Credit-based router-to-router flow control is one main link-level flow control mechanism proposed for Networks on Chip (NoCs). Based on network calculus, we analyze its performance and optimal buffer size. To model the feedback control behavior due to credits, we introduce a virtual network service element called flow controller. Then we derive its service curve, and further the system service curve. In addition, we give and prove a theorem that determines the optimal buffer size guaranteeing the maximum system service curve. Moreover, assuming the latency-rate server model for routers, we give closed-form formulas to calculate the flit delay bound and optimal buffer size. Our experiments with real on-chip traffic traces validate that our analysis is correct; delay bounds are tight and the optimal buffer size is exact.