Manufacturing System Modeling Using Petri Nets

Petri nets which are used for modeling and analyzing complex systems that can be characterized as synchronous, parallel, simultaneous, distributed, resource sharing, nondeterministic and/or stochastic form a powerful modeling tool and are widely used today. In this study, fundamental concepts of Petri nets and their extensions are presented. Since the application area of Petri nets is wide, the subject is handled in the view of flexible manufacturing systems. A two stage modeling approach which combines the modeling power of stochastic Petri nets together with fuzzy sets is also presented. A numerical example is given to present how the proposed approach can be applied. We believe that this approach better represents both dimensions of uncertainty, stochastic variability and imprecision, in system modeling.

[1]  MengChu Zhou,et al.  Parallel and sequential mutual exclusions for petri net modeling of manufacturing systems with shared resources , 1991, IEEE Trans. Robotics Autom..

[2]  C. Ramchandani,et al.  Analysis of asynchronous concurrent systems by timed petri nets , 1974 .

[3]  Li-Chih Wang,et al.  Modeling with colored timed object-oriented Petri nets for automated manufacturing systems , 1998 .

[4]  MengChu Zhou,et al.  Petri net synthesis and analysis of a flexible manufacturing system cell , 1993, IEEE Trans. Syst. Man Cybern..

[5]  Hisao Shiizuka,et al.  Modeling of AGV networks in flexible manufacturing systems , 1994 .

[6]  Adnan Yazici,et al.  A fuzzy Petri net model for intelligent databases , 2007, Data Knowl. Eng..

[7]  Hehua Zhang,et al.  Modeling job shop scheduling with batches and setup times by timed Petri nets , 2009, Math. Comput. Model..

[8]  Hoda A. ElMaraghy,et al.  Deadlock-free scheduling in flexible manufacturing systems using Petri nets , 2002 .

[9]  MengChu Zhou,et al.  Multiparadigm Modeling for Hybrid Dynamic Systems Using a Petri Net Framework , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[10]  Klaus Reinhardt,et al.  Reachability in Petri Nets with Inhibitor Arcs , 2008, RP.

[11]  Simon Peck,et al.  Practice of Petri Nets in Manufacturing , 1993 .

[12]  Gianfranco Balbo,et al.  Combining Queueing Networks and Generalized Stochastic Petri Nets for the Solution of Complex Models of System Behavior , 1988, IEEE Trans. Computers.

[13]  Philip Meir Merlin,et al.  A study of the recoverability of computing systems. , 1974 .

[14]  James J. Buckley,et al.  Simulating Fuzzy Systems , 2005, Studies in Fuzziness and Soft Computing.

[15]  Jie Zhang,et al.  A hybrid Petri nets model of networked manufacturing systems and its control system architecture , 2005 .

[16]  Ouajdi Korbaa,et al.  Two FMS scheduling methods based on Petri nets: A global and a local approach , 2003 .

[17]  Manuel Silva Suárez,et al.  A two phase optimization method for Petri net models of manufacturing systems , 2001, J. Intell. Manuf..

[18]  Tadao Murata,et al.  Temporal Uncertainty and Fuzzy-Timing High-Level Petri Nets , 1996, Application and Theory of Petri Nets.

[19]  Kimon P. Valavanis.  On the hierarchical modeling analysis and simulation of flexible manufacturing systems with extended Petri nets , 1990, IEEE Trans. Syst. Man Cybern..

[20]  Peter Buchholz.  Adaptive decomposition and approximation for the analysis of stochastic Petri nets , 2004, Perform. Evaluation.

[21]  M. Praveen,et al.  Analyzing Reachability for Some Petri Nets With Fast Growing Markings , 2008, Electron. Notes Theor. Comput. Sci..

[22]  MengChu Zhou,et al.  Modeling, Simulation, and Control of Flexible Manufacturing Systems - A Petri Net Approach , 1999, Series in Intelligent Control and Intelligent Automation.

[23]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[24]  Peter L. Lee,et al.  Scheduling of a mixed batch/continuous sugar milling plant using Petri nets , 2008, Comput. Chem. Eng..

[25]  MengChu Zhou,et al.  Modeling and performance analysis of a resource-sharing manufacturing system using stochastic Petri nets , 1990, Proceedings. 5th IEEE International Symposium on Intelligent Control 1990.

[26]  Wlodzimierz M. Zuberek,et al.  Timed petri nets in modeling and analysis of simple schedules for manufacturing cells , 1999 .

[27]  MengChu Zhou,et al.  A hybrid methodology for synthesis of Petri net models for manufacturing systems , 1992, IEEE Trans. Robotics Autom..

[28]  Fuming Wu,et al.  Fuzzy time semirings and fuzzy‐timing colored Petri nets , 1999 .

[29]  Luís Gomes,et al.  Structuring and composability issues in Petri nets modeling , 2005, IEEE Transactions on Industrial Informatics.

[30]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[31]  Andrea Bobbio,et al.  System Modelling with Petri Nets , 1990 .

[32]  F. D. J Bowden,et al.  A brief survey and synthesis of the roles of time in petri nets , 2000 .

[33]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[34]  Yadati Narahari,et al.  A Petri net approach to the modelling and analysis of flexible manufacturing systems , 1985 .

[35]  Zuohua Ding,et al.  Fuzzy timed Petri nets - analysis and implementation , 2006, Math. Comput. Model..

[36]  Günter Hommel,et al.  Modelling and Evaluation of Manufacturing Systems Using Dedicated Petri Nets , 1999 .

[37]  Marco Ajmone Marsan,et al.  Modelling with Generalized Stochastic Petri Nets , 1995, PERV.

[38]  Guido Maione,et al.  Hybrid Petri net and digraph approach for deadlock prevention in automated manufacturing systems , 2005 .

[39]  Yu Sun,et al.  Scheduling of flexible manufacturing systems based on Petri nets and hybrid heuristic search , 2008 .

[40]  Marc Courvoisier,et al.  Control of Flexible Production Systems and Petri Nets , 1982, European Workshop on Applications and Theory of Petri Nets.

[41]  Massimo Bertolini,et al.  Reliability design of industrial plants using Petri nets , 2006 .

[42]  Feng Chu,et al.  Modeling and performance evaluation of supply chains using batch deterministic and stochastic Petri nets , 2005, IEEE Transactions on Automation Science and Engineering.

[43]  Dimitri Lefebvre.  Estimation of the firing frequencies in discrete and continuous Petri nets models , 2001, Int. J. Syst. Sci..

[44]  MengChu Zhou,et al.  Petri net synthesis for discrete event control of manufacturing systems , 1992, The Kluwer international series in engineering and computer science.

[45]  Tatsuya Suzuki,et al.  FMS scheduling based on timed Petri Net model and reactive graph search , 2007 .

[46]  Li Jiao,et al.  Property-preserving subnet reductions for designing manufacturing systems with shared resources , 2005, Theor. Comput. Sci..

[47]  Reinhard German.  Transient analysis of deterministic and stochastic Petri nets by the method of supplementary variables , 1995 .

[48]  Murat Uzam,et al.  An Optimal Deadlock Prevention Policy for Flexible Manufacturing Systems Using Petri Net Models with Resources and the Theory of Regions , 2002 .

[49]  Nawel Gharbi,et al.  Performance Analysis of Retrial Queueing Systems Using Generalized Stochastic Petri Nets , 2002, Theory and Practice of Timed Systems @ ETAPS.

[50]  Fabrice Druaux,et al.  Some contributions with Petri nets for the modelling, analysis and control of HDS , 2007 .

[51]  Ouajdi Korbaa,et al.  Cyclic scheduling for F.M.S.: Modelling and evolutionary solving approach , 2008, Eur. J. Oper. Res..

[52]  Simon C. K. Shiu,et al.  Fuzzy coloured petri nets in modelling flexible manufacturing systems , 1996, Proceedings Mexico-USA Collaboration in Intelligent Systems Technologies..

[53]  Yueh-Min Huang,et al.  Standardized course generation process using Dynamic Fuzzy Petri Nets , 2008, Expert Syst. Appl..

[54]  MuDer Jeng,et al.  Petri nets for modeling automated manufacturing systems with error recovery , 1997, IEEE Trans. Robotics Autom..

[55]  James Lyle Peterson,et al.  Petri net theory and the modeling of systems , 1981 .

[56]  MengChu Zhou,et al.  Modeling, analysis, simulation, scheduling, and control of semiconductor manufacturing systems: A Petri net approach , 1998 .

[57]  F. F. Chen,et al.  Performance Modelling and Evaluation of Dynamic Tool Allocation in Flexible Manufacturing Systems using Coloured Petri Nets: An Object-Oriented Approach , 2003 .

[58]  R. Valette,et al.  A Petri net-based object-oriented approach for the modelling of hybrid productive systems , 2005 .

[59]  L. Zadeh.  Probability measures of Fuzzy events , 1968 .

[60]  Wlodzimierz M. Zuberek,et al.  Throughput analysis of manufacturing cells using timed Petri nets , 1994, Proceedings of IEEE International Conference on Systems, Man and Cybernetics.

[61]  Witold Pedrycz,et al.  Fuzzy timed Petri nets , 2003, Fuzzy Sets Syst..

[62]  H. Zimmermann,et al.  Fuzzy Set Theory and Its Applications , 1993 .

[63]  C. A. Petri.  "Forgotten Topics" of Net Theory , 1986, Advances in Petri Nets.

[64]  D. Gracanin,et al.  Approximate reasoning with fuzzy Petri nets , 1993, [Proceedings 1993] Second IEEE International Conference on Fuzzy Systems.

[65]  Lalit M. Patnaik,et al.  A Generalized Stochastic High-Level Petri Net Model for Performance Analysis , 1997, J. Syst. Softw..

[66]  Antonio Ramírez-Treviño,et al.  Building reduced petri net models of discrete manufacturing systems , 2005, Math. Comput. Model..

[67]  T. Ross.  Fuzzy Logic with Engineering Applications , 1994 .

[68]  R. Viertl,et al.  FUZZY INFORMATION AND STOCHASTICS , 2004 .

[69]  Janette Cardoso,et al.  Monitoring manufacturing systems by means of Petri nets with imprecise markings , 1989, Proceedings. IEEE International Symposium on Intelligent Control 1989.

[70]  Miryam Barad,et al.  Flexibility in manufacturing systems: definitions and Petri net modelling , 1988 .

[71]  Dimitris Kiritsis,et al.  A generic Petri net model for dynamic process planning and sequence optimization , 1996 .

[72]  Reinhard German,et al.  New results for the analysis of deterministic and stochastic Petri nets , 1995, Proceedings of 1995 IEEE International Computer Performance and Dependability Symposium.

[73]  C. A. Petri.  Nets, Time and Space , 1996, Theoretical Computer Science.

[74]  Ouajdi Korbaa,et al.  Scheduling analysis of FMS: An unfolding timed Petri nets approach , 2006, Math. Comput. Simul..

[75]  Michael K. Molloy.  Performance Analysis Using Stochastic Petri Nets , 1982, IEEE Transactions on Computers.

[76]  Murat Uzam,et al.  The use of the Petri net reduction approach for an optimal deadlock prevention policy for flexible manufacturing systems , 2004 .

[77]  Alan A. Desrochers,et al.  Performance evaluation of automated manufacturing systems using generalized stochastic Petri nets , 1990, IEEE Trans. Robotics Autom..

[78]  C. Seatzu,et al.  Modelling and simulation of a bottling plant using hybrid Petri nets , 2005 .

[79]  Zuohua Ding,et al.  Fuzzy timed petri net definitions, properties, and applications , 2005, Math. Comput. Model..

[80]  Hong-Sen Yan,et al.  Modelling, scheduling and simulation of flexible manufacturing systems using extended stochastic high-level evaluation Petri nets , 1998 .

[81]  Xuan F. Zha,et al.  A knowledge Petri net model for flexible manufacturing systems and its application for design and verification of FMS controllers , 2002, Int. J. Comput. Integr. Manuf..

[82]  MuDer Jeng,et al.  A Petri net synthesis theory for modeling flexible manufacturing systems , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[83]  Samir M. Koriem,et al.  A new Petri net modeling technique for the performance analysis of discrete event dynamic systems , 2004, J. Syst. Softw..

[84]  Marco Ajmone Marsan,et al.  A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems , 1984, TOCS.

[85]  Nicholas G. Odrey,et al.  An augmented Petri Net approach for error recovery in manufacturing systems control , 2005 .

[86]  MuDer Jeng,et al.  Process nets with resources for manufacturing modeling and their analysis , 2002, IEEE Trans. Robotics Autom..

[87]  Huiran Liu,et al.  Modeling of large-scale complex re-entrant manufacturing systems by extended object-oriented Petri nets , 2005 .

[88]  Alexander Fronk,et al.  State space analysis of Petri nets with relation-algebraic methods , 2009, J. Symb. Comput..

[89]  MengChu Zhou,et al.  Resource-Oriented Petri Net for Deadlock Avoidance in Flexible Assembly Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.