Unless this has changed, at least in 06 the priorities have nothing to do with trains taking priority over each other, they are an attempt at making certain trains take certain tracks... If you have two similar routes to get from Point A to Point B, with a Priority marker of 1 on one of them ("D") (unmarked tracks default to Priority 2, which we'll call "E"), and three trains groing from A to B, one Priority 1, one Priority 2, and one Priority 3, then the Priority 1 train will prefer to travel through point D, P2 train will prefer point E, and the P3 train will take either one.
This is not a perfect system and does not garantee that only trains matching the track's priority will take that track, nor that trains matching a track's priority will always take that track, but the AI will try to "prefer" these routes when calculating its route to its destination. It is a more automatic method of using trackmarks in the routing of trains over specific tracks, but again not perfect. It will not necessarily mean that a freight on the track ahead will move over to a siding to allow a higher priority train go by, nor does it mean that trains will wait for meets at passing sidings on single-track routes in the manner expected.
One thing I've discovered a while ago with AI is that each AI train is looking out for itself and only itself. Alistair driving a slow 3000 ton coal train doesn't care that Geoff is slowly putting along behind him at 25 mph in his express passenger train. He won't wait at a passing for the express to go by, and Geoff can try zipping by on a long enough passing siding while Alistair keeps on trucking, but chances are by the time Geoff hits the other end and wants to get back to the main Alistair will still have the switch providing for that movement locked in his direction. I've tried the 4-track main idea before and even with the priorities it was imperfect. Alistair would see Tom driving another slow freight ahead of him on the P3 track, going at the same speed. Even though he could never get by him due to speed limits he would break priority and go back to the P2 NB track and hold up the all the traffic behind instead of sticking to the P3 track and letting the faster traffic by. This is where the AI needs the greatest improvement, IMO, is working together with other trains to make things run smoothly, not just doing what it wants regardless of the other trains around it.
(Driver names are by example only, I still think Alistair should never be allowed to drive
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