We propose a comprehensive admission control and resource management strategy that exploits statistical multiplexing to support connections with diverse characteristics and requirements. At the first level traffic is classified into three broad categories: real-time, which has both delay and loss constraints, non-real-time, which is only loss-sensitive, and best-effort. Due to their tight delay constraints, real-time traffic cannot tolerate extensive buffering in the network. Thus the network cannot rely on the smoothing effect of buffers and must achieve small losses only by multiplexing a large number of sources so that the aggregate input rate rarely exceeds the capacity. We present an accurate estimate of the overflow probability for real-time traffic based on a theorem by Bahadur and Rao. On the other hand, existing results of large buffer asymptotics, such as effective and decoupling bandwidths, lend themselves to the analysis of non-real-time sources. We propose a simple resource allocation scheme in which service priority is given to real-time traffic. The non-real-time traffic is then buffered and served with the remaining capacity. Furthermore, we present a result that simplifies the tasks of traffic description and policing for real-time sources. We show that for fixed mean and peak rates, the on-off sources result in the largest overflow probability. Thus one can devise a call admission policy that bases its acceptance decision on these simple parameters and the worst-case assumption, such that the decision will always satisfy the quality of service constraints for arbitrary traffic distribution.