As for the testing procedures, for good or ill ours in Fife *all* get tested, and we get sent letters with appointment times at the council's depot soon after the tariff increase takes affect. They do them all over a few days, testing the flagfall distance and then the first tickover, I think.
At one point they intended doing them on a rolling road, but that didn't work out, so they still take them out onto the public roads.
So the procedure is basically the same as the annual inspections, which are all done in March and April rather than on a rolling basis (apart from vehicle substitutions, obviously). But obviously the meter testing is a lot quicker so just takes a few days rather than weeks.
Not sure if it's still the same in Dundee, but back 20 or so years ago they also called ALL the cars in, and had some sort of rough rota system, which I think was based on specified plate numbers over a slot of several hours, eg plates 251-300 on Tuesday morning. So although every taxi in Dundee wouldn't turn up at once, you could still have to wait in a lengthy queue.
The appointments system in Fife means we rarely have to wait long, although of course things can get delayed and a bit behind schedule