how to add dotted line and arc line?

I wish to add dotted line connecting two nodes and an arc line as described in the photo.

Here is my code:

\documentclass[tikz]{standalone}
\usetikzlibrary{
shapes.geometric,
positioning,
fit,
calc
}
\usepackage{tikz}
\begin{document}

\tikzset{
block/.style = {circle, draw,
text width=1em,align=center,inner sep=0pt},
line/.style = {draw,thick,->},
}
\begin{tikzpicture}
\node [block] (s1) {1};
\node [block, below = of s1](s2){2};
\path [line] (s1) -- node [right] {b} (s2);
\end{tikzpicture}
\end{document}

-

I've used the calc library to shift the a path to the left a bit.

\documentclass[tikz]{standalone}
\usetikzlibrary{
positioning,
calc
}
\usepackage{tikz}
\begin{document}

\tikzset{
block/.style = {circle, draw,
text width=1em,align=center,inner sep=0pt},
line/.style = {draw,thick,->},
}
\begin{tikzpicture}
\node [block] (s1) {1};
\node [block, below = of s1](s2){2};
\path [line] (s1) -- node [right] {b} (s2);
\draw[dashed,->]  (s1.west) to[bend right=30] (s2);
\draw[->]  ($(s1.west)+(-1,0)$) to[bend right=30] node[left,block]{a}($(s2)+(-1,0)$);
\end{tikzpicture}
\end{document}

-