On fairness and conflicts in Petri nets

The notions of fairness and conflicts in live, bounded, and strongly connected Petri nets (PNs) are formally related. The PN model of a resource-sharing concurrent system (RSCS) is conflict free when the firing of an enabled transition does not disable another transition in the net. Conflicts in the PN represent unresolved resource allocation conditions. The PN is fair when the firing of any transition more than a given number of times is a sufficient condition for all the transitions in the net to have fired. When the PN is fair, no process in the system can be starved; that is resources are allocated so that all tokens progress through the net. Although these concepts are not equivalent, it is shown that they are strongly related to each other when the PN model is live, bounded, and strongly connected. A computational method for finding conflicts is presented, and the concepts are illustrated with an example of buffer allocation in a sorting algorithm.<>