TITLE: In what area of study does one encounter this principle in timetabling?
QUESTION [9 upvotes]: A while ago I saw an image like the one below in a lecture, which was supposed to represent a rail network in a (square) city:

The circles represent trains that are moving either North/South or East/West along the vertical and horizontal tracks.  The purpose of this picture was to show that, even though the grid is unevenly spaced, it is always possible to schedule the trains so that connections were perfectly timed:  that is, any time a train arrives at an intersection, there is another train also arriving at that intersection, in a perpendicular direction.
The math behind this is very simple, so my question is:  what is the area of study in which one would encounter an image like this?

REPLY [3 votes]: Not an answer, but two related, almost inverse topics suggesting in which
areas of mathematics they fall:
(1) The Lonely Runners Conjecture.
See, e.g., Terry Tao, "Some remarks on the lonely runner conjecture." Perhaps this could be classified as a mixture of number theory
and combinatorics.



Guillem Perarnau, Oriol Serra, "Correlation Among Runners and Some Results on the Lonely Runner Conjecture." Electr. J. Comb. 2016.

(2) "At Museum of Mathematics, Meet 2 Beavers That’ll Never Meet." This construction uses
Truchet Tiling.
Perhaps this could be classified as a mixture of topology and combinatorics.