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We consider an optical hybrid switch that can function as an optical burst switch and/or optical circuit switch. We propose and describe in detail a new implementation whereby circuits have nonpreemptive priority over bursts. To achieve nonpreemptive priority, during circuit setup time, if there exist bursts that use wavelength channels (also called links) required by the circuit, the circuit is allowed to queue for a relatively short period of time until these bursts are cleared. We present an analysis based on a 3-D Markov chain that provides exact results for the blocking probabilities of bursts and circuits, the proportion of circuits that are delayed and the mean delay of the circuits that are delayed. Because it is difficult to exactly compute the blocking probability in realistic scenarios with a large number of wavelengths, we derive computationally scalable and accurate approximations based on reducing the 3-D state space into a single dimension. These scalable approximations that can produce performance results in few seconds can readily enable switch dimensioning. Extensive numerical results are presented to demonstrate the accuracy and the use of the new approximations.