Clarke Ching has found an interesting (and long) report that uses Theory of Constraints to study the UK Network Rail's capacity: UK Network Rail and Theory of Constraints.
Thanks to a a fellow TOC enthusiast David C who pointed out Network Rail's 85 page CONSULTATION ON CAPACITY STUDY FOR EAST COAST MAIN LINE. I'm excited because they use Theory of Constraints as their methodology. This is important stuff.
The good stuff starts on page 7 with their description of how they think about TOC and the rail network. I don't quite see what they claim as the goal, but from the writing, I would guess something like increased capacity to deliver the right trains to the right places.
I wonder how the results here compare to combinatorial mathematics-style optimizations which are typically applied to this kind of problem. Transportation networks are a very common target of optimization, though I have usually seen variations of the "traveling salesman" problem where one tries to optimize an object traveling over the network and touching a specific set of nodes.