Observations
So I've got a fortress tavern with a few dozen performers hanging out, but only one of them asks to be made permanent. Time goes by. The caravans arrive, and we trade with them oodles of expensive earthenware crafts. Immediately after completing the trades, about a dozen of the visitors ask to be made permanent. So I'm guessing that visitor petition rate is tied to exported wealth. The huge wave of petitions was more than I had beds for, so I don't think the number of beds assigned to your tavern has anything to do with petition rate.
Also, I'm playing a FuFo game with lots of civilizations. The farthest civilizations send me lots of visitors. The civilization near enough to send a caravan doesn't send me any visitors. However, there is a dark pit civilization that has sieged us twice and sent a few performers as visitors. I visited the dark pit and dark fortress assigned to that civ in adventure mode and found them completely empty, except for a team of humans who had apparently either conquered the site or reclaimed for themselves. I'm pretty sure but not completely sure that the abandoned dark fortress belonged to the civ that is now sieging me, except that I didn't think they had any other sites in the area, so it's a bit of a puzzle.
There is an Ogre civ somewhere, and one time an Ogress Dancer game to visit. Hilariously, the ogress could not contain herself and smashed a bunch of buildings on the way down to the tavern. She took a long time standing around next to the buildings before destroying them, as though conflicted about whether or not to give in to her building destroyer instincts. The militia was dispatched to dispatch her, and no obvious retribution has resulted from the death of the ogress dancer.
Also, a dwarf poet who joined my leokin fortress had a strange mood and claimed a workshop. Unfortunately, the game crashed before the poet could finish his artifact. Or perhaps it crashed because of the artifact.