Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri’s general systems theory and have very different interpretations, ranging from Einstein’s relativity theory to elementary information processing gates. Despite their simple defini tions, their properties are still not completely understood. This contribution provides for the first time a formal definition together with new results concerning their structure. Cycloids are proved to be live and safe. It is shown that the minimal length of a cycle is the length of a local basic circuit, possibly decreased by an integer multiple of the number of semi-active transitions. These results allow to find the defining parameters of a cycloid from the static properties of the net system. Similar results are obtained for degenerate cycloids.

This correspondence introduces a deadlock-avoidance algorithm for a class of manufacturing systems with the following characteristics: 1) Production orders are allowed to have assembly operations (which give the nonsequential nature to the resource allocation system model) but not disassembly operations, 2) the use of system resources must be conservative (resources are neither created nor destroyed), and 3) actions related to the granting of resources are controllable. The proposed solution represents a sufficient condition for a given system state to be safe and is based on an adaptation of the well-known Banker's approach for deadlock avoidance. The time complexity of the proposed solution is proved to be polynomial with the size of the Place/Transition net model.