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

**M. Gribaudo, M. Sereno, A. Horváth, A. Bobbio**

### Abstract:

Fluid (or Hybrid) Petri Nets are Petri net based model 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.

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*András Horváth, 2008-06-25*