Schedulability Analysis of Petri Nets Based on Structural Properties

Authors:
Cong Liu;Alex Kondratyev;Yosinori Watanabe;Alberto Sangiovanni-Vincentelli;Jorg Desel
Affiliations:
University of California, Berkeley;Cadence Berkeley Labs Berkeley, CA;Cadence Berkeley Labs Berkeley, CA;University of California, Berkeley;Katholische Universitat Eichstatt-Ingolstadt, Germany
Venue:
ACSD '06 Proceedings of the Sixth International Conference on Application of Concurrency to System Design
Year:
2006

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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.