\documentclass{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{dateplot}
\usepgfplotslibrary{units}
\usepackage{siunitx}
\usepackage{tikz}
\usepackage{pgfplotstable}
\usepackage[utf8]{inputenc}
\pgfplotsset{/pgf/number format/use comma}

\begin{document}
\pgfplotstableread{
0 0.16
1 286.87
2 977.17
4 286.50
8 1233.80
16 294.61
32 1661.17
64 5119.18
128 341.65
256 807.20
512 359.30
1024 4582.34
2048 425.47
4096 805.06
8192 1238.56
16384 1859.28
32768 2307.79
65536 7490.86
}\imballtoall

\begin{tikzpicture}
    \begin{axis}[
    	xmin=1,
    	xmax=65536,
    	xmode=log,
        ymin=0,
    	log basis x=2,
        xlabel={Nachrichtengröße [MiB]},
        ylabel={Zugriffszeit [ms]},
        width=15cm, height=10cm,
        change y base=true,
        y SI prefix=kilo
    ]
    	\addplot[smooth,blue] table {\imballtoall};
    \end{axis}
\end{tikzpicture}
\end{document}