Individuals, populations and fluid approximations: A Petri net based perspective

As the linearization of a continuous dynamical system, the fluidization of a DES is a relaxation that has to be used with care, depending on the problem at hand. This abstraction is here considered from two complementary perspectives: at logical and at performance levels, both for untimed and timed PNs. On the one hand, the expressive power of timed fluid PNs under infinite server semantics is such that the simulation of Turing machines is possible. From a complementary perspective, the expression of modeling capabilities such as non-monotonicities and bifurcations may also be revealed for steady-state behaviors. Symmetries (more generally, lumping) seek to group together “equivalent” behaviors and decolorization seeks to abstract identities, in order to create new collectivities of processes and resources. The synergy between symmetry-decolorization state-aggregation approaches and fluid relaxations is highlighted. In fact, the first approaches not only reduce the state space, but also “produce” populations, thus proceed upgrading the applicability of fluidization. Opening the window, related issues such as control, optimization, observation or diagnosis are briefly pointed out. For conciseness, this work is limited to fully fluid (or continuous) PN models and their relationships with the corresponding discrete systems.