Urban air mobility with electric vertical takeoff and landing (eVTOL) vehicles is envisioned to become a fast and flexible urban transportation mode. Apart from technical challenges for eVTOLs regarding vehicle design and manufacturing, airspace design and traffic control mechanisms are most desired on the operation side. In particular, from an operational point of view, the arrival phase is expected to be the main bottleneck, with restricted vertiport resources, high air traffic density, frequent flight maneuvers, and limited eVTOL remaining battery energy, all leading to complex operational constraints. This work provides a framework to enable optimal and efficient on-demand eVTOLs arrivals in the context of on-demand urban air mobility. This paper investigates the throughput of a double-landing-pad vertiport by proposing a new vertiport terminal area airspace design and a novel rolling-horizon scheduling algorithm with route selection capability to compute the optimal required time of arrival for eVTOLs in a tactical manner. Finally, a case study on arrivals in a hexagonal vertiport network is performed to show the algorithm performance with different configurations. Our simulation results show that up to 50 s delay per eVTOL is expected during the commuter peak hours and less than 10 s delay is expected during off-peak hours.