Considering phusion/baseimage has been around for more than 2 years and plenty of people have been using an init system inside their containers that contain multiple process, why didn't Yelp just pick something up off the shelf? Why not use runit or one of the plenty of more mature lightweight init systems?
I can't speak to the others that have been mentioned in this thread (tini in particular seems to be identical), but the solution used by phusion/baseimage is written in python[0] - a C-based solution allows for lighter-weight containers
