Bounds for quasi-lumpable Markov chains
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Approximate Markov chain aggregation involves the construction of a smaller Markov chain that approximates the behaviour of a given chain. We discuss two different approaches to obtain a nearly optimal partition of the state-space, based on different notions of approximate state equivalence. Both approximate aggregation methods require an explicit representation of the transition matrix, a fact that renders them inefficient for large models. The main objective of this work is to investigate the possibility of compositionally applying such an approximate aggregation technique. We make use of the Kronecker representation of PEPA models, in order to aggregate the state-space of components rather than of the entire model.