The register queues are not independent, but they are not related as simply as you say.
Sorry but that's simply not true. everyone uses different variables and judgment to make a phone call, yet phone calls follow an exponential distribution! everyone uses different variables and judgment to hit the internet, yet network traffic follows a Lavalette distribution. everyone uses different variables and judgment to buy stocks, yet equity prices follow a lognormal distribution.
Individual behavior in aggregate will almost always follow some distribution, regardless of each individual using different variables and judgment for himself. The whole point of statistics is to uncover the underlying probability distribution given tons of (seemingly random) data. Math does the opposite ( ie. given the distribution, a mathematician can tell you how to derive nice things like the moment generating function & the first & second moments & density functions & related family of distributions & so on, & in general give you n sample variates that fit the distribution. By saying "everyone uses different variables and judgment" you are in essence saying its just too complicated, but even if that were true, that is just another distribution ( white noise )
Instead, I think you should do the math; it will teach you that the probability that a given queue is slow is smaller than the probability that, given a person in a queue, that person is in a slow queue.
So, you spend more time in slow queues than in fast ones. Once you know that, train yourself to accept it.