(a train or airplane is) now boarding
When a train, bus, or airplane is "boarding", it means that passengers are being let onto it.
When airport or train station employees are making announcements, they say:
Now boarding.
But when you want to talk about the flight or train that you're taking, you say:
My flight's boarding now, so I've got to go. I'll call you later.
I think our train is boarding.
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