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Optical buffers realized with fiber delay line (FDL) have been used in optical packet switching networks for contention resolution. The dimension of delay granularity is the key to employ FDL efficiently. In this paper, we develop an approximate model for evaluating the performance of wavelength division multiplexing (WDM) based optical buffers for asynchronous variable length packets. The theoretical model is verified through simulation and the results show that the delay granularity of FDL is slightly dependent on the buffer length and the number of wavelength in a fiber for a given traffic load.