Journal Article

Boundedness and conservativeness of augmented marked graphs

K. S. Cheung

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 24, issue 2, pages 235-244
Published in print June 2007 | ISSN: 0265-0754
Published online June 2007 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnl019
Boundedness and conservativeness of augmented marked graphs

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Augmented marked graphs are often used in modelling shared resource systems. A major reason is that they possess a structure especially desirable for modelling shared resources. Yet, the properties of augmented marked graphs are not extensively studied. Only some siphon-based and cycle-based characterisations for deadlock freeness, liveness and reversibility are reported in the literature. This paper investigates the boundedness and conservativeness of augmented marked graphs. Based on R-transform, a necessary and sufficient condition for bounded and conservative augmented marked graphs is proposed. This is useful in analysing the capacity overflow for systems modelled as augmented marked graphs.

Keywords: Petri nets; augmented marked graphs; boundedness; conservativeness

Journal Article.  0 words. 

Subjects: Mathematics

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