Relaxed continuous views of discrete event systems: considerations on Forrester diagrams and Petri nets

Petri nets (PNs) constitute a formal paradigm for discrete systems. Some discrete models can be relaxed into continuous models. Infinite server semantics continuous Petri nets (ISSCPNs) is one of the most relevant timed interpretation of continuous PNs. ISSCPNs can be seen as piecewise linear systems. Forrester diagrams (FD) are specific modelling tools inside system dynamics, a methodology for the analysis of complex continuous systems. This paper explores and compares the modelling power of both formalisms, ISSCPNs and FD. Previous comparative views focused on the formalisms and on positive and compartmental systems, constitute the basis of this work. The comparison is complemented taking into account the interpretation of linear ordinary differential equation systems (LODES), the information delays and some methodological considerations. ISSCPNs permit to model any LODES when known upper and lower bounds of the state variables exists. Therefore systems with cyclic behaviour or delays in the information can be modelled.