We at our dojo line up at the start and end of the lesson, roughly divided in two, hakama and non-hakama.
Normaly new (fresh) students coming in are still a bit timide and often set themselves at the most left part (as viewed from shimoza) of the line. Sometimes not and then they are told where to go.
Line up at start does not have to do with rank, but with experience. As we are taught (and train others) to be responsible for the people training for a shorter time, it is quite handy to have the people you have to care for and watch over on your left side only, especially during aiki taiso and ukemi practise.
With the start of partner training it is quite enjoyable to see the beginner being surprised by the invitation to train from the more experienced aikidoka who got up and crossed the mat in the same time as it took the beginner just to get up.
At the end a same kind of line up is made as at the beginning.
I know rules can seem quite formal, but this rule is observed in such a natural manner that a lot of the people at our dojo dont even realize the rule exists. They just go with flow!