\documentclass{article}
\usepackage{pgfgantt}
\usepackage[margin=1cm]{geometry}
\newganttlinktype{arr}{
  \draw [/pgfgantt/link]
  (0.5,-0.5) --
  (0.5, 0);}
\newganttlinktype{rel}{
  \ganttsetstartanchor{on left=0}
  \ganttsetendanchor{on left=1}
  \draw [/pgfgantt/link]
  (\xLeft, \yLower) --
  (\xLeft, \yUpper);}
\newganttlinktype{done}{
  \ganttsetstartanchor{on right=0}
  \ganttsetendanchor{on right=1}
  \draw [/pgfgantt/link]
  (\xRight, \yUpper) --
  (\xRight, \yLower);}
\newcommand{\barstart}{+2}
\newcommand{\barend}  {+1}
\newcommand{\taskarrive}[2]{
  \draw [/pgfgantt/link] (#1*0.5+0.5, #2*-2+1) -- (#1*0.5+0.5, #2*-2+2);
}
\begin{document}
\pagenumbering{gobble}
\begin{center}
  \begin{ganttchart}[
      x unit = 0.5cm,
      bar height = 0.5,
      bar top shift = 0.5,
      title right shift=1,
      title/.style={draw=none, fill=none},
      title top shift=1,
      include title in canvas=false,
      canvas/.style={draw=none}
    ]{0}{50}

    % t1
    \ganttbar{$t_{1}$}{0\barstart}{2\barend}
    \ganttlink[link type=rel]{elem0}{elem0}
    \ganttlink[link type=done]{elem0}{elem0}

    \ganttbar{$t_{1}$}{10\barstart}{12\barend}
    \ganttlink[link type=rel]{elem1}{elem1}
    \ganttlink[link type=done]{elem1}{elem1}

    \ganttbar{$t_{1}$}{20\barstart}{22\barend}
    \ganttlink[link type=rel]{elem2}{elem2}
    \ganttlink[link type=done]{elem2}{elem2}

    \ganttbar{$t_{1}$}{30\barstart}{32\barend}
    \ganttlink[link type=rel]{elem3}{elem3}
    \ganttlink[link type=done]{elem3}{elem3}

    \gantttitlelist{0,,2,,,,,,,,10,,12,,,,,,,,20,,22,,,,,,,,30,,32}{1}
    \\\\

    % t2
    \ganttbar{$t_{2}$}{2\barstart}{6\barend}
    \ganttlink[link type=rel]{elem4}{elem4}
    \ganttlink[link type=done]{elem4}{elem4}

    \ganttbar{$t_{2}$}{15\barstart}{19\barend}
    \ganttlink[link type=rel]{elem5}{elem5}
    \ganttlink[link type=done]{elem5}{elem5}

    \ganttbar{$t_{2}$}{32\barstart}{36\barend}
    \ganttlink[link type=rel]{elem6}{elem6}
    \ganttlink[link type=done]{elem6}{elem6}

    \gantttitlelist{0,,2,,,,6,,,,,,,,,15,,,,19,,,,,,,,,,,30,,32,,,,36}{1}
    \\\\

    % t3
    \ganttbar{$t_{3}$}{6\barstart}{10\barend}
    \ganttlink[link type=rel]{elem7}{elem7}

    \ganttbar{$t_{3}$}{12\barstart}{15\barend}
    \ganttbar{$t_{3}$}{19\barstart}{20\barend}
    \ganttbar{$t_{3}$}{22\barstart}{30\barend}

    \gantttitlelist{0,,,,,,6,,,,10,,12,,,15,,,,19,20,,22,,,,,,,,30}{1}

    \taskarrive{0}{1}
    \taskarrive{10}{1}
    \taskarrive{20}{1}
    \taskarrive{30}{1}

    \taskarrive{0}{2}
    \taskarrive{15}{2}
    \taskarrive{30}{2}

    \taskarrive{0}{3}
  \end{ganttchart}
  \begin{description}
    \item[digits] time
    \item[left column] tasks
    \item[up arrow, {\em tall}] arrival
    \item[up arrow, {\em short}] release
    \item[down arrow] completion
    \item[bar] execution (task allocated CPU)
    \item[{\em beginning} of bar, no arrow] preemption (context switch {\em load})
    \item[{\em end} of bar, no arrow] preemption (context switch {\em save}); or, failure to meet deadline
  \end{description}
\end{center}
\end{document}