From bd3f086a5e5f3733a141444a7bf3e14d7c6ef535 Mon Sep 17 00:00:00 2001
From: Camil Staps
Date: Fri, 23 Oct 2015 10:16:42 +0200
Subject: Assignment 8

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+\documentclass[10pt,a4paper]{article}
+
+\usepackage[margin=2cm]{geometry}
+\usepackage{pdfpages}
+
+% textcomp package is not available everywhere, and we only need the Copyright symbol
+% taken from http://tex.stackexchange.com/a/1677/23992
+\DeclareTextCommandDefault{\textregistered}{\textcircled{\check@mathfonts\fontsize\sf@size\z@\math@fontsfalse\selectfont R}}
+
+\usepackage{fancyhdr}
+\renewcommand{\headrulewidth}{0pt}
+\renewcommand{\footrulewidth}{0pt}
+\fancyhead{}
+\fancyfoot[C]{Copyright {\textcopyright} 2015 Camil Staps}
+\pagestyle{fancy}
+
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{mathtools}
+
+\usepackage{enumitem}
+\setenumerate[1]{label=\alph*.}
+\setenumerate[2]{label=(\roman*)}
+
+\usepackage{graphicx}
+
+\parindent0pt
+
+\title{Operating Systems - assignment 8}
+\author{Camil Staps\\\small{s4498062}}
+
+\begin{document}
+
+\maketitle
+\thispagestyle{fancy}
+
+\section*{10.2}
+See Figure \ref{fig:10.2}.
+
+\begin{figure}[h]
+    \centering
+    \includegraphics[width=.95\linewidth]{10-2}
+    \caption{Different scheduling algorithms}
+    \label{fig:10.2}
+\end{figure}
+
+\section*{10.7}
+Suppose we have two jobs with $C_1=C_2=1$ and $T_1=T_2=2$, whose deadlines match. Clearly, we can successfully schedule these jobs, by always scheduling job 1 directly after its deadline and job 2 directly after job 1. The equation doesn't hold however: $$\frac{C_1}{T_1}+\frac{C_2}{T_2} = 1 \ge 2\sqrt2 - 2 = 2\left(2^{\tfrac12}-1\right).$$ Therefore, this equation is a sufficient condition (as has been proven by Liu \& Layland (1973), but not a necessary condition, since we have found a counterexample.
+
+\end{document}
+
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