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This paper provides new loss models for a hybrid optical switch (HOS) combining optical circuit switching (OCS) and optical burst switching (OBS). Exact blocking probabilities are computed when 1) no priority is given to either circuits or bursts and 2) circuits are given preemptive priority over bursts. Because it is difficult to exactly compute in realistic scenarios, computationally scalable approximations are derived for the blocking probability. The sensitivity of the analytical results to burst length and circuit holding-time distributions is quantified by simulation. It is demonstrated how the proposed approximations can be used for multiplexing-gain evaluation of a hybrid switch. In addition, the extension of the proposed single-node model to a network model composed of OCS, OBS, and hybrid switches is outlined.