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The author evaluates the performance of bufferless optical packet switches equipped with shared tuneable optical wavelength converters (TOWC) and supporting the quality of service (QoS). The TOWCs are shared per output fibre and, hence each output fibre has a dedicated pool of TOWCs. The TOWCs are not completely shared within the node. The QoS, expressed in terms of the packet loss probability, is differentiated by giving the packets different priorities in accessing both the output wavelengths and the TOWCs. A scheduling algorithm is proposed and its complexity is evaluated. The QoS technique's effectiveness is studied by means of an analytical model based on a probabilistic approach and validated by simulation results. The results show that the proposed technique to support the QoS facilitates a good differentiation of the QoS offered to packets.