Introduction to fluid Petri nets

The fluidization of Petri nets is a relaxation technique introduced in the literature in order to avoid the so called state explosion problem. This technique results in a model, named continuous or fluid, whose state variables (the marking at the places) take real nonnegative values. Among the implications, the fluidization opens the possibility for transferring concepts and techniques from the continuousstate systems paradigm to the discrete event systems one. In this chapter, the concept of non-forced continuous Petri net is recalled, together with the most usual firing semantics for the timed interpretation of this model. Certain properties on the resulting fluid models are described, remarking limitations and advantages found in the analysis of fluid Petri nets. The focus is on the relationships between the discrete and the continuous Petri nets. It is also discussed the quality of the relaxation, from qualitative and quantitative perspectives. In particular, questions like the preservation of liveness, boundedness or the marking evolution, are addressed. 16.