In a typical hub airport, incoming flights from many origins feed outgoing flights to many destinations. If an incoming flight is late, outgoing flights which are fed by it may also be delayed eventually. Alternately, planes may leave before some feeding flights arrive, thereby incurring high misconnection penalties. Clearly, if we plan for very long scheduled ground time between the last incoming flight and the first outgoing one, we can reduce the risk of unscheduled delays or misconnections. However, such a schedule may cost the airline too much in terms of idle personnel and equipment and will not be attractive to the passenger either. On the other hand, if we plan for very short scheduled ground time, we run the risk of excessive unscheduled delays, and/or misconnection penalties. In this paper we develop models designed to optimize the scheduled ground time under two pure policies (i) to wait as long as necessary to ensure all connections, and (ii) not to wait at all (i.e., pay misconnection penalties rather than delay penalties). The models can also be applied to similar problems such as express parcel deliveries and ground transportation hubs. Keywords: Scheduling; Air transportation; Airports; Airline scheduling.