\begin{tikzpicture}%[every node/.style={scale=0.7}]

% configurable parameters
\def\eps{0.1};
\coordinate[label ={[xshift=0*\eps cm, yshift=2*\eps cm]$t_0$}] (t0) at ($(-2.0,0)$) {};
\coordinate[label ={[xshift=-0*\eps cm, yshift=2*\eps cm]$t$}] (t) at ($(+3.0,0)$) {};

% axes
\draw [->,help lines] (-2.5, 0)--(3.5,0) node[below]{$t$};

% path
\draw[
    domain=-2.0:3.0,
    densely dotted,
    thick,
    decoration={markings, mark=at position 0.625 with {\arrow{>}}},
    postaction={decorate}
    ] plot ({\x},{\eps});

\draw[
    densely dotted,
    thick,
    ] (3.0,\eps) to[out=-30,in=+30] (3.0, -\eps);

\draw[
    domain=-2.0:3.0,
    densely dotted,
    thick,
    decoration={markings, mark=at position 0.375 with {\arrow{<}}},
    postaction={decorate}
    ] plot ({\x},{-\eps});

% dots and ticks
\node at ($(t0)+(0,\eps)$)[circle,fill,inner sep=0.8pt]{};
\node at ($(t0)-(0,\eps)$)[circle,fill,inner sep=0.8pt]{};

\draw ($(t0)+(0,1pt)$) -- ($(t0)-(0,1pt)$);
\draw ($(t)+(0,1pt)$) -- ($(t)-(0,1pt)$);

\end{tikzpicture}