Although I'm familiar with this concept since the implementation of ITF (integrated clock-face timetables) in Central Europe, I found the second half of this article (as of this revision [1]) hard to read. After finishing it, I felt like I understood less about clock-face scheduling than I did before.

Nonetheless, I know that the key desirable features are (1) to ensure that hub-like nodes have services from all directions arrive and leave at the same time, so that connecting passengers don't need to wait for long, and (2) that a future arrival/departure time at a major node is somewhat predictable without consulting the full timetable.

For trains, it's also a nice feature that trains of opposite directions will meet somewhere predictable, so track improvements like double-tracking can be targeted at places where crossings are likely to occur, which can cost less than double-tracking the entire line.

Integrated clock-face timetables work best when rigid, but it requires the spacetime of transport geography to fit into a regular pattern. But this can mean that some improvements that would result in faster service on portions of the network would put the the network out of sync. Because of this complication, such incremental improvements may not happen.

[1] https://en.wikipedia.org/w/index.php?title=Symmetry_minute&o...