An Aggregation Technique For Large-Scale PEPA Models With Non-Uniform Populations

Abstract: Performance analysis based on modelling consists of two major steps: model construction and model analysis. Formal modelling techniques significantly aid model construction but can exacerbate model analysis. In particular, here we consider the analysis of large-scale systems which consist of one or more entities replicated many times to form large populations. The replication of entities in such models can cause their state spaces to grow exponentially to the extent that their exact stochastic analysis becomes computationally expensive or even infeasible. In this paper, we propose a new approximate aggregation algorithm for a class of large-scale PEPA models. For a given model, the method quickly checks if it satisfies a syntactic condition, indicating that the model may be solved approximately with high accuracy. If so, an aggregated CTMC is generated directly from the model description. This CTMC can be used for efficient derivation of an approximate marginal probability distribution over some of the model's populations. In the context of a large-scale client-server system, we demonstrate the usefulness of our method.