A simple modification of deadlock prevention policy of S 3 PR based on elementary siphons

We propose to extend our proprietary approach of siphon synthesis to a new simple deadlock control policy. To prevent each strict minimal siphon (SMS) S from becoming empty of tokens, we often add a control place V_S and associated arcs to form an invariant to control the number of tokens leaking from S. In a disturbanceless approach, the control (called Type-1) arcs are chosen to disturb the original uncontrolled model as little as possible, to reach as many states as possible. However, this policy may generate new SMSs and hence require adding too many control places and arcs to the original Petri net model. Thus, Ezpeleta et al. moved all output (called Type-2) arcs of each V_S to the output transition of the entry (called idle place) of input raw materials to limit their rate into the system, called all-sided, or SMSless approach. This may overly constrain the system so that many reachable states are no longer attainable. We hence propose an intermediate, called the one-sided, approach, which does not generate new SMS, based on our siphon-synthesis theory, by appropriately choosing the locations of Type-1 arcs and it can reach more states than the all-sided approach. The same results can be extended to the elementary-siphon approach by Li et al. except with no need to fine-tune the locations of Type-1 arcs. Comparison with other approaches has been made.