Many designs for integrated service networks offer a bounded delay packet delivery service to support real-time applications. To provide bounded delay service, networks must use admission control to regulate their load. Previous work on admission control mainly focused on algorithms that compute the worst case theoretical queueing delay to guarantee an absolute delay bound for all packets. In this paper we describe a measurement-based admission control algorithm for predictive service, which allows occasional delay violations. We have tested our algorithm through simulations on a wide variety of network topologies and driven with various source models, including some that exhibit long-range dependence, both in themselves and in their aggregation. Our simulation results suggest that, at least for the scenarios studied here, the measurement-based approach combined with the relaxed service commitment of predictive service enables us to achieve a high level of network utilization while still reliably meeting the delay bound.