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After accepting my invitation to random dungeon, I traveled to another location by shrine only to find myself out of the que and with this 15min time restriction?! Why?
Did you enter the dungeon and then leave it?
If so, you were probably marked as a deserter, hence you are 'punished' with a 15 minute time restriction.
ESO was better in the good old days when it only crashed because your computer was too much potato to have 50+ players on your screen at the same time.
OP, did you by any chance port elsewhere via wayshrine after accepting the queue pop but before getting ported to the dungeon by the game?
Doing that is Very Bad and causes all kinds of negative effects to happen, because it confuses the game as to where you should be placed.
For example, if you do that after accepting a Cyrodiil queue pop, you are stuck as both "being in the queue" and "not being in the queue" - can't queue again and can't port to Cyro either, only logout fixes that.
(edit: oops typos)