An adaptive aggregation/disaggregation algorithm for hierarchical Markovian models

Abstract

A new analysis technique for large continuous time Markov chains resulting from hierarchical models specified as stochastic Petri nets or queueing networks is introduced. The technique combines iterative solution techniques based on a compact representation of the generator matrix, as recently developed for different modeling paradigms, with ideas from aggregation/disaggregation and multilevel algorithms. The basic step is to accelerate convergence of iterative techniques by integrating aggregation steps according to the structure of the transition matrix which is defined by the model structure. Aggregation is adaptive analyzing aggregated models only for those parts where the error is estimated to be high. In this way, the new approach allows the memory and time efficient analysis of very large models which cannot be analyzed with standard means.