| Author | : King Sing Cheung |
| File Size | : 52,7 Mb |
| Publisher | : Unknown |
| Language | : English |
| Release Date | : 27 April 2024 |
| ISBN | : 3902613122 |
| Pages | : null pages |
Augmented Marked Graphs and the Analysis of Shared Resource Systems by King Sing Cheung Book PDF Summary
In the past decade, augmented marked graphs have evolved into a sub-class of Petri nets. They are often used for modelling shared resource systems, such as manufacturing systems. One major reason is that augmented marked graphs possess a special structure which is desirable for modelling shared resources. However, the properties of augmented marked graphs are not extensively studied. In the literature, there are a few published works on augmented marked graphs. This paper consolidates our earlier works on augmented marked graphs with a special focus on liveness, boundedness, reversibility and conservativeness. We provide a number of characterisations for live and reversible augmented marked graphs. In particulars, some of these characterisations are based on cycles, instead of siphons. Besides, we introduce the Rtransformation, on which characterisations for bounded and conservative augmented marked graphs are obtained. With these characterisations, some pretty simple conditions and procedures for checking the liveness, reversibility, boundedness and conservativeness of an augmented marked graph are derived. These have been illustrated using the dining philosophers problem. Typically, in designing shared resource systems, one need to achieve design objectives on two folds. On one hand, the resources are scarce and should be maximally shared. On the other hand, the system should be carefully designed so that erroneous situations due to the sharing of resources, such as deadlock and capacity overflow, can be avoided. Yet, the verification of liveness, boundedness and reversibility is very difficult and time-consuming. This paper contributes to provide an effective means to analysing these essential properties. By modelling a shared resource system as an augmented marked graph, its liveness, boundedness, reversibility and conservativeness can be effectively analysed, based on the characterisations and properties of augmented marked graphs. We specifically show the application to the analysis of manufacturing systems which are typically shared resource systems. Promising results are obtained.