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Advances in CMOS-compatible photonic elements have made it plausible to exploit nanophotonic communications to overcome the limitations of traditional NoCs. Amongst various proposed nanophotonic architectures, optical crossbars have been shown to provide high performance in terms of bandwidth and latency.In general, optical crossbars provide a vast volume of network resources that are shared among all the cores within the chip. In this paper, we present a fair and efficient admission control mechanism for shared wavelengths and buffer space in optical crossbars. We model buffer management and wavelength assignment as a utility-based convex optimization problem, whose solution determines the admission control policy. Thanks to efficient convex optimization techniques, we obtain the globally optimal solution of the admission control optimization problem by using simple and yet efficient iterative algorithms. We cast our solution procedure as an iterative algorithm to be implemented a central admission controller. Our experimental results corroborate the gain that can be obtained by using such an admission controller to manage the shared resources of the system. Furthermore, they confirm that the proposed admission control algorithm works well for various traffic patterns and parameters, and evinces a tractable scalability with increase in the number of cores of the crossbar.