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.
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).
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.