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

TL;DR

This paper introduces an approximate aggregation algorithm for large-scale PEPA models with non-uniform populations, enabling efficient analysis by reducing state space complexity while maintaining high accuracy.

Contribution

The paper presents a novel syntactic condition check and an aggregation method that simplifies large PEPA models for faster approximate analysis.

Findings

Effective in large client-server systems

Reduces computational complexity significantly

Maintains high accuracy in probability distribution estimates

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.