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Buffers are essential components of any packet switch for resolving contentions among arriving packets. Currently, optical buffers are composed of fiber delay lines (FDL), whose blocking and delay behavior differ drastically from that of conventional RAM at least two-fold: 1) only multiples of discrete time delays can be offered to arriving packets; 2) a packet must be dropped if the maximum delay provided by optical buffer is not sufficient to avoid contention, this property is called balking. As a result, optical buffers only have finite time resolution, which may lead to excess load and prolong the packet delay. In this paper, a novel queueing model of optical buffer is proposed, and the closed-form expressions of blocking probability and mean delay are derived to explore the tradeoff between buffer performance and system parameters, such as the length of the optical buffer, the time granularity of FDLs, and to evaluate the overall impact of packet length distribution on the buffer performance.