I've long thought that those "take a number" queuing systems (commonly used at fast food places) should be random not linear. When someone with a larger number than you gets called first it feels like such an injustice! However, most people wouldn't be the wiser if the numbers were randomized. I bet it would reduce wait time complaints substantially.
I'd say that goes directly against one of the theses of the article -- that "uncertainty magnifies the stress of waiting".
The most excruciating waits that I've had to deal with in the last many years are at the Ausländerbehörde here in Germany -- the "foreigners' office". It's the place that you have to go to get a work permit if you're not German.
They use a randomized system. You don't have any idea if you're going to be waiting 10 minutes, 3 hours or even if you'll make it through the line at all before they close for the day. Combined with the stress of the possibility of rejection or missing some critical piece of paperwork, the uncertainty adds a huge amount of cognitive load. Need to go to the bathroom after you've been waiting for an hour? What if they call your number while you're away for 5 minutes? I would love for them to switch to a linear system so that I could produce a ballpark estimate of where I am in the queue.
The appearance of fairness is often as important as fairness itself. With randomness, you completely destroy that appearance. I'll even bet that a lot of people will make up their own theories about how the tokens are given out ("Oh, that other machine usually gives smaller numbers"). So, my hunch is complaints will actually rise.
Btw, one strategy the article doesn't mention is making queues seem more asynchronous-- this is what Starbucks does when they employ "expeditors", those employees who walk the line and take orders (but not cash). The (partial) success of having ordered your coffee mitigates the agony of waiting to reach the cash register (it also makes people less likely to abandon the line).
Maybe those restaurants should use people's names instead; on the other hand the article indicates that people like feedback on their wait times. Perhaps people would be happier if they were instead given time estimates that the restaurant could reliably beat.
At least processing them linearly gives a reasonable upper bound on the wait time. With random waits, some customers would be processed instantly ("WHY do THEY get to skip the entire line when I'm still sitting here?") and others would never be processed.
I think what the GP meant was that the numbers on the slip would be randomized, but the queue still ordered like a queue with the numbers in some database.
Absence of observed order and provable fairness due to sequential order will inevitably lead to many people suspecting injustice and developing all kinds of theories, from flawed randomness generators (in last 10 numbers only 4 were even, the system is clearly broken!) to conspiracy theories (they hate me so they gave me a special number that gets called an hour later!)
Best medicine for that is a linear observable order, which is easily controlled and obviously hard to subvert - if you see you're number 42 you know you're going after 41 and everybody knows that, and if somebody doubts it you can just show your number and prove it's fair.
