Ethernet switches are typically found in many large-scale distributed real-time systems providing low-end transactions as well as bulk backbone routing to real-time applications. The FTT-SE protocol (Flexible Time-Triggered communication over Switched Ethernet) is a recent proposal to bypass the limitations of conventional switches in terms of real-time behavior while catering for growing requirements on dynamic reconfigurability and adaptability. For this end, this paper develops linear time-complexity and memory-efficient on-line admission control tests based on utilization bounds for Rate-Monotonic and EDF scheduling on Ethernet switches using FTT-SE, which are suited for dynamic Quality of Service (QoS) management. Our analysis also has broader applicability in general periodic task sets with bounded release delays. For FTT-SE with 100 Mbps links and 1500 bytes of maximum packet size, our sufficient schedulability condition achieves an utilization bound of 61% for RMS and 88% for EDF. Simulation results on randomly generated task sets demonstrate that such bounds are within 18% and 5% utilization of the ideal tests for RMS and EDF, respectively.