Petri Net Theory and Applications Petri Net Theory and Applications Edited by Vedran Kordic I-TECH Education and Publishing Published by the I-Tech Education and Publishing, Vienna, Austria Abstracting and non-profit use of the material is permitted with credit to the source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. Publisher assumes no responsibility liability for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained inside. After this work has been published by the Advanced Robotic Systems International, authors have the right to republish it, in whole or part, in any publication of which they are an author or editor, and the make other personal use of the work. © 2008 I-Tech Education and Publishing www.i-techonline.com Additional copies can be obtained from: publication@i-techonline.com First published February 2008 Printed in Croatia A catalog record for this book is available from the Austrian Library. Petri Net, Theory and Applications, Edited by Vedran Kordic p. cm. ISBN 978-3-902613-12-7 1. Petri Net. 2. Theory. 3. Applications. Preface Although many other models of concurrent and distributed systems have been de- veloped since the introduction in 1964 Petri nets are still an essential model for concurrent systems with respect to both the theory and the applications. The main attraction of Petri nets is the way in which the basic aspects of concurrent systems are captured both conceptually and mathematically. The intuitively ap- pealing graphical notation makes Petri nets the model of choice in many applica- tions. The natural way in which Petri nets allow one to formally capture many of the basic notions and issues of concurrent systems has contributed greatly to the development of a rich theory of concurrent systems based on Petri nets. This book brings together reputable researchers from all over the world in order to provide a comprehensive coverage of advanced and modern topics not yet re- flected by other books. The book consists of 23 chapters written by 53 authors from 12 different countries. In the name of I-Tech, editor is very much indebted to all the authors entrusted us with their newest research results. Contents Preface V 1. Petri Net Transformations 001 Hartmut Ehrig, Kathrin Hoffmann, Julia Padberg, Claudia Ermel, Ulrike Prange, Enrico Biermann and Tony Modica 2. Modelling and Analysis of Real-time Systems with RTCP-nets 017 Marcin Szpyrka 3. Petri Net Based Modelling of Communication in Systems on Chip 041 Holger Blume, Thorsten von Sydow, Jochen Schleifer and Tobias G. Noll 4. An Inter-working Petri Net Model between SIMPLE and IMPS for XDM Service 073 Jianxin Liao, Yuting Zhang and Xiaomin Zhu 5. Modelling Systems by Hybrid Petri Nets: an Application to Supply Chains 091 Mariagrazia Dotoli, Maria Pia Fanti, Alessandro Giua and Carla Seatzu 6. Modeling and Analysis of Hybrid Dynamic Systems Using Hybrid Petri Nets 113 Latefa Ghomori and Hassane Alla 7. Use of Petri Nets for Modeling an Agent-Based Interactive System: Basic Principles and Case Study 131 Houcine Ezzedine and Christophe Kolski 8. On the Use of Queueing Petri Nets for Modeling and Performance Analysis of Distributed Systems 149 Samuel Kounev and Alejandro Buchmann 9. Model Checking of Time Petri Nets 179 Hanifa Boucheneb and Rachid Hadjidj 10. A Linear Logic Based Approach to Timed Petri Nets 207 Norihiro Kamide VIII 11. From Time Petri Nets to Timed Automata 225 Franck Cassez and Olivier H. Roux 12. Timed Hierarchical Object-Oriented Petri Net 253 Hua Xu 13. Scheduling Analysis of FMS Using the Unfolding Time Petri Nets 281 Jong kun Lee and Ouajdi Korbaa 14. Error Recovery In Production Systems: A Petri Net Based Intelligent System Approach 303 Nicholas G. Odrey 15. Estimation of Mean Response Time of Multi-Agent Systems Using Petri Nets 337 Tomasz Babczyniski and Jan Magott 16. Diagnosis of Discrete Event Systems with Petri Nets 353 Dimitri Lefebvre 17. Augmented Marked Graphs and the Analysis of Shared Resource Systems 377 King Sing Cheung 18. Incremental Integer Linear Programming Models for Petri Nets Reachability Problems 401 Thomas Bourdeaud'huy, Saad Hanafi and Pascal Yim 19. Using Transition Invariants For Reachability Analysis Of Petri Nets 435 Alexander Kostin 20. Reliability Prediction and Sensitivity Analysis of Web Services Composition 459 Duhang Zhong, Zhichang Qi and Xishan Xu 21. Petri Nets for Component-based Software Systems Development 471 Leandro Dias da Silva, Kyller Gorginio and Angelo Perkusich 22. Formalizing and Validating UML Architecture Description of Service-oriented Applications 497 Zhijiang Dong, Yujian Fu, Xudong He and Yue Fu 23. Music Description and Processing: An Approach Based on Petri Nets and XML 525 Adriano Barata [...]... of Petri Nets In Proc Integrated Design and Process Technology (IDPT), volume 1, pages 186— 193 Society for Design and Process Science, 1996 [16] K Hoffmann Formal Approach and Applications of Algebraic Higher Order Nets PhD thesis, Technical University Berlin, 2005 [17] K Hoffmann, H Ehrig, and T Mossakowski High-Level Nets with Nets and Rules as Tokens In Proc Application and Theory of Petri Nets... 5 Petri net PN4 7 8 Petri Net: Theory and Applications 4.1 Place/transition nets and net morphisms Let us first present a notation of place/transition net that is suitable for our transformation approach We assume that the nets are given in the algebraic style as introduced in [21] A place/transition net N = (P, T, pre, post) is given by the set of places P, the set of transitions , the pre-domain and. .. RTCP-nets theory and to describe the possibilities of practical applications of the nets The chapter is organized as follows The first section deals with a formal definition of RTCP-nets The behaviour of the nets is presented in details so as to emphasize the differences between RTCP-nets and CP-nets This part of the chapter is illustrated with an example of a non-hierarchical RTCP -net 18 Petri Net: Theory. .. 10 Petri Net: Theory and Applications The illustration of a transformation can be found for our case study in Fig 2, where the rule revacuate is applied to the net Firefighters 1-3 with match m As explained above, the first pushout denotes the gluing of the nets L1 and C along the net Kl resulting in the net Firefighters 1-3 The second pushout denotes the gluing of the nets R1 and C along the net. .. Fig 1 and N2 constructed as union in four steps of the nets Officer, Firefighter 4, Start and End, or in parallel to the union N = N1 +IN2, where I consists of two places which are preserved by both transformations N1 M1 and N2 M2 This allows 12 Petri Net: Theory and Applications to obtain the same net M by union M = M1 +IM2 and by transformation N applying rule r3 = rexpand to M leads to the net PN4... etc.), and so on For place/transition nets, algebraic high-level nets and Coloured Petri nets the most important results for rule-based refinement are presented in Table 1 For more details see [27] Table 1 Achieved results 5 Conclusion The main idea of Petri net transformations is to extend the classical theory of Petri nets by a rule-based technique that allows to model the changes of the Petri net structure... distribution, and visual modelling A state of the art report for applications, languages and tools for graph transformation on the one hand and for concurrency, parallelism and distribution on the other hand is given in volumes 2 and 3 of the Handbook of Graph Grammars and Computing by Graph Transformation [8] and [12] In our paper [14], we have presented a comprehensive presentation of graph and net transformations... Theory of Petri Nets, volume 1248 of LNCS, pages 407-426 Springer, 1997 2 Modelling and Analysis of Real-Time Systems with RTCP-Nets Marcin Szpyrka AGH University of Science and Technology, Krakow Poland 1 Introduction RTCP-nets (Real-Time Coloured Petri nets, (Szpyrka 2006a), (Szpyrka & Szmuc 2006c)) are a subclass of timed coloured Petri nets (CP-nets, (Jensen 1992-1997)) defined for modelling and analysis... place/transition nets L, K and R, called leftA rule hand side, interface and right-hand side net respectively, and two injective net morphisms Given a rule , a direct transformation N 1 N 2 from N 1 to N 2 is given by two pushout diagrams (1) and (2) in the following diagram The morphisms m:L N 1 and n : R N 2 are called match and comatch, respectively The net C is called pushout complement or the context net. .. types and initial 26 Petri Net: Theory and Applications markings Global fusion sets only are allowed in RTCP-nets Fig 5 Coverability graph for the RTCP -net presented in Fig 1 4.1 Canonical form A special form of hierarchical RTCP-nets called canonical form has been defined to speed up and facilitate drawing of models (Szpyrka and Szmuc 2006c) RTCP-nets in canonical form consist of four types of subnets . of Petri net transform- ations for the case of place/transition nets. Petri Net Transformations 7 Fig. 5. Petri net PN4 Petri Net: Theory and Applications 8 4.1 Place/transition nets and net. Petri Net Theory and Applications Petri Net Theory and Applications Edited by Vedran Kordic I-TECH Education and Publishing Published by the I-Tech Education and Publishing,. Library. Petri Net, Theory and Applications, Edited by Vedran Kordic p. cm. ISBN 978-3-902613-12-7 1. Petri Net. 2. Theory. 3. Applications. Preface Although many other models of concurrent and