Bounded Decomposition of Stochastic Models

In this extended abstract we discuss bounding techniques for a collection of interacting simple QN and SAN models that we have been developing. Each simple model produces bounded output when presented with bounded inputs. A collection of bounded models can be used to construct larger models that have the same bounding properties. Additionally, the constructed model can be decomposed at the boundaries of the sub-structures, resulting in bounded submodels that can exchange bounded results. These bounds explicitly demonstrate the accuracy of the solution, and can be used to determine if the models need to be refined to increase the accuracy of the solution. This work is based on the observation that many simple Petri net structures can be compared to G/GI/1 queues either directly or indirectly. Bounds exist for total delay of customers through G/GI/1 queues, and for other quantities. We have developed new bounds for the departure process based upon existing bounds.