TITLE: What property of queuing systems does 'first-come-first-served' maximize?
QUESTION [7 upvotes]: 'First come, first served' is a very very common way of organizing access to a limited resource or service in the real world. It can be explained by saying that whenever the resource is available the person who has been waiting the longest is served, and visualized by thinking of people standing in a single-file line, where the person at the front is always served next and new arrivals join the back of the queue.
If you ask someone why this system is the best, they might instinctively say 'It is the most fair'. But can we express what this fairness means in terms of some property, which is maximized for this system and no other? It doesn't mean for instance that people all wait the same time, or even that people who arrive at nearly the same time don't get served a long time apart.
Or does it optimize some other property, such as the incentive to arrive as soon as possible or the incentive not to arrive at busy times?
Can we make formal why it should be preferred to other arrangements? Or is it just a human tendency to do something simple/something that most people feel is fair/something we all know?

REPLY [4 votes]: First-come-first-served ensures that provided that the time between served customers is bounded, any customer who enters the queue will within a worst-case wait time that can be determined based upon the number of preceding customers.  Even if the time between customers is bounded only probabilistically, the wait time will still have a reasonable probabilistic bound.  For example, if one flips a coin once per second, and each "heads" means someone enters the queue and each "tails" means someone is serviced (unless the queue is empty, in which case nothing happens), someone who enters when there are 39 people ahead of him will know that the time until he is serviced will be the amount of time required for a total of 40 tails to appear.  That might or might not happen within 80 seconds, but will likely happen within 90.  Although would be possible that the person might have to wait an hour or more, it would be exceptionally improbable.  The probability of a person not having been served within a given length of time will rapidly approach zero as the time increases.
Suppose that the same parameters were applied with a LIFO stack.  While someone who entered the stack would have a 50% of being served in one second, they'd have a 3/8 chance of not getting served within 3 seconds (as compared with a 1/8 chance if they'd been first in a queue), a 5/16 chance of not getting served in 5 (versus 1/32), and a 35/128 chance of not getting served in 7 (vs 1 in 128).  The probability of not getting served within N seconds drops as N increases, but very slowly.  One would have roughly a one in nine chance of having to wait a minute, a one in 75 chance of having to wait an hour, and a one in 251 chance of having to wait a week or more.
If one assigns priorities to different items, then other service orders become practical, but behavior modeling is much more apt to focus much more on heuristics than absolute probability calculations.