Do Timetable Ai Trains Keep Running/spawning Forever?

If I start a timetable, and spend hours wandering around, will trains continue to come and go or will they end, eventually?

I'm not sure if I am explaining correctly. What I'd like to know is if timetables have a finite set of trains scheduled (a pre-defined pool, if you will) for a few minutes or if new trains just keep spawning as time passes infinitely.

 

Okay, so if I want to keep finding traffic, the sooner I start, the better. Thanks!

 

Are timetables not a self-perpetuating 24 hour loop...? I thought they could go on indefinitely, starting at any point in the 24 hour cycle.