The local Chevy dealer has two lanes in their service department. One labeled "appointments", the other labeled "service". I asked a service rep one time if having an appointment meant faster service. He said no, it was still basically first come first serve. The appointment lane basically meant getting logged into their system faster after arrival.
I think most service departments work that way whether warranty or owner paid. And the busier they are, the longer it will be whether you have an appointment or just drop in. When someone drops off their unit (what ever that may be) with a vague description of the problem, they have no real idea of how long they will be working on that particular unit to move on to the next. A service department that guarantees to start work based on an appointment time would be one to hold on to.
