You could optimize the many queues so they're just as efficient as the one single queue but you'd have to know everyone's processing time in advance - impossible in a real world setting.
Not quite impossible. You might not know individually, but on average for a group or segment you could get this information and optimize. Banks can do this by splitting consumer and merchant lines. Merchants typically take longer (who knows by how much), and get their own queue.
With this system, you have 2 queues, 1 for each group. There may be a lot of variation within each group, but the averages work out. Consumers wait the average minimum processing time for the consumer group, and merchant wait the average processing time for the merchant group.
This still leaves room for underutilization. What if the merchant line is backed up and the consumer line is empty? Ideally, the extra tellers would work to pick up the slack, but if this isn't possible then it's still not an ideal system.
Another common example would be airport check-in. You have economy and first-class.
Often the first-class line is empty - do you let 'the rabble' check-in there and risk a first class passenger having to (gasp) wait a couple of minutes behind them; or make the long line of economy passengers stare at the unused desk and mutter about the airline.
(Though given that airports are really just a series of queues feeding each other the different in practice is pretty minimal.)
Not quite impossible. You might not know individually, but on average for a group or segment you could get this information and optimize. Banks can do this by splitting consumer and merchant lines. Merchants typically take longer (who knows by how much), and get their own queue.
With this system, you have 2 queues, 1 for each group. There may be a lot of variation within each group, but the averages work out. Consumers wait the average minimum processing time for the consumer group, and merchant wait the average processing time for the merchant group.
This still leaves room for underutilization. What if the merchant line is backed up and the consumer line is empty? Ideally, the extra tellers would work to pick up the slack, but if this isn't possible then it's still not an ideal system.