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Slotted optical burst switching (SOBS) has recently caught the attention of the optical networking community due to performance gains achievable with synchronous infrastructures. In this paper, we study the loss probabilities in a slotted optical burst switching node fed with Poisson burst traffic where the fixed burst size is an integer multiple of the slot length. We develop a discrete-time Markov chain (DTMC) based framework to obtain the loss probabilities in systems with and without quality of service (QoS) differentiation. In particular, we focus on analytical modeling of priority scheduling and offset-based QoS differentiation mechanisms for SOBS networks. The latter problem suffers from the curse of dimensionality which we address by a discrete phase type distribution approximation for the discrete Poisson distribution leading to an accurate approximation for the loss probabilities. A hybrid QoS mechanism which jointly utilizes offset-based differentiation together with priority scheduling is also analyzed.