This paper addresses the challenge of optimizing handover (HO) performance in non-terrestrial networks (NTNs) to enhance user equipment (UE) effective service time, defined as the active service time excluding HO delays and radio link failure (RLF) periods. Availability is defined as the normalized effective service time which is effected by different HO scenarios: Intra-satellite HO is the HO from one beam to another within the same satellite; inter-satellite HO refers to the HO from one satellite to another where satellites can be connected to the same or different GSs. We investigate the impact of open radio access network (O-RAN) functional splits (FSs) between ground station (GS) and LEO satellites on HO delay and assess how beam configurations affect RLF rates and intra- and inter-satellite HO rates. This work focuses on three O-RAN FSs -- split 7.2x (low layer 1 functions on the satellite), split 2 (layer 1 and layer 2 functions on the satellite), and gNB onboard the satellite -- and two beam configurations (19-beam and 127-beam). In a realistic dynamic LEO satellite constellation where different types of HO scenarios are simulated, we maximize effective service time by tuning the time-to-trigger (TTT) and HO margin (HOM) parameters. Our findings reveal that the gNB onboard the satellite achieves the highest availability, approximately 95.4%, while the split 7.2x exhibits the lowest availability, around 92.8% due to higher intra-satellite HO delays.
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