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diff --git a/assignment8/10-2.jpg b/assignment8/10-2.jpg Binary files differnew file mode 100644 index 0000000..896245b --- /dev/null +++ b/assignment8/10-2.jpg diff --git a/assignment8/assignment8.tex b/assignment8/assignment8.tex new file mode 100644 index 0000000..73049a6 --- /dev/null +++ b/assignment8/assignment8.tex @@ -0,0 +1,51 @@ +\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} + |