Automated Manufacturing Systems (AMS) consisting of many cooperating devices incorporated into multiple cooperating production lines, sharing common resources, represent industrial Multi-Agent Systems (MAS). Deadlocks may occur during operation of such MAS. It is necessary to deal with deadlocks (more precisely said, to prevent them) to ensure the correct behavior of AMS. For this purpose, among other methods, methods based on Petri nets (PN) are used too. Because AMS are very often described by PN models, two PN-based methods will be presented here, namely based on (i) PN place invariants (P-invariants); and (ii) PN siphons and traps. Intended final results of usage these methods is finding a supervisor allowing a deadlock-free activity of the global MAS. While the former method yields results in analytical terms, latter one need computation of siphons and traps.

This paper is devoted to Petri net (PN)-based models of automated manufacturing systems (AMSs) with resources in order to prevent deadlocks in them. Their sustainability can be seen as the result of their deadlock freeness, leading to correct and fluent production, because AMSs with deadlocks work neither correctly nor fluently, need reconstruction and cause downtime in production. The paradigm of such PN models, S³PRs (systems of simple sequential processes with resources), is well known from the deadlock prevention point of view. Here, an extended S³PR (ES3PR) will be explored, with respect to its modelling and deadlock prevention. While in the case of S³PRs, ordinary Petri nets (OPNs) are used for these aims, here, for ES³PRs, generalized Petri nets (GPNs) are used. The reason for such a procedure is the possible presence of multiplex-directed arcs in the structure of PN models of AMSs. The significant alternation is that while, in the former case, the elementary siphons and dependent ones are sufficient for supervisor synthesis, here, in the later case, the GPNs and their siphons have to satisfy the max cs property.

Modern AMSs (automated manufacturing systems) on the one hand bring many benefits, but on the other hand, they are cumbersome to coordinate. AMSs consist of various subsystems (e.g., production lines) that share a finite number of resources (robots, machines, buffers, automated guided vehicles, etc.). This forces AMS designers to build flexible and decentralized systems. However, in these cases, the danger of deadlocks exists. Consequently, such a situation requires the application of advanced supervisors. One solution to the deadline problem is the application of Petri nets. This paper is motivated by AMS control based on deadlock prevention by means of ordinary Petri nets (OPNs) and generalized Petri nets (GPNs). This paper examines two areas of AMS Petri net-based model structures and presents methods of deadlock prevention. First, simpler structures of AMSs modeled by OPNs and GPNs will be investigated, and then more complex structures of AMSs modeled by the same kinds of Petri nets (PNs) will be analyzed. The siphon-based approach will be used for deadlock prevention in all of these cases. The principal results are introduced, explained, and illustrated through examples. Key results are introduced, especially in Example 1 and Example 2.