ON SUPERVISORY POLICIES THAT ENFORCE GLOBAL FAIRNESS AND BOUNDED FAIRNESS IN PARTIALLY CONTROLLED PETRI NETS

In this paper we consider the notions of global-fairness (G-fairness) and bounded-fairness (B-fairness) for arbitrary Petri nets (PNs). G-fa irness in a PN guarantees every transition occurs infinitely often in every valid firing sequence of infinite length. B-fairness guarantees a bound on the number of times a transition in the PN can fire without some transition firing at least once. These properties are guaranteed without recourse to assumptions on firing time distributions or conte ntion resolution policies. We present a necessary and sufficient condi tion for the existence of supervisory policies that enforce G-fairness and B-fairness along with various observations on the closure propert ies of policies that enforce these notions of fairness in controlled P Ns with a (possibly) non-empty set of uncontrollable transitions. We a lso derive a necessary and sufficient condition that guarantees a mini mally restrictive supervisor that enforces these notions of fairness f or bounded PNs. These results are illustrated via examples.