On the hierarchical evaluation of stochastic Petri net models with waiting time resonance

The author considers generalized stochastic Petri net (GSPN) models of reliable flexible manufacturing systems (FMSs). Such models are analytically solved by aggregating GSPN subnets to substitute nets of lower complexity. It is shown that the heuristically motivated, common application of flow equivalent aggregation (Norton's theorem) to subnets of FMS models yields enormous approximation errors in the case of subnets bearing a resonance behavior in the mean waiting time of tokens. A new kind of substitute network for reducing the approximation error is proposed. The estimation of the substitute net's parameters is derived. The aggregation method is demonstrated by means of a model of a FMS where waiting time resonance arises due to reliability provisions.<
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