We develop a new model for studying the phenomenon of congestion in a transient environment, focusing on the problem of aircraft landings at a busy "hub" airport. Our model is based on a Markov/semi-Markov treatment of changes in the weather, the principal source of uncertainty governing service times, together with a treatment of the arrival stream as time-varying but deterministic. The model is employed to compute moments of queue length and waiting time via a recursive algorithm. To test the model, we conduct a case study using traffic and capacity data for Dallas-Fort Worth International Airport. Our results show that the model's estimates are reasonable, though substantial data difficulties make validation difficult. We explore, as examples of the model's potential usefulness, two policy questions: schedule interference between the two principal carriers, and the likely effects of demand smoothing policies on queueing delays.