Schedulability Analysis of Petri Nets Based on Structural Properties

  • Authors:

  • Cong Liu;Alex Kondratyev;Yosinori Watanabe;Jörg Desel;Alberto Sangiovanni-Vincentelli

  • Affiliations:

  • (Correspd.) Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA. congliu@eecs.berkeley.edu;Cadence Berkeley Labs, Berkeley, CA 94704, USA. {kalex, watanabe}@cadence.com;Cadence Berkeley Labs, Berkeley, CA 94704, USA. {kalex, watanabe}@cadence.com;Lehrstuhl für Angewandte Informatik, Katholische Universität Eichstätt-Ingolstadt, Ostenstr. 28, 85071 Eichstätt, Germany. joerg.desel@ku-eichstaett.de;University of California, Berkeley, CA 94720, USA. alberto@eecs.berkeley.edu

  • Venue:
  • Fundamenta Informaticae - Application of Concurrency to System Design (ACSD'06)
  • Year:
  • 2008

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Abstract

A schedule of a Petri Net (PN) represents a set of firing sequences that can be infinitely repeated within a bounded state space, regardless of the outcomes of the nondeterministic choices. Schedulability analysis for a given PN answers the question whether a schedule exists in the reachability space of this net. This paper suggests a novel approach for schedulability analysis based solely on PN structure. It shows that unschedulability can be caused by a structural relation among transitions modelling nondeterministic choices. A method based on linear programming for checking this relation is proposed. This paper also presents a necessary condition for schedulability based on the rank of the incidence matrix of the underlying PN. These results shed a light on the sources of unschedulability often found in PN models of embedded multimedia systems.