In: IEEE Trans. on Automatic Control, Vol. 45, No. 9, pages 1760-1761. 2000.
Abstract: In the domain of flexible manufacturing systems, given a structural (static) model of the system, the existence of cycles of resources in such a model is a necessary condition for a deadlock to be reached. This condition is not sufficient in the general case because we cannot ensure that a state which establishes a circular wait situation is reachable (cycles of resources are only potential circular waits). In the paper indicated in the title (by Xing, Hu and Chen, IEEE Trans. on Automatic Control, Vol. 41, No. 2, pp.289-295, 1996), two results, which directly imply that the existence of cycles of resources is also a sufficient condition, are presented. These results are established for a subclass of FMSs, where choices are not allowed in in the process plans, and where each part uses one and only one system resource in each state during its processing. This note shows that the proof of the results in the indicated paper is not correct, although the result itself is correct. A different approach is recommended which is clearer and which provides a better insight into the problem.
Keywords: Petri nets, deadlock avoidance, flexible manufacturing systems.