Comparison of tree and straight-line clocking for long systolic arrays

A critical problem in building long systolic arrays lies in efficient and reliable synchronization. We address this problem in the context of synchronous systems by introducing probabilistic models for two alternative clock distribution schemes: tree and straight-line clocking. We present analytic bounds for the Probability of Failure and the Mean Time to Failure, and examine the trade-offs between reliability and throughput in both schemes. Our basic conclusion is that as the one-dimensional systolic array gets very long, tree clocking becomes more reliable than straight-line clocking.