Fluid Stochastic Petri Nets Augmented with Flush-out Arcs: Modelling and Analysis

Abstract

Fluid (or Hybrid) Petri Nets are Petri net based models with two classes of places: discrete places that carry a natural number of distinct objects (tokens), and fluid places that hold a positive amount of fluid, represented by a real number. With respect to previous formulations, the FSPN model presented in this paper, is augmented with a new primitive, called flush-out arc. A flush-out arc connects a fluid place to a timed transition, and has the effect of instantaneously emptying the fluid place when the transition fires. The paper discusses the modeling power of the augmented formalism, and shows how the dynamics of the underlying stochastic process can be analytically described by a set of integro-differential equations. A procedure is presented to automatically derive the solution equations from the model specifications. The whole methodology is illustrated by means of various examples.