New Controllability Condition for Siphons in Ws3PR Nets

Existing policies for deadlock control are mainly based on siphons due to their ability to indicate deadlocks, and can be used as a powerful tool to deal with deadlock situations in flexible manufacturing systems. In order to avoid deadlocks, researchers often add monitors to control siphons. This may result in redundant monitors, unnecessary cost, and restriction of the behavior permissiveness. For example, for a system of sequential systems with shared resources ((SR)-R-4), the existing deadlock control policies based on max, max or max-controlled siphons tend to overly restrict the behavior of a controlled system. To ensure maximal permissive behavior of controlled systems, a new concept of siphon controllability named W-control is defined and then a sufficient and necessary condition under which a (WSPR)-P-3 is live if all its siphons are W-controlled. Examples are given to demonstrate them.