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Current on-chip and macro networks use multi-stage arbitration schemes which independently assign different resources such as crossbar inputs and outputs to individual traffic streams. To use these networks in real-time systems, their worst-case behavior must be proved analytically in order to ensure the required timing guarantees. Current analysis approaches, however, do not capture the multi-stage arbitration accurately. In this paper, we propose an analysis that maps the multi-stage arbitration to a schedulability analysis of multiprocessors with shared resources. This allows the exploitation of knowledge about the worst-case behavior of the individual traffic streams, which is required to provide non-symmetric guarantees. Using this scheduling analysis approach, a detailed analysis solution for a common multi-stage arbitration scheme (iSLIP) is presented. Finally, we evaluate the proposed approach experimentally and compare it to previous work.