TIMED PETRI NETS: THEORY AND APPLICATION
by: Jiacun Wang, Kluwer Academic Publishers, 1998
PREFACE
Driven by the request for increased productivity, flexibility, and competitiveness, increasingly modern civilization has created high-performance discrete event dynamic systems (DEDS’s). These systems exhibit concurrent, sequential, competitive activities among their components. They are often complex and large in scale, and necessarily flexible and thus highly capital-intensive. Examples of systems are manufacturing systems, communication networks, traffic and logistic systems, and military command and control systems. Modeling and performance evaluation play a vital role in the design and operation of such high performance DEDS’s and thus have received widespread attention of researchers in the past two decades. One methodology resulting from this effort is based on timed Petri nets and related graphical and mathematical tools.
The popularity that Petri nets have been gaining in modeling of DEDS’s is due to their powerful representational ability of concurrency and synchronization, while these properties of DEDS’s can not be expressed easily in traditional formalisms developed for analysis of "classical" systems with sequential behaviors.
By cooperating time variables into Petri nets, timed Petri nets further allow us to derive production cycle time, identify bottleneck workstations, verify timing constraints, and so on, in and for modeled DEDS’s when the time variables are deterministic. They can also be used to obtain production rates, throughput, average delays, critical resource utilization, reliability measures, and so on, for the modeled DEDS’s when the time variables are random.
There are a large number of papers dedicated to the theories and applications of timed Petri nets, but they are scattered on hundreds of journals or conference proceedings, and often lack of unity in concepts, notations, and terminologies. This makes it very difficult for new researchers and practicing engineers to understand the potential applications of timed Petri nets due to mathematical complexity and the various interpretations presented by different authors. This book aims at introducing the theories and applications of timed Petri nets systematically. Moreover, this book also presents many practical applications in addition to theoretical developments. It presents the latest research results and industrial applications of timed Petri nets.
Book Layout
Chapter 1 first examines the characteristics and available performance models of and for DEDS’s, then presents the merits of timed Petri nets for the modeling and analysis of DEDS’s, and gives the classification of various types of timed Petri net models in common use.
Chapter 2 introduces the fundamentals of Petri nets, including the definition, basic terminologies, transition firing rules, representational power, properties, and analysis methods of Petri nets. The basic concepts given in this chapter are used throughout the book.
Chapter 3 focuses on the definition, analysis method, and application of deterministic timed transition Petri nets. It also gives a brief introduction to deterministic timed places Petri nets and deterministic timed arcs Petri nets.
Chapter 4 addresses time Petri nets. The enumerative analysis technique and a set of reduction rules for time Petri nets are presented; the compositional time Petri net models and their applications to command and control systems and flexible manufacturing systems are also given.
Chapter 5 first discusses the definition, firing policies, memory properties, and the corresponding stochastic processes of stochastic timed Petri nets. After a brief review of continuous time Markov chain and queuing networks, it then introduces stochastic Petri nets and analysis techniques.
Chapter 6 pays attention to generalized stochastic Petri nets. Three kinds of analysis methods for GSPN models, the net-level aggregation technique, and the hierarchical time-scale decomposition approach for a class of GSPN models are addressed. The application to the protocol of Ethernet is also presented.
Chapter 7 describes the theory and application of two types of high-level stochastic Petri nets: colored stochastic Petri nets, and stochastic high-level Petri nets.
Chapter 8 addresses two types of semi-Markovian SPN models: extended stochastic Petri nets and deterministic-stochastic Petri nets.
Chapter 9 explores the analysis technique of arbitrary stochastic Petri net. It gives a detail description of the hybrid state analysis method.
Audience
The book serves two natural groups:
- faculty, staff, and graduate students who are interested in research and teaching in (timed) Petri nets and performance models for discrete event dynamic systems; and
- performance modeling engineers and managers responsible for the design and efficient operation of automated production systems, flexible manufacturing cells, flexible assembly station, and computer integrated systems and networks.
CONTENTS
PREFACE
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INTRODUCTION 1
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PETRI NETS 9
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DETERMINISTIC TIMED PETRI NETS 37
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TIME PETRI NETS 63
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SHOCHASTIC TIMED PETRI NETS AND STOCHASTIC PETRI NETS 125
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GENERALIZED STOCHASTIC PETRI NETS 155
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HIGH-LEVEL STOCHASTIC PETRI NETS 195
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SEMI-MARKOVIAN STOCHASTIC PETRI NETS 213
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ARBITRARY STOCHASTIC PETRI NETS 241
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BIBLIOGRAPHY 263
INDEX 275
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