Modular Petri Net based modeling, analysis, synthesis and performance evaluation of random topology dedicated production systems

Ordinary t-timed modular Petri Nets are used for modeling, analysis, synthesis and performance evaluation of random topology dedicated production systems. Each system is first decomposed into production line, assembly, disassembly and parallel machine modules followed by derivation of their modular Petri Net models. Two sets of modules, generic and generalized respectively, are derived corresponding to the simplest and most general cases. Overall system Petri Net model is obtained via synthesis of the individual modules satisfying system features (production rates, buffer capacities, machine expected up, down or idle times). Detailed mathematical expressions are derived for modules P-invariants (and T-invariants when exist); they are further generalized for a random topology and complexity dedicated production system. Total number of the individual Petri Net module nodes as well as of the combined system Petri Net model is also calculated. Results show the applicability of the proposed methodology and justify its modeling power and generality.