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\documentclass[10pt,a4paper]{article}
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\title{Operating Systems - assignment 8}
\author{Camil Staps\\\small{s4498062}}
\begin{document}
\maketitle
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\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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