I only have experience of Delta but last few times I used it in the US they had a very organised system with a TV screen at each gate updated real-time showing non-rev's in priority (based on service entry date of the relevant employee - which was displayed on the screen) order along with the cut-off line showing the current number of unallocated seats. As and when Rev's or higher priority non-rev's presented at the gate, the list was reshuffled.
They had S1-4 priorities although I think S1 & S2 were some kind of weird emergency as I only every used S3 & 4.