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Based on feasible concepts of all-optical switching and all-optical buffering, this paper considers the implementation of travelling buffers in an all-optical packet switched cross-connect. Because of the fundamental limitations of an input-buffered architecture, an output-buffered architecture is investigated to determine the influencing factors on the performance. We investigate the feasibility of developing an all-optical cross-connect with travelling buffers in terms of the amount of fibre required to obtain an acceptable packet loss ratio in the cross-connect. By simulating a travelling fibre delay line buffer using traffic with self-similar characteristics, it is shown that the traffic load and characteristics influence the buffer performance, as well as the cross-connect size and the selection of the fibre delay line distributions. Furthermore, the internal use of wavelengths to increase the effective buffer size has a significant influence on the total amount of fibre required for buffering, in particular in DWDM systems where hundreds of wavelengths can share a single fibre.