A hidden semi-markov model or hsmm is a modified version of a hidden markov model (HMM) that, as far as I can tell, explicitly encodes durations for each of the states rather than including a loop to itself as one of the possible transitions. It is used in [statistical-parametric-speech-synthesis], including that done with the [hts] framework, to generate speech features that are fed to a [vocoder] and synthesize speech.