[ryanwaggoner]

I may just be misunderstanding, but if you were to represent a queue of people waiting in line as a data structure, wouldn't they each have a number, like their index in an array, etc? How is that different than a take-a-number system?

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.