Aggregation Ordering for Massively Compositional Models

Compositional modeling is a powerful way of expressing the behavior of a complex system through the interaction of its components. Analysis of compositional models is difficult because of the state space explosion. One solution is compositional aggregation where composition and aggregation steps are intertwined. This approach has proven particularly useful in the area of compositional performance and dependability modelling. However, one open question remains: in which order should the models be composed, a question that is especially important for massively compositional models derived automatically from higher level descriptions. Finding the optimal composition ordering is generally infeasible, so heuristics are necessary to find good orderings. In this paper we present a comparative study of compositional aggregation algorithms which harvest and refine heuristics originating from Tai and Koppol. The heuristics take into account the interaction between components, the size of the component models and uses early elimination of bad composition orders to dramatically decrease computation time. We present an implementation of the algorithms and study its effectiveness by applying it to case studies from different application areas.