Queue management organises waiting: assigning an order, calling people forward, and telling everyone where they stand. Screens are how the state gets communicated, whether that is a ticket number, a counter call, or an estimated wait.
The measurable gains are real. A virtual queue lets people wait somewhere other than a line, which in retail means they keep shopping. A visible position reduces the anxiety that makes people ask staff how long it will be, which is itself a load on the counter.
The caveat is that perceived wait matters more than actual wait, and a badly chosen display makes it worse. An estimate that turns out optimistic is worse than no estimate, because the customer measured it. A counter that visibly stalls draws attention to the delay. Unexplained waiting feels roughly twice as long as explained waiting, so the honest content is what is happening, not a number counting down.
Fairness is the other half. People tolerate a long wait far better than one where somebody who arrived later is served first, so if the system routes by service type, show it, or the queue will police itself loudly.