If "random" is the quickest, then perhaps that means we have yet to find the most efficient way of boarding.

Now what would totally speed up the process would be to remove the overhead bins altogether; what you carry on has to go under the seat in front of you. If you feel it won't fit you check it. This way, no one is standing in the aisles above their seat trying to shove a foot locker into a bin; you get on the plane and assuming you know that the rows start at 1 and end at 30 something you ought to be able to find your seat pretty quickly.