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Schedulability Analysis of Petri Nets Based on Structural Properties

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Liu C. , Kondratyev A. , Watanabe Y. , Desel J. , Sangiovanni-Vincentelli A.

Fundamenta Informaticae

2008

tom Vol. 86, nr 3

325-341

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.

Quasi-static Scheduling for Concurrent Architectures

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Cortadella J. , Kondratyev A. , Lavagno L. , Taubin A. , Watanabe Y.

Fundamenta Informaticae

2004

tom Vol. 62, nr 2

171--196

This paper presents a synthesis approach for reactive systems that aims at minimizing the overhead introduced by the operating system and the interaction among the concurrent tasks, while considering multiple concurrent execution resources. A formal model based on the notion of scheduling of Petri nets is used to perform the synthesis. We show how the notion of projections of a schedule for the complete system onto the components implemented on separate resources is essential to define the correctness of the partitioned schedule.