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The performance of single-wavelength fiber delay line buffer with finite waiting places is evaluated in this paper. For Poisson arriving packets with arbitrarily distributed lengths, the generating function of delay time distribution can be derived from the quantized delay buffer model. Then queue length distributions, loss probability, and other important performance measures can be figured out. Specifically, two important cases of negative-exponentially distributed packet lengths and fixed packet lengths are considered and compared. The accuracy of the proposed approach is verified through simulation. It is also observed that the buffer system performs more effectively for the fixed-length packets.