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queue2 also queue up [intransitive] British English
1 to form or join a line of people or vehicles waiting to do something or go somewhere [= line up American English]
2 if people are queueing up to do something, they all want to do it very much
queue up to do something 
The school is one of the best, and parents are queueing up to send their children there.
The school is one of the best, and parents are queueing up to send their children there.