According to click here it is a ligit epson process called the Epson Bi-directional Request Router The description is as follows
ebrr.exe is a process associated with Epson printers. Instigates bi-directional communication between computer and printer allowing for realtime status monitoring etc.
It states on that list thou that it does not use the network or internet. At a guess I would say that it is your printer itself trying to communicate with your pc.