On Supervisory Policies that Enforce Global Fairness andBounded Fairness in Partially Controlled Petri Nets

• Authors: Ramavarapu S. Sreenivas
• Venue: Discrete Event Dynamic Systems
• Year: 1997

In this paper we consider the notions of global-fairness(G-fairness) and bounded-fairness (B-fairness) for arbitraryPetri nets (PNs). G-fairness in a PN guarantees every transitionoccurs infinitely often in every valid firing sequence of infinitelength. B-fairness guarantees a bound on the number of timesa transition in the PN can fire without some transition firingat least once. These properties are guaranteed without recourseto assumptions on firing time distributions or contention resolutionpolicies. We present a necessary and sufficient condition forthe existence of supervisory policies that enforce G-fairnessand B-fairness along with various observations on the closureproperties of policies that enforce these notions of fairnessin controlled PNs with a (possibly) non-empty set of uncontrollabletransitions. We also derive a necessary and sufficient conditionthat guarantees a minimally restrictive supervisor that enforcesthese notions of fairness for bounded PNs. These results areillustrated via examples.