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Silicon nanophotonics is an emerging technology platform for offering high-bandwidth connectivity with extreme energy efficiency for future networks-on-chip. Using circuit-switching as an arbitration mechanism takes advantage of the low transmission energy in end-to-end communication and high bandwidth density of wave guides using WDM. However, pure circuit-switching requires an electronic control network which suffers from unfairness under heavy loads and can lead to high latencies, low network utilization, and an overhead in power dissipation. We propose time division multiplexed distributed arbitration, which provides round-robin fairness to setting up photonic circuit paths. Our design can supply 2-4× the bandwidth at network saturation for random traffic, and is an order of magnitude more efficient when simulated with scientific application traces compared to both electronic and other photonic network architectures.