[Tex/LaTex] Merge arrows with TikZ

arrowstikz-pgf

I am still learning to use TikZ and now I find myself in a tight spot.

I want to draw three processes on the lhs and one on the rhs. These processes are represented by a circle. I then want three arrows comming from the lhs to merge in the space between and go to the process on the rhs.

Further more I would like the arrow from the bottom one to be dotted at the midway.

I have the following to create the four processes and join them with arrows, but how do I merge them in between

\begin{tikzpicture}
  \tikzstyle{every node}=[draw,shape=circle]; 
  \node (P0) at (0,  0.0) {$P_0$};
  \node (P1) at (0, -1.0) {$P_1$};
  \node (Pn) at (0, -2.5) {$P_n$};

  \node (Q) at (2, -1) {$Q$};

  \draw [dotted] (P1) -- (Pn);
  \draw [->] (P0) -- (Q);
  \draw [->] (P1) -- (Q);
  \draw [->] (Pn) -- (Q);
\end{tikzpicture}

My very bad hand drawing from Google Drawing can be seen below

enter image description here

Best Answer

Changing the line type along a path is not so easy, so I guess it's not worth to implement it if this is the only place to apply. A quick fix can be applied by the following: 

\begin{tikzpicture}[every node/.style={draw,circle}]
\draw[style=help lines] (-1cm,0cm) grid[step=1cm] (5cm,5cm);% remove later
  \node (P0) at (0, 4cm) {$P_0$};
  \node (P1) at (0, 2.5cm) {$P_1$};
  \node (Pn) at (0, 1cm) {$P_n$};

    \node (Q) at (3.5cm, 2.5cm) {$Q$};
    \coordinate (Qf) at ([xshift=-0.5cm]Q.west); % we collect the edges in front of Q

\draw (P0) .. controls (2,4) and (1,2.5) .. (Qf) -- (Q); % (Q) is for a better line join
\draw (P1) -- (Qf);
\draw[->] (Qf) -- (Q); % the arrow
\draw  (Qf) arc (90:150:1cm) coordinate (temp1); %We stop and change line type
\draw[dashed] (temp1) arc (-45:-80:2cm and 3.5cm) coordinate (temp2); % Again
\draw (temp2) -- (Pn);

\end{tikzpicture}

enter image description here

Now I see that there is a space between Pn and the rest, but that can be fixed by changing the arc specs.

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