Is it? A thread-safe blocking queue sounds like one of those take-a-number systems you find in some shops. But it would be very common to instead rely on the standard waiting-customer algorithm, in which, after waiting for some period of time, the customer gets frustrated and rings the bell at the counter. Take-a-number systems are vanishingly rare by comparison. Why do you need the queue?
I don't know why I picked such a complicated example.
Did you ever go to the grocery store and had to wait for the people in front of you? That's also queue and yet nobody is taking numbers.
Queues are inherently ordered, right? The take-a-number system is still a queue, it just replaces physical ordering with a paper that shows your place in line.