But if we get pedantic we accept this will never satisfy the definition of a geometric line and the Brits were right all along to call them queues.
You're always 'in the' queue (or queuing) though, not 'on' it. So if you must call it a 'line' or a 'line-up', I sympathise most with 'in'.
But if we get pedantic we accept this will never satisfy the definition of a geometric line and the Brits were right all along to call them queues.