But then if you are in a queue already the most efficient response is to leave and rejoin at the front. Quite soon you don't have a queue, you have a brawl.

Perhaps I'm missing something.

It works when joining the queue has a high enough transaction cost. For example, a website or phone support line cutting off a pending connection, forcing the requester to notice and then reconnect, or give up and leave (which makes service faster for others waiting)

No, that's still not allowed. And, of course, perfect rational agents would never cheat.

So you can never leave a queue? Queuing would then be discouraged, wouldn't it? Making the move to buy something would often ensure you can't buy it but can also not buy anything else because someone else will cut in front of you and if you're out of luck, you'll be stuck in the queue forever, abandoning it is not allowed. Enjoy starving for greater efficiencies.

With normal queuing, you get served eventually and can calculate the time it will take to get what you need. I fail to see how removing both of those parts makes it more efficient, and intuitively it seems that it would mostly lead everyone to avoid queuing unless absolutely necessary or to only try to buy things that surely nobody else wants. Mean wait time down, only the least desired products get bought, and even those only when starvation is the alternative.

I never mentioned money, where on earth did you get that from??

I’m saying the most efficient queue is a stack. End of story.

Queueing at the front would imply that there's a possibility of never being served. Queueing at the back never has that being the case.

It seems to me that the math about the queueing isn't properly weighing that scenario.

Because a queue is about fairness, not efficiency, we join at the back.

Exactly. Probably why we shouldn't turn to economists for ethics advice.

Is this one of those purely theoretical economics thing or Does this assume there is a different queuing stage from a moving stage? Otherwise it seems like there are too many physical mechanics at play, like should I be able to join the line as soon as I see the line for the roller coaster start moving. How are ties broken if everyone tried to join the line at the same time.

Huh? Who prefers to stay longer in line?

With enough queue jumpers the line collapses into a crowd shouting for service - a crowd that is bigger than the line. Meaning the average service rate has fallen - that is, a less efficient system.