Semi-Markov modelling paradigms are more expressive than their Markovian counterparts but are equally vulnerable to the state space explosion problem. This paper addresses this issue by presenting an exact state-by-state aggregation algorithm for semi-Markov models. Empirical evidence shows that the computational complexity of our method depends critically on the order in which the states are aggregated. We investigate different state-ordering strategies and find one that aggregates a large proportion (circa 75%) of our example state spaces at minimal cost. This leaves a significantly smaller model which can then be analysed for performance-related quantities such as passage-time quantiles. We demonstrate our technique on several examples, including a 541,280 state model which is reduced to 173,101 states.
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