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This work addresses the challenge of computing worst-case response times of hard real-time applications deployed on multiprocessor systems. In particular, the worst-case response time analysis (WCRTA) focuses on the communication between distributed tasks of hard real-time applications. The proposed WCRTA models the communication as a pipelined communication resource model. This model incorporates the effect of pipelining, and the parallel transmission of data. Applications of such a model include multiprocessor systems that use complex interconnects such as network-on-chips (NoC)s with priorities. In this paper, we present an exponential analysis, and a polynomial analysis, and prove its correctness. As an application, we apply the pipelined communication resource model to priority-aware NoCs, and we compare the proposed analyses against prior analysis techniques. Our experimental evaluation on two instances of 4 × 4 and 8 × 8 NoCs with 512,000 synthetic benchmarks shows 48.3% and 66.7% improvement in schedulability for the two NoC sizes over prior work.