Deadlock Control for Weighted Systems of Simple Sequential Processes with Resources Requirement (WS3PR)

Current deadlock control approaches for WSPR (Weighted Systems of Simple Sequential Processes with Resources Requirement) suffer from incorrect liveness characterization based on the concept of deadly marked siphons (DMS). We discover that nonlive transitions may exist even though there are no DMS. That is, the net model may be weakly live or in livelock states under no DMS. It is live under a new liveness condition: all siphons must be max*-controlled. We extend the liveness analysis for S PR (systems of simple sequential processes with resources) to WS PR (Weighted Systems of Simple Sequential Processes with Resources Requirement). We develop a new liveness condition called max*-controlled siphons to replace that of the absence of empty siphons. We propose further a deadlock control policy for WS PR by adding control nodes and arcs similar to that for S PR.