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The fiber delay line (FDL) buffer is widely used in optical packet switching networks for contention solution. In this paper, a quantized delay buffer model is proposed to analyze the performance of the single-wavelength FDL buffer. Considering the delay quantization in the FDLs, the delay time and the waiting time of the packet are discussed. Without specific assumptions of the packet arrival process and length distribution, the model presents a generic approach to study the delay time distribution and modify the integral equation for the waiting time distribution. Analytic and exact results of the two aforementioned distributions can be obtained without any approximation. The accuracy of the model is validated through simulation.