The general queue can benefit from a single line, multiple server, set up. And where the operator can resist the temptation to shorten the line by building up mini-queues in front of each of the multiple servers, it works well. A side-line set up to deal with sizeable subset of arrivals, but with a very limited number of servers, is going to be less efficient, more difficult to handle.

The single time I joined the dedicated premium-class line at LHR was some time back, travelling with a friend carrying a non-UK, non-EU, passport. The queue was served by only one agent, until a second joined him at an adjacent desk. It required only one or two interesting visas to hold up the line, and there were a few of these: it took a very long time to get through. Part of the problem might have been the way queue-access vouchers were handed out on board - ours came from a cabin-crew member smitten by my rather glamorous companion. We'd travelled in economy class.

An alternative might be to dribble-leak a priority line into the the head of the general queue, in the way some airports handle priority inspections of departing passengers. But that can be a difficult system to manage without generating a measure of friction.

Adopting a paid for system, with the price of access set at a level to match demand with capacity might be the economist's solution, but it would be a solution some would find uncomfortable.