The Roman Empire lasted 1400-odd years, bordered hundreds of states (and as many non-state entities), and it often re-evaluated how it interacted with neighboring states on a regular basis. Sometimes the Romans built walls (like in Britain), sometimes they built a chain of forts behind a river (like in Germania), sometimes they built garrisons and fortifications to protect the roads they built (like in Arabia), and sometimes they had vast tracts of open land because there was no conceivable way to actually garrison all of it (like in Tripolitania).

So... could you be a little more specific?