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We develop a performance model for an optical burst switch employing fiber delay lines (FDLs) to enhance system performance. An M/M/k queueing model with balking is derived to predict the system behavior for both classless and prioritized traffic. Simple closed-form expressions are obtained for the burst loss probability of classless traffic. Using a conservation relation, the balking model is extended to model the performance of prioritized traffic classes. A discrete event-driven simulator is constructed to verify the accuracy of the proposed models. Numerical results show that the classless model fits simulation results very well. The model for prioritized traffic provides an accurate fit for the performance of the highest traffic class and lower bounds for the other traffic classes that are tighter than earlier known results.