commit 33e444cb0f929734d10d70dd42fec8b913f26603
parent 983dc9b289dc69d866bde84cee4fc75bd182f559
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Fri, 14 Jul 2017 14:37:42 +0300
Add slides.
Diffstat:
16 files changed, 5466 insertions(+), 9 deletions(-)
diff --git a/Makefile b/Makefile
@@ -1,20 +1,25 @@
build/main.pdf: *.tex *.bib bib/* build src/* tex/* dot/* \
-build/sc12.pdf \
-build/sc1.pdf \
-build/sc2.pdf \
-build/sc3.pdf \
build/ppl.pdf \
build/test-1-phys.pdf \
build/test-1-virt.pdf \
build/test-2-phys.pdf \
-build/test-2-virt.pdf
- max_print_line=65536 latexmk \
+build/test-2-virt.pdf \
+build/graph.eps
+ latexmk \
-interaction=nonstopmode \
-output-directory=build \
-pdf \
-bibtex \
-shell-escape \
-f main.tex
+ latexmk \
+ -interaction=nonstopmode \
+ -output-directory=build \
+ -xelatex \
+ -pdf \
+ -bibtex \
+ -shell-escape \
+ -f slides.tex
build/test-1-phys.pdf: R/test-1.R R/common.R
./R/test-1.R data/test-1-phys $@
@@ -35,12 +40,13 @@ data/test-2-virt/run-*/*
$@ \
xy
-build/sc%.pdf: img/sc%.svg
+build/%.eps: figures/%.svg
inkscape \
--without-gui \
--export-area-drawing \
--file=$< \
- --export-pdf=$@
+ --export-eps=$@
+
build/ppl.pdf: dot/ppl.dot
dot -Tpdf -o $@ $<
diff --git a/dot/ppl.dot b/dot/ppl.dot
@@ -1,7 +1,7 @@
graph Pipeline {
node [fontname="Times",fontsize=7,margin="0.01,0.01",shape=box,height="0.1",width="0.1",penwidth="0.5"]
- graph [fontname="Times",fontsize=8,nodesep="0.07",ranksep="0.05",rankdir="LR",margin="-0.1,-0.1"]
+ graph [fontname="Times",fontsize=8,nodesep="0.07",ranksep="0.05",rankdir="LR",margin="-0.1,-0.1",bgcolor=transparent]
edge [arrowsize=0.66,penwidth="0.5"]
subgraph cluster_daemon {
diff --git a/figures/factory-3000.eps b/figures/factory-3000.eps
@@ -0,0 +1,751 @@
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diff --git a/slides.tex b/slides.tex
@@ -0,0 +1,267 @@
+% Created 2017-07-14 Пт 11:23
+% Intended LaTeX compiler: pdflatex
+\documentclass[12pt,aspectratio=169]{beamer}
+\usepackage{graphicx}
+\usepackage{booktabs}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{hyperref}
+\usepackage{tikz}
+\usetikzlibrary{shapes}
+\usepackage{cite}
+\usepackage{url}
+\usepackage{polyglossia}
+\input{preamble}
+\AtBeginSection[]{\frame{\sectionpage}}
+\usetheme{SaintPetersburg}
+
+\author{I.\,Gankevich \quad Yu.\,Tipikin \quad V.\,Korkhov}
+\date{July, 2017}
+\title{Subordination: Providing resilience to simultaneous failure of multiple cluster nodes}
+\institute{Saint Petersburg State University}
+\setdefaultlanguage{english}
+
+
+\definecolor{spbuGreen}{RGB}{40,160,40}
+\tikzset{Process/.style={ellipse,draw=spbuGreen,line width=3pt,dashed}}
+\tikzset{ProcessEdge/.style={draw=spbuGreen,line width=3pt,solid}}
+\tikzset{Node/.style={rectangle,draw=spbuDarkGray,thick}}
+\tikzset{Task/.style={Process,anchor=center,draw=spbuGreen}}
+\tikzset{TaskEdge/.style={ProcessEdge,draw=spbuGreen,solid,->}}
+\tikzset{Label/.style={label distance=0.1cm,text=spbuTerracotta}}
+\tikzset{TaskLabel/.style={label distance=0.1cm,text=spbuGreen}}
+
+\begin{document}
+
+\maketitle
+
+\begin{frame}{Motivation}
+\end{frame}
+
+\begin{frame}{System architecture}
+\end{frame}
+
+\begin{frame}{Application architecture}
+ \centering
+ \includegraphics{build/ppl.pdf}
+\end{frame}
+
+\section{Node discovery algorithm}
+
+\begin{frame}{Hierarchy of cluster nodes}
+ \begin{equation*}
+ \forall n_1 \forall n_2 \in \mathcal{N},
+ \forall f \colon \mathcal{N} \rightarrow \mathcal{R}^n
+ \Rightarrow (f(n_1) < f(n_2) \Leftrightarrow \neg (f(n_1) \geq f(n_2)))
+ \end{equation*}
+ Here \(n\) is node rank~--- node's position in the network IP-address
+ range.
+ \vfill
+ \begin{columns}[T]
+ \begin{column}{0.35\textwidth}
+ \begin{itemize}
+ \item Strict total order.
+ \item Static node positions in the hierarchy.
+ \end{itemize}
+ \end{column}
+ \begin{column}{0.55\textwidth}
+ \begin{tikzpicture}[remember picture,x=2.5cm,y=-1cm]
+ \node[Node] (M) at (2,0) {\texttt{10.0.0.1}};
+ \node[Node] (S1) at (1.25,1) {\texttt{10.0.0.2}};
+ \node[Node] (S2) at (2.75,1) {\texttt{10.0.0.3}};
+ \node[Node] (S3) at (0.75,2) {\texttt{10.0.0.4}};
+ \node[Node] (S4) at (1.75,2) {\texttt{10.0.0.5}};
+ \node[Node] (S5) at (2.75,2) {\texttt{10.0.0.6}};
+ \path[thick] (M) edge (S1);
+ \path[thick] (M) edge (S2);
+ \path[thick] (S1) edge (S3);
+ \path[thick] (S1) edge (S4);
+ \path[thick] (S2) edge (S5);
+ \end{tikzpicture}
+ \begin{center}
+ \texttt{fanout=2, nodes=6}
+ \end{center}
+ \end{column}
+ \end{columns}
+\end{frame}
+
+\begin{frame}{Example}
+ \framesubtitle{\texttt{fanout=2, nodes=100, network=10.0.0.0/8}}
+ \centering
+ \includegraphics<1>[width=0.9\linewidth]{build/graph.eps}
+ \includegraphics<2>[width=0.9\linewidth,trim={20cm 10cm 10cm 5cm},clip]{build/graph.eps}
+\end{frame}
+
+\begin{frame}{Performance of node discovery algorithm}
+ \framesubtitle{4 physical nodes, 400 virtual nodes, fanout=2}
+ \centering
+ \includegraphics[width=0.8\linewidth]{figures/node-discovery.eps}
+\end{frame}
+
+\begin{frame}{Node discovery algorithm: summary}
+ \begin{itemize}
+ \item Arranges cluster nodes into the hierarchy with strict total
+ order.
+ \item Scalable to a large number of cluster nodes.
+ \item Simple and reliable.
+ \end{itemize}
+ \vfill
+ \begin{center}
+ The purpose of node hierarchy is to distribute the load on the cluster.
+ \end{center}
+\end{frame}
+
+\section{Kernel processing algorithm}
+
+\begin{frame}
+ \frametitle{Hierarchical dependence between tasks}
+ \bigskip\bigskip%
+ \includegraphics<1>[width=\textwidth]{figures/tasks-and-queue}
+ \includegraphics<2>[width=\textwidth]{figures/tasks-and-queue-1}
+ \includegraphics<3>[width=\textwidth]{figures/tasks-and-queue-2}
+ \includegraphics<4>[width=\textwidth]{figures/tasks-and-queue-3}
+ \includegraphics<5>[width=\textwidth]{figures/tasks-and-queue-4}
+ \includegraphics<6>[width=\textwidth]{figures/tasks-and-queue-5}
+ \includegraphics<7>[width=\textwidth]{figures/tasks-and-queue-6}
+ \note<1>{
+ \begin{itemize}
+ \item Left --- kernels, right --- execution queue (pool). Animation shows how kernels create subordinates and collect results from them.
+ \item The main difference compared to the jobs is that a task completes only when all its subordinates complete (it can not complete earlier). So, this model is more like asynchronous execution of subroutines (coroutines), but coroutines also do not have hierarchy.
+ \end{itemize}
+ }
+\end{frame}
+
+\section{Evaluation}
+
+\begin{frame}{Case study: Ocean wavy surface generator}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Case study: NDBC dataset preprocessing}
+ \begin{center}
+ \begin{tabular}{ll}
+ \toprule
+ Dataset size & 144MB \\
+ Dataset size (uncompressed) & 770MB \\
+ No.~of wave stations & 24 \\
+ Time span & 3 years (2010--2012) \\
+ Total no.~of spectra & 445422 \\
+ \bottomrule
+ \end{tabular}
+ \end{center}
+ \vfill
+ Spectrum reconstruction formula:
+ \begin{equation*}
+ S(\omega, \theta) = \frac{1}{\pi}\!
+ \left[
+ \frac{1}{2} +
+ r_1 \cos \left( \theta - \alpha_1 \right) +
+ r_2 \sin \left( 2 \left( \theta - \alpha_2 \right) \right)
+ \right]\!
+ S_0(\omega).
+ \end{equation*}
+ \note{
+ Master node fail over technique is evaluated on the example of wave energy spectra processing application. This programme uses NDBC (\href{http://www.ndbc.noaa.gov/}{National Data Buoy Center}) dataset to reconstruct frequency-directional spectra from wave rider buoy measurements and compute variance. Each spectrum is reconstructed from five variables using the following formula.
+ \begin{equation*}
+ S(\omega, \theta) = \frac{1}{\pi}
+ \left[
+ \frac{1}{2} +
+ r_1 \cos \left( \theta - \alpha_1 \right) +
+ r_2 \sin \left( 2 \left( \theta - \alpha_2 \right) \right)
+ \right]
+ S_0(\omega).
+ \end{equation*}
+ Here $\omega$ denotes frequency, $\theta$ is wave direction, $r_{1,2}$ and $\alpha_{1,2}$ are parameters of spectrum decomposition and $S_0$ is non-directional spectrum; $r_{1,2}$, $\alpha_{1,2}$ and $S_0$ are acquired through measurements. Properties of the dataset which is used in evaluation are listed in Table.
+ }
+\end{frame}
+
+\begin{frame}
+ \frametitle{Handling master node failure}
+ \centering
+ \begin{tikzpicture}[remember picture,x=3cm,y=-3cm]
+ \node[Node] (A1) at (0,0) {A};
+ \node[Node] (B1) at (1,0) {B};
+ \node[Node] (C1) at (0,1) {C};
+ \node[Node] (D1) at (1,1) {D};
+ \end{tikzpicture}
+ \begin{tikzpicture}[remember picture,overlay]
+ \path[thick] (A1) edge (B1);
+ %\path[thick] (A1) edge (C1);
+ %\path[thick] (A1) edge (D1);
+ \path[thick] (B1) edge (C1);
+ \path[thick] (B1) edge (D1);
+ %\path[thick] (C1) edge (D1);
+ \end{tikzpicture}
+ \only<2->{%
+ \begin{tikzpicture}[remember picture,overlay]
+ \node[Task,label={[TaskLabel]90:Master\vphantom{p}}] (Master) at (A1.center) {\phantom{A}};
+ \end{tikzpicture}%
+ }
+ \only<3->{%
+ \begin{tikzpicture}[remember picture,overlay]
+ \node[Task,label={[TaskLabel]90:Backup}] (MasterCopy) at (B1.center) {\phantom{A}};
+ \path[TaskEdge] (Master) edge (MasterCopy);
+ \end{tikzpicture}%
+ }
+ \only<4->{%
+ \begin{tikzpicture}[remember picture,overlay]
+ \node[Task,label={[TaskLabel]0:Task1}] (Task1) at (B1.center) {\phantom{A}};
+ \end{tikzpicture}%
+ }
+ \only<5->{%
+ \begin{tikzpicture}[remember picture,overlay]
+ \node[Task,label={[TaskLabel]180:Sub1}] (Sub1) at (A1.center) {\phantom{A}};
+ \node[Task,label={[TaskLabel]180:Sub2}] (Sub2) at (C1.center) {\phantom{A}};
+ \node[Task,label={[TaskLabel]0:Sub3}] (Sub3) at (D1.center) {\phantom{A}};
+ \path[TaskEdge] (Task1) edge[bend left] (Sub1);
+ \path[TaskEdge] (Task1) edge (Sub2);
+ \path[TaskEdge] (Task1) edge (Sub3);
+ \end{tikzpicture}%
+ }
+ \note<5>{
+ \begin{itemize}
+ \item Here A, B, C, D --- cluster nodes and Master, Backup, Task1, Sub1, Sub2, Sub3 --- tasks.
+ \item Backup is a copy of Master which is sent along with Task1 to the subordinate node.
+ \item Task1 represent one sequential step of a programme. There can be any number of seq. steps in a programme, and when Backup node fails, the current step is restarted from the beginning.
+ \item When node B, C or D fails, corresponding master task restarts failed subordinates (Task1 restart Sub1, Master restarts Task1 etc.). When node A fails, Master task is recovered from Backup (its copy).
+ \end{itemize}
+ }
+\end{frame}
+
+
+\begin{frame}{Performance in case of master node failure}
+ \centering
+ \includegraphics[width=0.9\linewidth]{figures/mpp-time-color.eps}
+\end{frame}
+
+\begin{frame}{Performance in case of master node failure}
+ \centering
+ \includegraphics[width=0.9\linewidth]{figures/mpp-time-color-ndbc.eps}
+\end{frame}
+
+\begin{frame}{Overhead of recovery from multiple node failures}
+ \begin{columns}[T]
+ \begin{column}{0.45\textwidth}
+ \vskip-1cm
+ \includegraphics[width=\linewidth]{test-1-phys}\newline\vspace{-1cm}
+ \includegraphics[width=\linewidth]{test-2-phys}
+ \end{column}
+ \begin{column}{0.45\textwidth}
+ \vskip-1cm
+ \includegraphics[width=\linewidth]{test-1-virt}\newline\vspace{-1cm}
+ \includegraphics[width=\linewidth]{test-2-virt}
+ \end{column}
+ \end{columns}
+\end{frame}
+
+\begin{frame}{Conclusions}
+ \begin{itemize}
+ \item Having hierarchy (strict total order) between tasks (kernels) is
+ sufficient to devise algorithms for recovery from cluster node
+ failures.
+ \item Each cluster node having IP-address (or any other unique
+ identifier) is the only assumption of these algorithms.
+ \end{itemize}
+\end{frame}
+
+\end{document}
