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2014 | Buch

Augmented Marked Graphs

verfasst von: King Sing Cheung

Verlag: Springer International Publishing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Petri nets are a formal and theoretically rich model for the modelling and analysis of systems. A subclass of Petri nets, augmented marked graphs possess a structure that is especially desirable for the modelling and analysis of systems with concurrent processes and shared resources.

This monograph consists of three parts: Part I provides the conceptual background for readers who have no prior knowledge on Petri nets; Part II elaborates the theory of augmented marked graphs; finally, Part III discusses the application to system integration. The book is suitable as a first self-contained volume on augmented marked graphs, and will be useful to both researchers and practitioners in the fields of Petri nets and system integration.

Inhaltsverzeichnis

Frontmatter

Basic Concepts

Frontmatter

Chapter 1. Introduction

Abstract

This chapter aims to provide some background for the readers to understand the motivation of using augmented marked graphs in the modelling and analysis of systems. It starts with some basic concepts of system design. The challenges in system integration are discussed. It then introduces augmented marked graphs, and discusses how they can be effectively used in modelling and analyzing systems to address the challenges in system integration. An overview of the subsequent chapters of this book is also provided.

King Sing Cheung

Chapter 2. Petri Nets

Abstract

This chapter provides the fundamentals of Petri nets to be used in this book, especially for readers who have no prior knowledge of Petri nets. It starts with the basic definition and terminology of Petri nets. These are followed by a comprehensive description of the properties of Petri nets, such as liveness, boundedness, reversibility and conservativeness. Algebraic characterizations of the properties are also provided. We then discuss two well-known subclasses of Petri nets, namely, state machines and marked graphs. They will be referenced in the subsequence chapters of this book.

King Sing Cheung

Theory of Augmented Marked Graphs

Frontmatter

Chapter 3. Augmented Marked Graphs

Abstract

This chapter provides a comprehensive description of augmented marked graphs and their properties. It starts with the basic definition and terminology of augmented marked graphs. Some special properties pertaining to cycles and siphons for augmented marked graphs are then discussed. These are followed by a detailed investigation of the liveness, reversibility, boundedness and conservativeness of augmented marked graphs. Algorithms for checking these properties are derived accordingly.

King Sing Cheung

Chapter 4. Proper Augmented Marked Graphs

Abstract

A special type of augmented marked graphs, proper augmented marked graphs, not only inherit the properties of augmented marked graphs but also possess some special properties. This chapter provides a comprehensive description of proper augmented marked graphs. It starts with the definition of proper augmented marked graphs. A detailed analysis of the special properties of proper augmented marked graphs then follows.

King Sing Cheung

Chapter 5. Composition of Augmented Marked Graphs

Abstract

This chapter investigates the composition of augmented marked graphs with a special focus on the preservation of properties. It starts with defining the composition of two augmented marked graphs via common resource places. We show that the integrated PT-net so obtained is also an augmented marked graph. A detailed analysis on the preservation of liveness, reversibility, boundedness and conservativeness for this composition then follows.

King Sing Cheung

Chapter 6. The Dining Philosophers Problem

Abstract

This chapter illustrates the theories in Chaps. 3–5, using the well-known dining philosophers problem. It starts with modelling the dining philosophers problem with augmented marked graphs. The system properties, including liveness, boundedness, reversibility and conservativeness, are then analyzed. We also show the composition of augmented marked graphs for modelling and analyzing the dining philosophers problem. The beauty of property-preserving composition is discussed.

King Sing Cheung

Application to System Integration

Frontmatter

Chapter 7. Component-Based System Integration

Abstract

This chapter describes how the theories of augmented marked graphs described in the previous chapters can be effectively applied to system integration. It starts with introducing component-based system design, where the challenges in system integration are discussed. We show how augmented marked graphs can be used for modelling the components of a system. Then, we show how these augmented marked graphs can be composed as an integrated system whose properties can be effectively analyzed.

King Sing Cheung

Chapter 8. Manufacturing System Integration

Abstract

This chapter illustrates the practical application of augmented marked graphs in manufacturing system design and integration. It starts with introducing manufacturing system design where the challenges in system integration are highlighted. We show how augmented marked graphs can be used for modelling the components of a typical manufacturing system. Then, we show how these augmented marked graphs can be composed as an integrated manufacturing system whose properties can be effectively analyzed.

King Sing Cheung

Chapter 9. Conclusion

Abstract

This chapter briefly concludes this book. It summarizes the theories and application of augmented marked graphs, and discusses the possible direction of further studies.

King Sing Cheung

Backmatter

Titel: Augmented Marked Graphs
verfasst von: King Sing Cheung
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-06428-4
Print ISBN: 978-3-319-06427-7
DOI: https://doi.org/10.1007/978-3-319-06428-4