In context it would be:
- The marshall is responsible for verb the atheletes into the stadium in lane order.
- The MC is responsible for verb the guess speakers to present in the scheduled order.
- The receptionist verb the clients into the lawyers consulting room in the order of first in first served.
My original guess was marshall(ing/s) but that doesn't seem quite right to me but it seemed slightly better than arrange or order so I would appreciate your thought(s).