What is the distance between your signals? The AI have a set distance and if your signals are too far away, they can get stuck. There are other reasons why the AI are stopped that aren't obvious including a direction marker facing the wrong way for the siding or branch that they intend to take. To find out why the AI are sitting at a green signal, hover cursor over the signal. The signal will display a message.
The AI, however, do get stuck when things get busy. This occurs over time as the internal game threads become very busy and don't clear up. I had an extreme case of this back in TANE, and I reported this to N3V. What is interesting is initially I thought it was a signal script error because I switched signals to another kind. RRSignal instead of Jointed Rail or vice versa and the problem went away. Thinking at the time the issue was a scripting problem, I let it go because everything appeared to work, however, the problem occurred again much later after running for a long time instead of within a few minutes.
On this very large complex route, a combination of Deremmy's East Kentucky and Evansville & Western, Dave Snow's Ozark Valley, Midwest Grain from Jointed Rail, plus the add-on route Coldwater, and Jointed Rail's American Intermodal things got so bad I gave up on it and never ran it again. In TS2010 and TS12, the mega route ran fine. I'd have AI drivers, multiple of them, plying the lines for hours. When TANE came out, the route would run for about 30-minutes, before changing signals, before the AI got "dumb". They'd sit there and stare at green signals as though they were red. Inching them beyond the signals, and they'd continue on fine. Pressing Pause also worked, but that only worked once or twice. I'd end up exiting the session and reloading from the save, but that had another curve ball thrown in. The AI now were blowing through red signals, ignoring track marks, speed limits, and direction markers. Sometimes, the signals remained red while other times they remained dark. When I changed the signals out, the route ran for about an hour or two before they started kicking off, and I got to the point where I scrapped the route. TRS19 was much, much better, then TRS22 came out and we're back to the crap again as new sh*** has been added in.