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Journal of Information Science and Engineering, Vol. 25 No. 6, pp. 1963-1978 (November 2009)

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

Department of Management and Information Science
National Cheng Chi University
Taipei, 116 Taiwan

Current deadlock control approaches for WS3PR (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 S3PR (systems of simple sequential processes with resources) to WS3PR (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 WS3PR by adding control nodes and arcs similar to that for S3PR.

Keywords: Petri nets, siphons, traps, FMS, liveness, deadlock, control

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Received March 13, 2007; revised May 5, 2009; accepted May 21, 2009.
Communicated by Chin-Laung Lei.
+ The former name of the author is Yuh Yaw, which appeared in some of his earlier papers.