I am wondering if anyone put real-world details into mathematical models. In case of a single line and multiple cashiers, people tend to stand farther from the cashiers than they would be standing if they had chosen specific line and it requires tiny bit of attention and delay to scan cashiers constantly. Depending on the shop/service, if you choose the line you may start putting out your purchases onto the conveyor belt while the person in front of you is still being served, not so much when you do not know your cashier in advance.

From my airport experience, hybrid models tend to be pretty good: one single line to security scan or passport check and then it is ushered into many short ones. Probably should mathematically model that and see what happens.