This paper introduces new admission criteria that enable the use of algorithms based on the many sources asymptotics in real-life applications. This is achieved by a significant reduction in the computational requirements and by moving the computationally intensive tasks away from the timing-sensitive decision instant. It is shown that the traditional overflow-probability type admission control method can be reformulated into a bandwidth-requirement type and a buffer-requirement type methods and that these methods are equivalent when used for admission control. The original and the two proposed methods are compared through the example of fractional Brownian motion traffic.