Network-based real-time multimedia applications require guaranteed performance communicationservices. To provide guaranteed service, resources have to be reserved within the network. If reservation is based on the peak rate of each connection, the network will be under-utilized by guaranteed service traffic when the traffic is bursty. In this paper, we first show that local deterministic delay bounds can be guaranteed over a link for bursty traffic even when the sum of the peak rates of all the connections is greater than the link speed. Compared to previous admission control conditions, the new result allows a multi-fold increase in the number of admitted connections when the traffic is bursty. We then show that this new result can be efficiently extended from a single switch to a network of arbitrary topology by using rate-controlled service disciplines at the switches.