This paper proposes a general modeling framework adapted to the feedback control of traffic flows in Eulerian models of the National Airspace System (NAS). It is shown that the problems of scheduling and routing aircraft flows in the NAS can be posed as the control of a network of queues with load-dependent service rates. We can then focus on developing techniques to ensure that the aircraft queues in each airspace sector, which are an indicator of the air traffic controller workloads, are kept small. This paper uses the proposed framework to develop control laws that help prepare the NAS for fast recovery from a weather event, given a probabilistic forecast of capacities. In particular, the model includes the management of airport arrivals and departures subject to runway capacity constraints, which are highly sensitive to weather disruptions.