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Low latency is a critical requirement in some switching applications, specifically in parallel computer interconnection networks. The minimum latency in switches with centralized scheduling comprises two components, namely, the control-path latency and the data-path latency, which in a practical high-capacity, distributed switch implementation can be far greater than the cell duration. We introduce a speculative transmission scheme to significantly reduce the average control-path latency by allowing cells to proceed without waiting for a grant, under certain conditions. It operates in conjunction with any centralized matching algorithm to achieve a high maximum utilization and incorporates a reliable delivery mechanism to deal with failed speculations. An analytical model is presented to investigate the efficiency of the speculative transmission scheme employed in a non-blocking N times NR input-queued crossbar switch with R receivers per output. Using this model, performance measures such as the mean delay and the rate of successful speculative transmissions are derived. The results demonstrate that the control-path latency can be almost entirely eliminated for loads up to 50%. Our simulations confirm the analytical results.