Why is modeling required? Can’t we just put a sensor on every bus, and just return the empirical expected time it takes for the next bus to drive to your station given the time of day and day of week?
But:
> just return the empirical expected time it takes for the next bus
There is a world of complexity in "the empirical expected time", there... expected according to what models?
Anecdotally, I think it's especially hard to model because any given delay is probably attributable to one or a few specific incidents. This isn't a situation where everything averages out and we can use a nice tractable AWGN model; we're down in the muck and the shot-noise.
The issue here is the deviation between empirical expected time and actual arrival time. Unhandled exceptions abound.