Approximate solution of PEPA models using component substitution

Performance models specified using compositional algebra suffer the well-known state space explosion problem, where a relatively small definition leads to a Markov chain with a large state space that is problematic to solve. As a result it is widely recognised that the development of techniques to solve performance models efficiently is of particular practical importance. Recently the notion of behavioural independence was introduced to exploit the structure of Markovian process algebra models in order to solve models in a compositional manner. The opposite property, namely control, is now used to solve models by substituting components in the model with simpler versions. The approach is validated through two examples and by deriving a variety of performance measures.