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To support diverse real-time applications, the next-generation Internet needs to provide end-to-end performance guarantee on a per-connection basis in the integrated service environment. In addition to the issues of how to allocate resources to satisfy the specific quality-of-service (QoS) requirements in a single switch, we also need to prevent the burst arrivals due to complex interaction of the packets from different sources within intermediate switches. To address this problem, a new frame-based packet scheduling scheme: 2-tier hierarchical frame (2tHF) queueing, is proposed and investigated in this paper. The key idea of 2tHF queueing is that packets to be served within a frame are evenly distributed over the multiple sub-frames and served in the order of time with other packets. Through numerical analysis, we have shown that when using varying number of sub-frames, the proposed 2tHF queueing not only provides the differentiated end-to-end delay bound, but also solves the coupling problem between the bandwidth allocation granularity and delay performance.