Eric, as per Greyhound, anything over 350 miles is considered Long Distance. For example, there is a run from New Orleans to Shreveport Louisiana, this is considered a Local run. its 341 miles, so almost an LD run but not quite.
There is no real way to know where Greyhound will stick buses, except in certain cases *Bolt buses will stay in the Northeast* that sorta thing.
Most of the time, the decision is made based on whats available in the pool of buses waiting in the lot, out of the ones that arent in need of maintenance.
Lets say there are 4 buses available for the New Orleans to El Paso run. an X3, a D4505, a D4500, or a G4500..
If the G4500 needs maintenance, then that bus is not considered, so one bus down.
Lets say the D4500 got a transmission complaint by the driver upon its return from another run, well that bus isnt going anywhere because it will need to be looked at. *maintenance mode* Two buses down.
Now its between the X-3 and the D4505. Which one can be cleaned, inspected, and cleared to roll? If its the X-3, then that is the one chosen.
Now, if both buses are ready to roll, are there enough passengers to send both the X3 and the D4505 out on the same run? If yes, then the D4505 will be set up as the extra bus.
If the D4505 is spoken for on another run for instance New Orleans to Miami run, then so be it, the X3 goes it alone from New Orleans to El Paso.
I have seen Greyhound pull a bus out of Baton Rouge as an extra. I have also seen buses get completely replaced at Baton Rouge for various technical reasons.
I have driver friends who explained this as best as they could.