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For example, a queue in a post office. With FIFO every member has to wait for x units, where the unit is the time to handle one member and x is the size of the queue. With LIFO, most members have to wait for 1 units, but a few members have to wait on the order of x^2.

Someone correct me if my interpretation is incorrect.

I think LIFO queue would make an interesting experiment in a real world scenario, in contrast to FIFO used almost everywhere. Just make sure there is a maximum time limit set for those who are stuck in the back of the queue. This way most members get out quickly, and a few have to wait for whatever is the maximum time limit or close to that.