In order to manage the complexity of some practical systems, structuring reusable components is very useful; this is component-based system design. The components are obtained from the functional requirements, and then the system is synthesized from the integration of these components. However, when these components are integrated at a higher level, erroneous situations should be prevented, so formal techniques such as Petri nets and in particular the subclass of augmented marked graphs (introduced by Chu and Xie as an extension of marked graphs [1]) are welcome.

This book reviews a set of papers about augmented marked graphs, covering both theoretical and practical aspects of this subclass of Petri nets. There are three parts. Part 1 provides a background for Petri nets. In Part 2, the theory of augmented marked graphs is introduced. Finally, in Part 3, these concepts are applied to practical systems.

Part 1 gives an introduction to Petri nets and their fundamental properties. Also, state machines and marked graphs are introduced as subclasses of Petri nets.

In Part 2, augmented marked graphs and their most important properties are introduced. Concepts like cycles and siphons are studied in this context, giving and proving some lemmas so that the properties introduced can be better understood by the reader. Properties like liveness, reversibility, roundedness, and conservativeness are studied, and algorithms are proposed for checking them: two algorithms (one based on siphons and the other based on cycles characterizations, the second one being more effective) for liveness and reversibility, and a third algorithm, based on the replacement of each resource place by a set of places, to check the boundedness and conservativeness properties. A special type of augmented marked graphs is also presented: proper augmented marked graphs.

In order to deal with more complex systems, the book studies the integration of augmented marked graphs. It starts defining the composition of two augmented marked graphs via common resource places (the resulting graph will also be an augmented marked graph). After that, the relation between the properties (properness, liveness, reversibility, boundedness and conservativeness) of the individual graphs and the integrated one are studied. Two algorithms are shown for checking the liveness and reversibility of integrated augmented marked graphs.

To complete part 2 of the book, previous theoretical results are applied to a known problem in the context of shared resources, introduced by Dijkstra in 1965, the dining philosophers problem. This problem can be considered as a system involving shared resources and concurrent processes. Two versions for the operative of the philosophers are considered, and liveness, reversibility, boundedness, conservativeness, and T- and P-coverable properties are analyzed for the corresponding augmented marked graphs. The problem is also modeled as the composition of augmented marked graphs, considering each philosopher as a component, and its properties are studied from the preservation of properties of the composition.

In Part 3, the previous theory is applied to component-based systems integration. The real systems are usually large and complex, so a system may have many components. Systems integration is an essential step for this type of system, but it’s important to note that the properties of the components may not be preserved after integration. Based on the results provided in the previous chapters, it’s possible to check the properties of the components and after that, from the properties that preserve the composition of augmented marked graphs, the properties of the composed system can be determined. Four steps are presented to design this type of system: modeling the components as augmented marked graphs, composing the components, analyzing the properties of the individual components, and analyzing the properties of the integrated system.

Finally, the augmented marked graphs are applied to manufacturing systems integration, a special case of a component-based system. Four examples of flexible workstation systems are presented to illustrate the modeling and analysis procedure.

The book concludes with a summary of the previous results, addressing the possible direction for further studies. The appendices section presents a summary of the properties and the algorithms. This section can be used as a quick reference.

It’s an adequate book for a graduate course on the modeling and analysis of discrete event systems. Readers do not need a mathematical background. It’s not difficult to read because the formal aspects introduced are not very complex and are accompanied by many examples. Furthermore, the theoretical results are applied to real systems, which is very strong motivation for students.