Schedule two trains whose tracks overlap so they don't crash I've encountered scheduling problems in my algorithms class before like the type we use vertex cover to solve.

Recently I was asked this question and did not even know what algorithmic technique to use to answer it!

There are two trains, which run between stations and share a portion of track. For instance train 1 runs between stations A B C D E F G H and train 2 runs between stations I J K B C D E F L M so the trains share the track between B C D. At each end of the track the train turns around and goes the other way on its track. The trains go from station to station in 1 unit time. I need to prevent the trains from crashing head on on the shared track, I have the power to stop either train at any station and restart it again when I please.

How can I solve this problem without using a ton of if else clauses, what CS principles should I be using here?

edit

Some background, the first solution I wrote was just a simple check to see if the other train was on the shared track before sending the other train out. That seemed ad hoc to me and I'm sure it did to the company I interviewed for as well.

I figure there must be an algorithm or at least a school of thought for this type of problem, after all how do they build extensible systems for managing shared runway space at an airport, or managing traffic flow at stop lights. 

My intuition is that this is a very introductory problem to a school of thought in computational problem solving I have not yet encountered.

I might be wrong, but could anybody clear the air for me?
A related and well studied area is threading/multiprocessing. Your initial solution is a simple lock; the critical section of tracks can only be used by one train at a time. To extend this while avoiding deadlocks (two trains waiting in each other) or starvation (a train waits forever), you would want to use some more sophisticated locking mechanism and scheduler.