TCP flows generated by applications such as the Web or FTP require a minimum network throughput and can also benefit from an extra throughput due to their rate-adaptive algorithms. To build a guaranteed minimum throughput service, the authors propose a scheme with Admission Control (AC) using a small set of packet classes in a core-stateless network. At the ingress of the network, each flow packet is marked as one of the set of classes, and within the network, each class is assigned a different discarding priority. The AC method is based on edge-to-edge per flow measurements and requires flows to be sent at a minimum rate. The scheme is able to provide different minimum throughput to different users and protection against nonresponsive sources. The authors evaluate the scheme through simulation using different traffic loads consisting of TCP flows that carry files of varying sizes. In the simulation, TCP uses a new algorithm that forces the source to keep the short-term sending rate above a desired minimum rate. The authors study the influence of several parameters on the performance of the scheme in different network topologies. The results show that the scheme guarantees the requested throughput to accepted flows and achieves a high utilization of network resources, similar to the ideal results of a classical hop-by-hop AC.