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This work considers the performance of an all-optical packet-switched cross-connect. All-optical header processing and all-optical routing are implemented in the cross-connect architectures. The main metric considered to measure the performance is the packet loss ratio for the buffering. A recirculating buffer is implemented with a degenerate configuration. It is shown that the unsatisfactory performance achieved taking the self-similarity of the traffic into account can be improved using overflow buffering. Overflow buffering utilises available buffer positions in parallel wavelengths of the same physical buffer.