If you say that people are queuing up to do or have something, you mean that a lot of them want the opportunity to do it or have it. (mainly BRIT; in AM, usually use line up )
People are queueing up to work for me!...
There are a growing number of countries queueing up for membership.
PHRASAL VERB: usu cont, V P to-inf, V P for n
see also queue 3