Problematic configurations and choice-join pairs on Mono-T-Semiflow nets: towards the characterization of behavior-structural properties

Abstract

This work is concerned with the computation of problematic configurations and problematic choice-join pairs in timed continuous Petri nets under the infinite server semantics; those net structural objects explain possible bad/counter-intuitive behaviors of systems, such as non-monotonicities and discontinuities of the equilibrium throughput. The calculation of problematic configurations is a computationally complex task since their number grows exponentially with the input cardinality of join transitions. In order to alleviate this inconvenience, four type of reduction rules preserving the set of problematic configurations are addressed. Reduction rules are weighted versions of the macroplace, macrotransition, and fusion of transitions rules, the elimination of implicit places rule is also provided. Reduced nets are useful to better understand the net substructures leading to unexpected behaviors in the equilibrium throughput. They help to highlight that the structural objects named problematic choice-join pairs, defined in this work, are the actual responsible of these counter-intuitive throughput behaviors. The great advantage over the set of problematic configurations is that the set of problematic choice-join pairs grows polynomially in the size of the net.