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This paper compares the performance of hierarchical ring- and mesh-connected wormhole routed shared memory multiprocessor networks in a simulation study. Hierarchical rings are interesting alternatives to meshes since i) they can be clocked at faster rates, ii) they can have wider data paths and hence shorter message sizes, iii) they allow addition and removal of processing nodes at arbitrary locations, iv) their topology allows natural exploitation in the spatial locality of application memory access patterns, and v) their topology allows efficient implementation of broadcasts. Our study shows that for workloads with little locality, meshes scale better than ring networks because ring-based systems have limited bisection bandwidth. However, for workloads with some memory access locality, hierarchical rings outperform meshes by 20-40% for system sizes of up to 128 processors. Even with poor access locality, hierarchical rings will outperform meshes for these system sizes if the mesh router buffers are only 1-flit large, and they will outperform meshes in systems with less than 36 processors regardless of mesh router buffer size.