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As technology scales, the delay uncertainty caused by process variations has become increasingly pronounced in deep submicrometer designs. As a result, a paradigm shift from deterministic to statistical design methodology at all levels of the design hierarchy is inevitable. In this paper, we propose a variation-aware task and communication mapping methodology for multiprocessor system-on-chips that uses network-on-chip communication architecture so that the impact of parameter variations can be mitigated. Our mapping scheme accounts for variability in both the processing cores and the communication links to ensure a complete and accurate model of the entire system. A new design metric, called performance yield and defined as the probability of the assigned schedule meeting the predefined performance constraints, is used to guide both the task scheduling and the routing path allocation procedure. An efficient yield computation method for this mapping complements and significantly improves the effectiveness of the proposed variation-aware mapping algorithm. Experimental results show that our variation-aware mapper achieves significant yield improvements over worst-case and nominal-case deterministic mapper.