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This paper presents an evaluation of IP-based gateway discovery protocols for the interconnection of ad hoc networks to the Internet. There are three proposed internet discovery approaches: reactive, proactive and hybrid. This paper first compares these protocols performances with respect to different frequency of gateway advertisement considering random waypoint mobility model. The main contribution of this work is the study of the effect of applying realistic mobility models which has not been investigated so far in the related published work. Our results investigate the high impact of selected mobility models on the performance analysis of the discovery protocols.