On the algebraic structure of solutions to some livelock-avoidance problems in manufacturing systems modeled by petri nets

If at least one of the activities of an automated manufacturing system enters a state of suspended-animation for perpetuity, we say the system is experiencing livelock. We consider Petri Net (PN) models of manufacturing systems that are prone to livelocks, which can be made livelock-free by a supervisory policy. Specifically, we consider supervisory policies that are represented by structural additions to the original PN, known as monitors. The role of the monitor parallels that of a traffic-cop; it regulates the activities of a system in a manner that guarantees the supervised system is livelock-free. In this paper we relate the qualitative property of livelock-freedom and the quantitative property of maximizing throughput in a class of PN models. It identifies a necessary and sufficient condition for class of systems where the objective of achieving livelock-freedom in a minimally-restrictive manner, also accomplishes the objective of maximizing its throughput.