well, one way the FAA handles this problem is to assign "Flight Levels" for aircraft depending on the direction (North,South,East,West) that they are flying... i cannot remember off the top of my head, but just imagine N/S is even and E/W is odd.
so, say the flight levels are from 10,000ft to 35,000ft. N/S traffic would fly at a predetermined even level and E/W would fly at an odd level... further, N and S are separated by 1,000ft incriments to avoid head-on collisions.
i studied for the FAA Air Traffic Controller
test when i was in the Navy, but they were not hiring when i got out, so i went to college. i am still very interested in ATC, but i just turned 30, which is too old to start.