Boundedness and conservativeness of augmented marked graphs

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.