Lumpability and Aggregation of Markovian Submodels

Hierarchical Markovian models are an adequate paradigm for the modeling of complex systems. For the analysis of such models decomposition and aggregation techniques are very important, since the Markov chain described by a complex model often has a size that exceeds the capacity of contemporary computer equipment by orders of a magnitude. A class of hierarchical Markovian models is deened and a new aggregation technique is presented, which allows the aggregation of isolated submodels and the substitution of submodels by less complex aggregates and often reduces the size of the underlying Markov chain dramatically. The ag-gregation technique is based on the generation of (approximative) lumpable partitions on the submodels state space and allows the construction of aggregates introducing various degrees of approximation.