performance}
+\textit{\\3.c Network latency impacts on performance\\}
% environment
\begin{footnotesize}
Network & N1 : bw=1Gbs \\ %\hline
Input matrix size & N$_{x}$ =150 x 150 x 150\\ \hline\\
\end{tabular}
+
+Table 3 : Network latency impact \\
+
\end{footnotesize}
-Table 3 : Network latency impact
\begin{figure} [ht!]
\centering
-\includegraphics[width=60mm]{network_latency_impact_on_execution_time.pdf}
+\includegraphics[width=100mm]{network_latency_impact_on_execution_time.pdf}
\caption{Network latency impact on execution time}
%\label{overflow}}
\end{figure}
the multisplitting, even though, the performance was on the same order
of magnitude with a latency of 8.10$^{-6}$.
-\textit{3.d Network bandwidth impacts on performance}
+\textit{\\3.d Network bandwidth impacts on performance\\}
% environment
\begin{footnotesize}
Network & N1 : bw=1Gbs - lat=5E-05 \\ %\hline
Input matrix size & N$_{x}$ =150 x 150 x 150\\ \hline
\end{tabular}
+
+Table 4 : Network bandwidth impact \\
+
\end{footnotesize}
-Table 4 : Network bandwidth impact
\begin{figure} [ht!]
\centering
-\includegraphics[width=60mm]{network_bandwith_impact_on_execution_time.pdf}
+\includegraphics[width=100mm]{network_bandwith_impact_on_execution_time.pdf}
\caption{Network bandwith impact on execution time}
%\label{overflow}
\end{figure}
presents a better performance in the considered bandwidth interval with
a gain of 40\% which is only around 24\% for classical GMRES.
-\textit{3.e Input matrix size impacts on performance}
+\textit{\\3.e Input matrix size impacts on performance\\}
% environment
\begin{footnotesize}
Network & N2 : bw=1Gbs - lat=5E-05 \\ %\hline
Input matrix size & N$_{x}$ = From 40 to 200\\ \hline
\end{tabular}
+Table 5 : Input matrix size impact\\
+
\end{footnotesize}
-Table 5 : Input matrix size impact
\begin{figure} [ht!]
\centering
-\includegraphics[width=60mm]{pb_size_impact_on_execution_time.pdf}
+\includegraphics[width=100mm]{pb_size_impact_on_execution_time.pdf}
\caption{Pb size impact on execution time}
%\label{overflow}}
\end{figure}
deployment when focusing on the problem size scale up. Note that the
same test has been done with the grid 2x16 getting the same conclusion.
-\textit{3.f CPU Power impact on performance}
+\textit{\\3.f CPU Power impact on performance\\}
% environment
\begin{footnotesize}
Network & N2 : bw=1Gbs - lat=5E-05 \\ %\hline
Input matrix size & N$_{x}$ = 150 x 150 x 150\\ \hline
\end{tabular}
+Table 6 : CPU Power impact \\
+
\end{footnotesize}
-Table 6 : CPU Power impact
\begin{figure} [ht!]
\centering
-\includegraphics[width=60mm]{cpu_power_impact_on_execution_time.pdf}
+\includegraphics[width=100mm]{cpu_power_impact_on_execution_time.pdf}
\caption{CPU Power impact on execution time}
%\label{overflow}}
\end{figure}
after adding more powerful CPU. Note that the execution time axis in the
figure is in logarithmic scale.
- \textbf{V.4 Comparing GMRES in native synchronous mode and
+\subsection{Comparing GMRES in native synchronous mode and
Multisplitting algorithms in asynchronous mode}
The previous paragraphs put in evidence the interests to simulate the
classical GMRES time.
-The test conditions are summarized in the table below :
+The test conditions are summarized in the table below : \\
% environment
\begin{footnotesize}
Intra-Network & bw=1.25 Gbits - lat=5E-05 \\ %\hline
Inter-Network & bw=5 Mbits - lat=2E-02\\
Input matrix size & N$_{x}$ = From 62 to 150\\ %\hline
- Residual error precision: 10$^{-5}$ to 10$^{-9}$\\ \hline
+ Residual error precision: 10$^{-5}$ to 10$^{-9}$\\ \hline \\
\end{tabular}
\end{footnotesize}
