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Delay-line buffering has emerged as the current time-domain contention; solution in optical switching networks. Due to the unpredictability of future Internet traffic and the existence of various buffer architectures and wavelength scheduling policies, the study of such buffers under different traffic conditions is a very important issue. In this paper we present a generic-traffic analytical model for the FIFO delay-line buffer in an asynchronous network scenario that may be useful for buffer planning and performance evaluation. The model is traffic generic as it may assume any inter-arrival time process and packet length distribution.