A Heuristic Approach for the Aggregation of Markovian Submodels

Abstract

Decomposition and aggregation is a very important technique for the approximative analysis of large scale hierarchical models. In particular a decomposition on model level rather than on the underlying Markov chain allows to reduce the solution effort for a complex model significantly. We introduce here an extended approach for the aggregation of Markovian submodels including different types of entities. Aggregate construction is based on numerical pre-analysis of absorbing Markov chains. The resulting aggregates can be interpreted as queueing network stations with Coxian service time distributions, special subnets of coloured GSPNs or as specific station types in process interaction models. The aggregation approach has been automized and integrated in a tool environment. The resulting aggregation errors are most times much smaller than errors resulting from standard flow equivalent aggregation.