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Next generation satellite network (NGSN) possesses unique characteristics; large coverage area, quick deployment, native broadcasting/multicasting capability, multiple spotbeams, high bandwidth and on-broad processor (OBP). These features enable NGSN to play an important role in providing ubiquitous global Next Generation Internet (NGI). The original Internet is restricted mainly to terrestrial network and supports only best effort service. NGI is to support multiservice applications with service differentiation and extending Internet access beyond the reach of terrestrial network. Based on the integrated satellite- terrestrial network, a main infrastructure for global ubiquitous Internet is envisaged and Internet applications can be accessed anywhere anytime. However, one of the key successes depends mainly on the capabilities of the satellite OBP. Without it, the preservation of end-to-end (e2e) service differentiation has to be dealt with at ground hub stations, thus increasing e2e delay. This paper studies the impacts of different on-board queueing schemes on the quality of multiservice applications on NGI and suggests that the quality of multiservice applications is generally enhanced if the on-board service differentiation is supported.