No, I did everything by myself and did not do anything to 'expediate' (in fact I do not know!). I guess I got fast grant may be university 'endorsement'. I also have no idea of what priority is.
Thanks. I waited for a week to get called. I am based at Melbourne, I don't know how long in other places. According to Bupa, Immi has certain priorities as you may see from Bupa website.