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Real-time constraints pose a new challenge when performing real-time application mapping onto Network-On-Chip. To this problem, we first propose a new task graph description in this paper, to enable both computation mapping and communication scheduling. Based on the proposed graph, we then propose a contention and energy aware mapping algorithm to eliminate the communication conflicts and reduce energy cost, thus delivering higher throughput and lower energy consumption on communicational links. In the experiments, we show that different real-time constraints impacts the on-chip network a lot, and our algorithm is able to find a better mapping and scheduling solution for a given real-time application and on-chip network structure. For example, comparing to traditional mapping without considering timing constraints, our algorithm reduces the energy up to 44% on average. It also improves throughput of the system up to 25%.