Approximate analysis of stochastic models by self-correcting aggregation

We present an approximation algorithm for the analysis of large stochastic models. The fixed point iteration approach uses different approximate aggregations of the state space of a model. The stationary state probabilities of these aggregated models are calculated to derive refined aggregations which are used for the correction of the approximate aggregations. The presented method is then extended to benefit from components of higher level model descriptions by defining pairwise overlapping aggregations of the state space of a model. This construction of the aggregated models makes the automatic generation of appropriate aggregations possible, such that the interactions of the submodels are taken into consideration. Together with a well known aggregation formula and new and simple correction formulas the method is easy to implement. The good accuracy of the presented algorithm is shown by means of large examples and the results are compared with the results derived by simulation.