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We propose the Geometric Bounds (GBs), a new family of fast and accurate noniterative bounds on closed queueing network performance metrics that can be used in the online optimization of distributed applications. Compared to state-of-the-art techniques such as the Balanced Job Bounds (BJBs), GB achieves higher accuracy at similar computational costs, limiting the worst- case bounding error typically within 5-13 percent when, for the BJB, it is usually in the range of 15-35 percent. Optimization problems that are solved with GBs return solutions that are much closer to the global optimum than with existing bounds. We also show that the GB technique generalizes as an accurate approximation to closed fork-join networks commonly used in disk, parallel, and database models, thus extending the applicability of the method beyond the optimization of basic product-form networks.