# Compositional Approximation of Markov Chains

Here is the abstract of the talk:

We discuss two different approaches to approximately aggregate a Markov chain. In the first case, a clustering algorithm is used to approximate the minimisation of a measure that implies quasi-lumpability. In the second case, we use the spectral properties of the Markov chain to identify a nearly completely decomposable partition of the state-space.

Both approximate aggregation methods require an explicit representation of the transition matrix, a fact that renders them inefficient for large models. 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. We demonstrate the potential of the compositional approximate aggregation in a model that involves components of different size.

This is joint work with Stephen Gilmore