It is sufficient to just map the [`lanes`][1] of the road. Mapped lanes implicitly contain forks.
Example using your picture (I've reversed the car's driving direction with my incredible paint skills ;)):
![example image][2]
Also consider mapping `turn:lanes`. The wiki page about [`lanes`][3] is really helpful and has nice examples.
[1]: https://wiki.openstreetmap.org/wiki/Lanes
[2]: https://help.openstreetmap.org/upfiles/merging-video-teaser.jpg
https://help.openstreetmap.org/upfiles/merging-video-teaser_PtUPgPZ.jpg
[3]: https://wiki.openstreetmap.org/wiki/Lanes