Donald Norman (of The Design of Everyday Things fame) talks about the various strategies for this in his newest book, Living With Complexity. It's an interesting problem because it turns out enough people follow the antisocial strategy of taking from the larger roll (what Berners-Lee calls K in his protocol) that both rolls will often run out within short intervals of each other (less than µ).

Norman proposes the strategy of "nearest roll first" instead of "smallest roll first", which is an easier strategy to accommodate through toilet paper dispenser design. Many public stalls hide the spare roll inside a contraption for this purpose.