[Nick_C]

You have the additional rule that everything gives way to traffic already on the roundabout, which (in practice) means that particular timing event doesn't occur. The downstream car cannot enter the roundabout until the upstream car has gone past, or it can enter only if the upstream car is too far upstream and is not a threat. In either case, there is no collision.

In places I've driven where there might be confusion, they mark the lanes with arrows to show which ones are exiting and when.

They work pretty seamlessly in my experience. You only have to look one way (upstream), instead of two, to judge whether to enter the intersection, and you don't have the time-waste of traffic lights.