mjhjmtu

I am currently trying to split an edge in an automaton in tikz. What I already have is this:

I would like to get somethink like this (not in red, just to highlight):
The idea is to have a probabilistic automaton. If the automaton gets the input D, it changes with probability 2/3 to state q1 and with probability 1/3 it remains in state q3. That it why I would like to have one outgoing edge from q3 with input D, the edge should split after a while as you can see in the picture. How can I achieve that?

Here is my code (I needed some if the other tikzlibraries for other parts of my original code, so don't get confused):

documentclass[a4paper, 12pt, parskip=half+]scrreprt
usepackage[utf8]inputenc
usepackagetikz
usepackagepgffor
usetikzlibraryautomata,shapes.multipart % Import library for 
 drawing automata
usetikzlibrarycalc, trees %For graphics
usetikzlibrarypositioning % ...positioning nodes
usetikzlibraryarrows,shapes % ...customizing arrows
usetikzlibrarypatterns,decorations.pathreplacing
tikzsetnode distance=2.5cm, %Minimum distance between nodes
 every state/.style=minimum size=0pt, fill=gray!10, circle split, 
 align=center, %properties for each state
 initial text=, %No label on start state
 final/.style=accepting,
 every picture/.style=>=stealth',
 brace/.style=decorate,decoration=brace, semithick

begindocument
beginfigure
 centering
 begintikzpicture[node distance=1.5cm, ,shorten >=1pt,%Minimum 
 distance between nodes
 every state/.style=minimum size=0pt, inner sep=1pt, 
 fill=gray!10, circle, align=center, %properties for each state
 initial text=, %No label on start arrow
 final/.style=accepting,
 every picture/.style=>=stealth',
 brace/.style=decorate,decoration=brace, semithick,
 every loop/.style=min distance=5mm,looseness=5]
 node[state,initial] (q1) $q_i^1$ \ -------- \ A; 
 node[state] (q2) [right=of q1] $q_i^2$ \ -------- \ B; 
 node[state] (q3) [right=of q2] $q_i^3$ \ -------- \ B; 
 draw[->] (q1) to[loop above] node [above] textttC (q1);
 draw[->] (q1) edge node [above] textttD (q2);
 draw[->] (q2) edge node [above] textttD (q3);
 draw[->] (q3) to[loop above] node [above] textttC (q3); 
 endtikzpicture
endfigure
enddocument

Sorry, I just realised that the state I meant was named q2 in the picture. I'm sorry for that. I mean the state named q3 in the code if it was not clear (I changed it in the code). I am thankful for any help I get. You can also find nice examples of what I would like to get in this articles (page 4, figures 2 and 3)

It is rather easy to do that with decorations.markings. Below the same thing is achieved by a style.

documentclass[a4paper, 12pt, parskip=half+]scrreprt
usepackage[utf8]inputenc
usepackagetikz
usepackagepgffor
usetikzlibraryautomata,shapes.multipart % Import library for drawing automata
usetikzlibrarycalc, trees %For graphics
usetikzlibrarypositioning % ...positioning nodes
usetikzlibraryarrows,shapes % ...customizing arrows
usetikzlibrarypatterns,decorations.pathreplacing,decorations.markings
tikzsetnode distance=2.5cm, %Minimum distance between nodes
 every state/.style=minimum size=0pt, fill=gray!10, circle split, 
 align=center, %properties for each state
 initial text=, %No label on start state
 final/.style=accepting,
 every picture/.style=>=stealth',
 brace/.style=decorate,decoration=brace, semithick

begindocument
beginfigure
 centering
 begintikzpicture[node distance=1.5cm, ,shorten >=1pt,%Minimum 
 distance between nodes
 every state/.style=minimum size=0pt, inner sep=1pt, 
 fill=gray!10, circle, align=center, %properties for each state
 initial text=, %No label on start arrow
 final/.style=accepting,
 every picture/.style=>=stealth',
 brace/.style=decorate,decoration=brace, semithick,
 every loop/.style=min distance=5mm,looseness=5]
 node[state,initial] (q1) $q_i^1$ \ -------- \ A; 
 node[state] (q2) [right=of q1] $q_i^2$ \ -------- \ B; 
 node[state] (q3) [right=of q2] $q_i^3$ \ -------- \ B; 
 draw[->] (q1) to[loop above] node [above] textttC (q1);
 draw[->] (q1) edge node [above] textttD (q2);
 draw[->] (q2) edge node [above] textttD (q3);
 draw[->] (q3) to[loop above] node [above] textttC (q3); 
 draw[->,postaction=decorate,decoration=markings,
 mark=at position 0.25 with draw[->] (0pt,0pt) to[bend left] 
 coordinate[midway](aux) (q3);
 pgftransformreset
 node[above=2pt of aux]$1/3$;] (q3) to[out=135,in=45] 
 node[midway,above]$2/3$ (q1);
 endtikzpicture
endfigure
enddocument

Here is the same thing with a style

split connection=at <pos of splitting point> with ratio <label> to <additional target>

and an example in the code

documentclass[a4paper, 12pt, parskip=half+]scrreprt
usepackage[utf8]inputenc
usepackagetikz
usepackagepgffor
usetikzlibraryautomata,shapes.multipart % Import library for drawing automata
usetikzlibrarycalc, trees %For graphics
usetikzlibrarypositioning % ...positioning nodes
usetikzlibraryarrows,shapes % ...customizing arrows
usetikzlibrarypatterns,decorations.pathreplacing,decorations.markings
tikzsetnode distance=2.5cm, %Minimum distance between nodes
 every state/.style=minimum size=0pt, fill=gray!10, circle split, 
 align=center, %properties for each state
 initial text=, %No label on start state
 final/.style=accepting,
 every picture/.style=>=stealth',
 brace/.style=decorate,decoration=brace, semithick

begindocument
beginfigure
 centering
 begintikzpicture[node distance=1.5cm, shorten >=1pt,%Minimum 
 distance between nodes
 every state/.style=minimum size=0pt, inner sep=1pt, 
 fill=gray!10, circle, align=center, %properties for each state
 initial text=, %No label on start arrow
 final/.style=accepting,
 every picture/.style=>=stealth',
 brace/.style=decorate,decoration=brace, semithick,
 every loop/.style=min distance=5mm,looseness=5,
 split connection/.style args=at #1 with ratio #2 to #3postaction=decorate,decoration=markings,
 mark=at position #1 with draw[->] (0pt,0pt) to[bend left] 
 coordinate[midway](aux) (#3);
 pgftransformreset
 node[above=2pt of aux]$#2$;
 ]
 node[state,initial] (q1) $q_i^1$ \ -------- \ A; 
 node[state] (q2) [right=of q1] $q_i^2$ \ -------- \ B; 
 node[state] (q3) [right=of q2] $q_i^3$ \ -------- \ B; 
 draw[->] (q1) to[loop above] node [above] textttC (q1);
 draw[->] (q1) edge node [above] textttD (q2);
 draw[->] (q2) edge node [above] textttD (q3);
 draw[->] (q3) to[loop above] node [above] textttC (q3); 
 draw[->,split connection=at 0.25 with ratio $1/3$ to q3] (q3) to[out=135,in=45] 
 node[midway,above]$2/3$ node[midway,below]textttD (q1);
 endtikzpicture
endfigure
enddocument

An option using ..controls +(direction:module) and +(direction:module).. line because nodes in a path node[pos=0_to_1_value] does not work for bend or to[in.., out], using nodes in a path allows to put a node in ceirtain positions in this case at 0.12 for the D label using node[pos=0.12,below]... for the 2/3 label node[pos=0.8]... and to split the arrow an empty node node[pos=0.25](temp), temp is the node_name, and then drawing an arrow from temp.center to (q3) usign controls again to put a node in a path with the label 1/3...

RESULT:

MWE:

documentclass[tikz,border=15pt]standalone
usepackage[utf8]inputenc
usetikzlibraryautomata,shapes.multipart % Import library for drawing automata
usetikzlibrarycalc, trees %For graphics
usetikzlibrarypositioning % ...positioning nodes
usetikzlibraryarrows.meta,shapes % ...customizing arrows
usetikzlibrarypatterns,decorations.pathreplacing
%Fonts MAnagement
usepackage[scaled]helvet % For Sans Family
usepackagesansmath
sansmath 

begindocument
 begintikzpicture[
 %Environment Config
 node distance=1.5cm,
 shorten >=1pt,%Minimum distance between nodes
 semithick,
 font=sffamily,
 >=Stealth,
 %Environment Styles
 every state/.style=
 minimum size=0pt,
 inner sep=1pt,
 fill=gray!10,
 circle,
 align=center
 , %properties for each state
 initial text=, %No label on start arrow
 final/.style=accepting,
 brace/.style=
 decorate,
 decoration=brace
 , 
 every loop/.style=
 min distance=5mm,
 looseness=5
 ]
 node[state,initial] (q1) $q_i^1$ \ -------- \ A; 
 node[state] (q2) [right=of q1] $q_i^2$ \ -------- \ B; 
 node[state] (q3) [right=of q2] $q_i^3$ \ -------- \ B; 
 draw[->] (q1) to[loop above] node [above] textttC (q1);
 draw[->] (q1) edge node [above] D (q2);
 draw[->] (q2) edge node [above] D (q3);
 draw[->] (q3) to[loop above] node [above] textttC (q3);
 draw[->] (q3) .. controls +(140:2.5) and +(40:2.5) .. (q1)
 node[pos=0.12,below]D
 node[pos=0.8,above]scriptsize $2/3$
 node[pos=0.25](temp);
 draw[->] (temp.center) .. controls +(15:1) and +(120:1) .. (q3) node[pos=0.5,above]scriptsize $1/3$;
 endtikzpicture
enddocument