Jump Transitions in Second Order FSPNs

In this paper jump transitions for the fluid model part in second order fluid stochastic Petri nets (FSPNs) are introduced. The extended formalism is defined, and the underlying partial differential equations are derived. With a jump a certain amount of fluid is added to a fluid place or taken out at once. This amount, the jump height, is sampled from a probability distribution. The dynamics of a model are described by second order partial differential equations that include integrals. As examples the virtual waiting time (or unfinished work) in a queueing system and a performability model of a multi-processor system are modelled.