In this paper we study measurement-based admission control for bufferless multiplexing, which is very attractive for real-time traffic. We first discuss a novel large deviations (LD) approach to measurement-based admission control. We then provide an extensive review of the existing literature on measurement-based admission control. We conduct simulation studies with traces of MPEG 1 encoded movies to compare the performance of the admission rules in the literature with that of our large deviations approach. We demonstrate that our LD approach achieves higher link utilizations. Finally, we compare the performance of measurement-based admission control with that of traditional admission control, which relies on a priori traffic descriptors. Our numerical work indicates that measurement-based admission control achieves significant gains in link utilizations over traditional admission control