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IMA Journal of Mathematical Control and Information Advance Access published online on August 2, 2006
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dnl019
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received April 28, 2006

Article

Boundedness and conservativeness of augmented marked graphs

K. S. Cheung 1 *

1 SCE, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong

* To whom correspondence should be addressed.
K. S. Cheung, E-mail: cheungks{at}hkbu.edu.hk


  Abstract

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.
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