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Networks-on-chip (NoCs) have recently emerged as a scalable alternative to classical bus and point-to-point architectures. To date, performance evaluation of NoC designs is largely based on simulation which, besides being extremely slow, provides little insight on how different design parameters affect the actual network performance. Therefore, it is practically impossible to use simulation for optimization purposes. In this paper, we present a mathematical model for on-chip routers and utilize this new model for NoC performance analysis. The proposed model can be used not only to obtain fast and accurate performance estimates, but also to guide the NoC design process within an optimization loop. The accuracy of our approach and its practical use is illustrated through extensive simulation results.