Approximate closed-form aggregation of a fork-join structure in generalised stochastic petri nets
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
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Stationary analysis of GeneralizeStochastic PetriNets (GSPNs) often suffers from the state space explosion problem. Large reachability sets - isomorphicto continuous-time Markov chains - are not only expensive to generate, but related high-dimensional datastructures also put excessive demands on numerical algorithms. In particular, sequences of transitions andalternative branches contribute multiplicatively to thesize of the state space - if enabled concurrently.This paper examines under which circumstancessuch structures can be merged into a single timed transition while preserving the stationary token distributions in the embedding envir onment. For these aggregation steps on net level, novel formulae for the(locally) marking-dependent rates of the merged transition are developed, which solely rely on parameters ofthe aggregate dsubnet. These formulae bear a strongrelation to ow equivalence. Examples throughout thepaper demonstrate the gains both in drastically reducedstate spaces and shortened processing times of the numerical analysis.