Dual perspectives of equilibrium throughput properties of continuous mono-T-semiflow Petri nets: Firing rate and initial marking variations

Abstract

Somehow derived from the duality of places and transitions in Petri nets, the variations on the initial marking of places and on the firing rates of transitions allow to see several properties of the equilibrium throughput in Timed Continuous Petri nets from a dual perspective. This work presents novel results in this sense that are grouped in three parts. The first one focuses on the relationships among properties as monotonicity, continuity, and deadlock-free monotonicity of the equilibrium throughput when either the firing rate or the initial marking varies. It is done in a broad class of nets called Mono-T-Semiflow nets. The second one relates previous properties with some structural objects named configurations. In particular, it is shown that for both, firing rate and initial marking variations, the occurrence of undesired behaviors (non-monotonicities, discontinuities) is due to configurations whose associated set of places does not contain the support of a P-semiflow. Finally, based on the structural characterization, sets of firing rates and initial markings for avoiding undesired behaviors are derived.