Hybrid Modelling with Second Order Fluid Stochastic Petri Nets.pdf

in Pro c Workshop on Parallel and Distr RealTime Systems WPDRTS pp Geneva Switzerland April Hybrid Mo delling with Second Order Fluid Sto chastic Petri Nets Katinka Wolter Gun ter Hommel Technische Universitat Berlin Institut fur Technische Informatik Franklinstr Berlin Germany fkatinkahommelgcstub erlin de Abstract nets FSPNs FSPNs have b een develop ed to extend SPNs for the mo delling of continuous quantities and are Stochastic Petri nets have been extended for the mod meant to b e clearly divided into a discrete and a con el ling of hybrid systems by adding uid places that are tinuous submo del that can aect each other FSPNs l le d and emptied continuously at random normal ly allow a very exible denition of uid mo dels but no distributed rate The ow rates as wel l as the dis probabilistic variation of the uid ow is p ossible since crete transition rates may depend on the content a uid the uid ow is describ ed by a rst order uid ow plac e holds The dynamics of the model are described pro cess leading to a system of rst order partial dif by second order partial dierential equations that can ferential equations PDEs Each equation represents be solved by using an implicit CrankNicolson scheme a probability density function for one discrete state of Reward measures such as the uid throughput can be the net and dep ends on the uid variables and in the computed from the continuous part of the solution As transient case on time an