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The sharing of tunable wavelength converters (TWCs) is widely believed as a feasible way of reducing the cost of an optical-packet-switching (OPS) or optical-burst-switching (OBS) node. Theoretical analyses of the performance of different TWC sharing schemes in published works are mostly confined to synchronous switching nodes, and for asynchronous switching nodes, only simulation results are given. In this paper, a theoretical analysis of the performance of the TWC share-per-link (SPL) scheme for an asynchronous switching node is given with the assumptions of Poisson burst arrival and exponential burst-length distribution. Based on this analysis, the performance of a share-per-node (SPN) scheme can be evaluated by means of two approximate-evaluation models (AEMs). Quick evaluation methods for SPL and SPN schemes are also proposed. Simulation results show that the theoretical analysis is accurate and the approximate ones can get quite similar results. All results indicate that both SPL and SPN schemes will save TWCs in an OBS node, whereas SPN will save more than SPL to obtain the same burst-loss performance.