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Ordinary t-timed Petri nets are used for modeling, analysis and synthesis of random topology production systems and networks. Each production system is first decomposed into production line (transfer chain), assembly, disassembly and parallel machines modules and then their corresponding modular Petri net models are derived. The overall system PN model is obtained via synthesis of the generic modules satisfying system constraints. P- and T-invariants are calculated and given a random topology production system, the total number of the system PN model nodes (places, transitions) is calculated from the corresponding generic PN modules. Results show the applicability of the proposed methodology.