Second Order Fluid Stochastic Petri Nets : an Extension ofGSPNs for Approximate and Continuous

A Petri net formalism is presented that allows for mixed discrete and continuous stochastic models. The continuous part of the models consists of uid places that are lled and emptied at random (normally distributed) rate. Fluid places can be used for continuous approximation of heavily loaded discrete places in order to avoid state space explosion as well as for the modelling of continuous system components. The dynamics of a second order FSPN are described by second order partial diieren-tial equations. They can be solved by using an implicit Crank-Nicolson scheme. As an example a processing system with modulated arrival stream and service break downs is used. QoS measures such as waiting time, loss rate and throughput are calculated for both a discrete and a uid model.