Comments on "Deadlock avoidance policy for Petri net modeling of flexible manufacturing systems with shared resources

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 above mentioned paper (Xing et al., 1996) and Ezpeleta et al. (1998), 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 FMS, where choices are not allowed in the process plans, and where each part uses one and only one system resource in each state during its processing. Both approaches use Petri nets to model the systems, namely production Petri nets (PPN), and linear systems of simple sequential processes with resources. In fact, both models are very similar. Here we show that the proof of the result in the Xing et al. is not correct, we also show that the result itself is correct (it is implied by the result in Ezpeleta et al.). Moreover, we think that the approach in Ezpeleta et al. is clearer, and that it provides more insight into the problem.