The US airlines, at least in the USA, at many airports display the current boarding group on the info screen belonging to the gate.
Outside of the USA, I don't think this usually exists, because the airlines can't take control of what they display on information displays. Happy to be wrong.
Another technique I've seen is the use of barriers to make people line up in their boarding groups before boarding starts. I think I've seen BA do this at both LHR T5 as well as outstations. The fronts of the lines are blocked off and only opened when the boarding group is permitted to board.
I wonder if someone logs the system's use (i.e. tracks which customer was boarded, when, whether an override was needed, sees in what order the plane is filled), because if so that could give some insight into a query like this.