In networks that support quality of service, an admission control algorithm determines whether or not a new traffic flow can be admitted to the network such that all users will receive their required performance. Such an algorithm is a key component of future multiservice networks because it determines the extent to which network resources are utilized and whether the promised QoS parameters are actually delivered. The goals in this article are threefold. First, we describe and classify a broad set of proposed admission control algorithms. Second, we evaluate the accuracy of these algorithms via experiments using both on-off sources and long traces of compressed video; we compare the admissible regions and QoS parameters predicted by our implementations of the algorithms with those obtained from trace-driven simulations. Finally, we identify the key aspects of an admission control algorithm necessary for achieving a high degree of accuracy and hence a high statistical multiplexing gain.