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This paper addresses the real-time problem of scheduling aircraft in a terminal control area. We formulate this problem via the alternative graph formulation. A rolling horizon framework is introduced to manage busy traffic situations with a large number of delayed aircraft. As scheduling algorithms, we compare a branch and bound (BB) algorithm with a first come first served (FCFS) rule. The algorithms are evaluated on practical size instances from Roma Fiumicino and Milano Malpensa. Experimental results demonstrate that BB better minimizes aircraft delays and travel times compared to FCFS. BB also requires less frequent changes of aircraft scheduling decisions.