Fair control of Petri nets

Given a Petri net, we consider the problem of synthesizing the control policy, which the Petri net can be enforced by a 'fair' controller to meet the requirement that transitions are fairly (global-fairness and bounded-fairness) fire. We give a necessary and sufficient condition for the existence of 'fair' (notions of fairness: impartiality, justice and fairness) control policies that enforce global-fairness and bounded fairness. Furthermore, we investigate the fairness control policies that enforce global-fairness and bounded-fairness under the condition that Petri net is live.