Virtual waiting time in queues obtained from second order FSPNs

Fluid stochastic Petri nets consist of two parts. A discrete part, that is a GSPN and a continuous part, that is represented by fluid places and arcs. Fluid places are filled and emptied continuously along fluid (double lined) arcs, as long as the transition at the arcs origin or destination is enabled. In second order FSPNs the rate at which the fluid level changes is a normally distributed random variable, as opposed to the deterministic rates in standard FSPNs. Jump transitions are indicated by discrete (single-lined) arcs. When the transition at the arc´s origin or destination fires an amount of fluid, that is determined by a probability density, it is removed or deposited at once. The continuous flow is kept in a specified domain by reflecting barriers. To avoid jumps across the boundary, one out of two alternatives can be chosen: either the jump height is reduced (force jump) or the jump is cancelled at all (preserve). Both have been implemented and are applied to the example. The whole model is mapped on a Markov process, Kolmogorov forward equations can be formulated and solved in an implicit discretization