Petri Nets and Manufacturing Systems: An Examples-Driven Tour

  • Laura Recalde
  • Manuel Silva
  • Joaquín Ezpeleta
  • Enrique Teruel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3098)


There exists ample literature on Petri nets and its potential in the modelling, analysis, synthesis and implementation of systems in the manufacturing applications domain (see for example [54, 15, 18]; besides, in [66] an important bibliography is presented). This paper provides an examples-driven perspective. Nevertheless, not only complete examples from the application domain are considered. Manufacturing systems are frequently large systems, and conceptual complexity often appears because of some particular “local” constructions.

The examples considered in this selected tour try to introduce in a progressive way some applied concepts and techniques. The starting point is an assembly cell, for which models concerning several phases of the design life-cycle are presented. Afterwards, some pull control and kanban management strategies are modelled. Then, two coloured models of production lines are presented. After that, a manufacturing system with two cells is modelled, and the difficulty of the practical analysis is shown. For very populated manufacturing systems or systems with high cadence, relaxation of discrete event models leads to hybrid and continuous approximations, an example of which will be shortly introduced.


Manufacture System Manufacturing Cell Discrete Event System Reachability Graph Colour Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. Wiley, Chichester (1995)zbMATHGoogle Scholar
  2. 2.
    Alla, H., Cavaille, J.B., Le Bail, M., Bel, G.: Les systémes de production par lot: une approche discret-continu utilisant les réseaux de Petri Hybrides. In: Proc. of ADPM 1992, Paris, France (January 1992)Google Scholar
  3. 3.
    Alla, H., David, R.: Continuous and hybrid Petri nets. Journal of Circuits, Systems, and Computers 8(1), 159–188 (1998)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Avizenis, A., Kelly, J.P.: Fault tolerance by design diversity: Concepts and experiments. Computer 17(8), 67–80 (1984)CrossRefGoogle Scholar
  5. 5.
    Ayache, J.M., Azema, P., Diaz, M.: Observer, a concept for on line detection for control errors in concurrent systems. In: Proc. 9th IEEE Int. Sypm. Fault-Tolerant Computing, Madison, WI, USA, June 1992, pp. 79–86 (1992)Google Scholar
  6. 6.
    Balduzzi, F., Giua, A., Menga, G.: First-order hybrid Petri nets: A model for optimization and control. IEEE Trans. on Robotics and Automation 16(4), 382–399 (2000)CrossRefGoogle Scholar
  7. 7.
    Bemporad, A., Giua, A., Seatzu, C.: An iterative algorithm for the optimal control of continuous-time switched linear systems. In: Silva, M., Giua, A., Colom, J.M. (eds.) WODES 2002: 6th Workshop on Discrete Event Systems, Zaragoza, Spain, pp. 335–340. IEEE Computer Society, Los Alamitos (2002)CrossRefGoogle Scholar
  8. 8.
    Campos, J., Chiola, G., Colom, J.M., Silva, M.: Properties and performance bounds for timed marked graphs. IEEE Trans. on Circuits and Systems-I: Fundamental Theory and Applications 39(5), 386–401 (1992)zbMATHCrossRefGoogle Scholar
  9. 9.
    Campos, J., Chiola, G., Silva, M.: Ergodicity and throughput bounds of Petri net with unique consistent firing count vector. IEEE Trans. on Software Engineering 17(2), 117–125 (1991)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Champagnat, R., Valette, R., Hochon, J.C., Pingaud, H.: Modeling, simulation and analysis of batch production systems. Discrete Event Dynamic Systems: Theory and Application 11(1/2), 119–136 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Chaouiya, C., Dallery, Y.: Petri net models of pull control systems for assembly manufacturing systems. In: Procs. of the 2nd Int. Workshop on Manufacturing and Petri Nets, ICATPN, Toulouse, France, pp. 85–103 (1997)Google Scholar
  12. 12.
    Chretienne, P., Coffman, E.G., Lengstra, J.K., Liu, Z. (eds.): Wiley, Chichester (1995)Google Scholar
  13. 13.
    Colom, J.M., Silva, M., Villarroel, J.L.: On software implementation of Petri nets and colored Petri nets using high-level concurrent languages. In: Proc. 7th European Workshop on Application and Theory of Petri Nets, Oxford, England, July 1986, pp. 207–241 (1986)Google Scholar
  14. 14.
    David, R., Alla, H.: Continuous Petri nets. In: Proc. of the 8th European Workshop on Application and Theory of Petri Nets, Zaragoza, Spain, pp. 275–294 (1987)Google Scholar
  15. 15.
    David, R., Alla, H.: Petri Nets and Grafcet. Prentice-Hall, Englewood Cliffs (1992)zbMATHGoogle Scholar
  16. 16.
    David, R., Xie, X., Dallery, Y.: Properties of continuous models of transfer lines with unreliable machines and finite buffers. IMA Journal of Mathematics Applied in Business and Industry 6, 281–308 (1990)zbMATHMathSciNetGoogle Scholar
  17. 17.
    Desrochers, A., Al-Jaar, R.Y.: Applications of Petri Nets in Manufacturing Systems. IEEE Press, Los Alamitos (1994)Google Scholar
  18. 18.
    Desrochers, A.A., Al-Jaar, R.Y.: Applications Of Petri Nets In Manufacturing Systems, Modeling, Control, And Performance Analysis. IEEE Press, Los Alamitos (1995)zbMATHGoogle Scholar
  19. 19.
    Diaz, M., Juanole, G., Courtiat, J.P.: Observer — a concept for formal on-line validation of distributes systems. IEEE Trans. on Software Engineering 20(12), 900–913 (1994)CrossRefGoogle Scholar
  20. 20.
    Dijkstra, E.W.: Cooperating sequential processes. In: Genuys, F. (ed.) Programming Languages. Academic Press, London (1968)Google Scholar
  21. 21.
    Elwadi, E.I., Mitra, D.: Statistical multiplexing with loss priorities in rate-based congestion control of high-speed networks. IEEE Transactions on Communications 42(11), 2989–3002 (1994)CrossRefGoogle Scholar
  22. 22.
    Ezpeleta, J., Colom, J.M.: Automatic synthesis of colored Petri nets for the control of FMS. IEEE Transactions on Robotics and Automation 13(3), 327–337 (1997)CrossRefGoogle Scholar
  23. 23.
    Ezpeleta, J., Colom, J.M., Martínez, J.: A Petri net based deadlock prevention policy for flexible manufacturing systems. IEEE Trans. on Robotics and Automation 11(2), 173–184 (1995)CrossRefGoogle Scholar
  24. 24.
    Ezpeleta, J., Martínez, J.: Formal specification and validation in production plants. In: Proceedings of the 3th. International Conference on Computer Integrated Manufacturing, Rensselaer Polytechnic Institute, Troy, New York, May 1992, pp. 64–73 (1992) IMACSGoogle Scholar
  25. 25.
    Ezpeleta, J., Recalde, L.: A deadlock avoidance approach for non-sequential resource allocation systems. IEEE Trans. on Systems, Man, and Cybernetics (2004) (accepted)Google Scholar
  26. 26.
    Ezpeleta, J., Tricas, F., García- Vallés, F., Colom, J.M.: A Banker’s solution for deadlock avoidance in FMS with routing flexibility and multi–resource states. IEEE Transactions on Robotics and Automation 18(4), 621–625 (2002)CrossRefGoogle Scholar
  27. 27.
    Ezpeleta, J., Valk, R.: A polynomial solution for deadlock avoidance in assembly systems modelled with petri nets. In: Proceedings of the Multiconference on Computational Engineering in Systems Applications (CESA 2003), Lille, France, July 9-11, pp. 1–8 (2003)Google Scholar
  28. 28.
    Fanti, M.P., Maione, B., Turchiano, B.: Design of supervisors to avoid deadlock in flexible assembly systems. The International Journal of Flexible Manufacturing Systems 14, 157–175 (2002)CrossRefGoogle Scholar
  29. 29.
    Farwer, B., Moldt, D., Garcí-Vallés, F.: An approach to modelling fms with dynamic object petri nets. In: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, Hammamet, Tunisia (October 2002)Google Scholar
  30. 30.
    Gentina, J.C., Bourey, J.P., Kapusta, M.: Coloured adaptive structured Petri nets. Computer-Integrated Manufacturing 1(1), 39–47 (1988)CrossRefGoogle Scholar
  31. 31.
    Gentina, J.C., Bourey, J.P., Kapusta, M.: Coloured adaptive structured Petri nets (II). Computer-Integrated Manufacturing 1(2), 103–109 (1988)CrossRefGoogle Scholar
  32. 32.
    Gershwin, S.B.: Manufacturing Systems Engineering. Prentice-Hall, Englewood Cliffs (1994)Google Scholar
  33. 33.
    Habermann, N.: Prevention of systems deadlocks. Communications of the ACM 12(7), 373–385 (1969)CrossRefGoogle Scholar
  34. 34.
    Hanen, C., Munier, A.: Cyclic scheduling problems: An overview. In: Chretienne et al. [12]Google Scholar
  35. 35.
    Huang, Y., Jeng, M., Xie, X.: A deadlock prevention policy for flexible manufacturing systems using siphons. In: Proc. of the 2001 IEEE International Conference on Robotics and Automation, Seoul, Korea, May 2001, pp. 541–546 (2001)Google Scholar
  36. 36.
    Kummer, O., Wienberg, F.: Renew. the reference net workshop. Petri Net Newsletter (56), 12–16 (1999)Google Scholar
  37. 37.
    Leveson, N.G., Stolzy, J.L.: Safety analysis using Petri nets. IEEE Trans. on Software Engineering 13(3), 386–397 (1987)CrossRefGoogle Scholar
  38. 38.
    López-Mellado, E., Morales-Montelongo, J.G.: Agent-based distributed controllers for discrete manufacturing systems. In: Proceedings of the Multiconference on Computational Engineering in Systems Applications (CESA 2003), Lille, France, July 9-11, pp. 1–7 (2003)Google Scholar
  39. 39.
    Martínez, J., Muro, P., Silva, M.: Modeling, validation and software implementation of production systems using high level Petri nets. In: Silva, M., Murata, T. (eds.) Invited Sessions: Petri Nets and Flexible Manufacturing, IEEE Int. Conf. on Robotics and Automation, Raleigh, NC, USA, April 1987, pp. 1180–1185 (1987)Google Scholar
  40. 40.
    Martínez, J., Muro, P., Silva, M., Smith, S.F., Villarroel, J.L.: Merging artificial intelligence techniques and Petri nets for real time scheduling and control of production systems. In: Huber, R., et al. (eds.) Artificial Intelligence in Scientific Computation, pp. 307–313. Scientific Publishing Co., Singapore (1989)Google Scholar
  41. 41.
    Moldt, D., Ezpeleta, J.: A proposal for flexible testing of deadlock control strategies in resource allocation systems. In: Proceedings of the International Conference on Computational Intelligence for Modelling Control and Automation (CIMCA 2003), Vienna, Austria, February 2003, pp. 586–595 (2003)Google Scholar
  42. 42.
    Murata, T.: Petri nets: Properties, analysis and applications. Proceedings of the IEEE 77(4), 541–580 (1989)CrossRefGoogle Scholar
  43. 43.
    Park, J., Reveliotis, S.: Deadlock avoidance in sequential resource allocation systems with multiple resource acquisitions and flexible routings. IEEE Transactions on Automatic Control 46(10), 1572–1583 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  44. 44.
    Proth, J.M., Xie, X.: Petri Nets, A Tool for Design and Management of Manufacturing Systems. Wiley, Chichester (1996)Google Scholar
  45. 45.
    Recalde, L., Silva, M.: Petri Nets fluidification revisited: Semantics and steady state. APII-JESA 35(4), 435–449 (2001)Google Scholar
  46. 46.
    Renshaw, E.: A survey of stepping-stone models in population dynamics. Adv. Appl. Prob. 18, 581–627 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  47. 47.
    Roszkowska, E., Wojcik, R.: Problems of process flow feasibility in FAS. In: Leiviska, K. (ed.) IFAC CIM in Process and manufacturing Industries, Espoo, Finland, pp. 115–120. Pergamon Press, Oxford (1992)Google Scholar
  48. 48.
    Silva, M.: Las Redes de Petri: en la Automática y la Informática. AC (1985)Google Scholar
  49. 49.
    Silva, M.: Interleaving functional and performance structural analysis of net models. In: Ajmone Marsan, M. (ed.) ICATPN 1993. LNCS, vol. 691, pp. 17–23. Springer, Heidelberg (1993)Google Scholar
  50. 50.
    Silva, M.: Introducing Petri nets. In: Practice of Petri Nets in Manufacturing, pp. 1–62. Chapman & Hall, Boca Raton (1993)Google Scholar
  51. 51.
    Silva, M., Recalde, L.: Petri nets and integrality relaxations: A view of continuous Petri nets. IEEE Trans. on Systems, Man, and Cybernetics 32(4), 314–327 (2002)CrossRefGoogle Scholar
  52. 52.
    Silva, M., Recalde, L.: On fluidification of Petri net models: from discrete to hybrid and continuous models. In: IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2003, Saint-Malo, France, June 2003, pp. 9–20 (2003)Google Scholar
  53. 53.
    Silva, M., Teruel, E.: A systems theory perspective of discrete event dynamic systems: The Petri net paradigm. In: Borne, P., Gentina, J.C., Craye, E., El Khattabi, S. (eds.) Symposium on Discrete Events and Manufacturing Systems, CESA 1996 IMACS Multiconference, Lille, France, July 1996, pp. 1–12 (1996)Google Scholar
  54. 54.
    Silva, M., Teruel, E.: Petri nets for the design and operation of manufacturing systems. European Journal of Control 3(3), 182–199 (1997)zbMATHGoogle Scholar
  55. 55.
    Silva, M., Teruel, E., Colom, J.M.: Linear algebraic and linear programming techniques for the analysis of net systems. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491, pp. 309–373. Springer, Heidelberg (1998)Google Scholar
  56. 56.
    Silva, M., Teruel, E., Valette, R., Pingaud, H.: Petri nets and production systems. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1492, pp. 85–124. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  57. 57.
    Teruel, E., Colom, J.M., Silva, M.: Choice-free Petri nets: A model for deterministic concurrent systems with bulk services and arrivals. IEEE Trans. on Systems, Man, and Cybernetics 27(1), 73–83 (1997)CrossRefGoogle Scholar
  58. 58.
    Tricas, F., García-Vallés, F., Colom, J.M., Ezpeleta, J.: An iterative method for deadlock prevention in FMS. In: Boel, R., Stremersch, G. (eds.) Discrete Event Systems: Analysis and Control. Proc. of the Workshop On Discrete Event Systems 2000, Ghent, Belgium, August 2000, pp. 139–148. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
  59. 59.
    Valentin-Roubinet, C.: Modeling of hybrid systems: DAE supervised by Petri nets the example of a gas storage. In: Proc. of ADPM 1998, Reims, France, March 1998, pp. 142–149 (1998)Google Scholar
  60. 60.
    Valette, R., Courvoisier, M.: Petri nets and artificial intelligence. In: Zurawski, R., Dillon, T. (eds.) Modern Tools for Manufacturing Systems, pp. 385–405. Elsevier, Amsterdam (1993)Google Scholar
  61. 61.
    Valette, R., Courvoisier, M., Bigou, J.M., Albukerque, J.: A Petri nets based programmable logic controller. In: IFIP 1st Int. Conf. on Computer Applications in Production and Engineering, Amsterdam, Holland (April 1983)Google Scholar
  62. 62.
    Valk, R.: Petri nets as token objects - an introduction to elementary object nets. In: Desel, J., Silva, M. (eds.) ICATPN 1998. LNCS, vol. 1420, pp. 1–25. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  63. 63.
    Velilla, S., Silva, M.: The spy: A mechanism for safe implementation of highly concurrent systems. In: Real Time Programming 1988, 15th IFAC/IFIP Workshop, Valencia, Spain, May 1988, pp. 95–102. Pergamon, Oxford (1988)Google Scholar
  64. 64.
    Villarroel, J.L., Martínez, J., Silva, M.: GRAMAN: A graphic system for manufacturing system design. In: Tzafestas, S., Eisinberg, A., Carotenuto, L. (eds.) IMACS Symp. on System Modelling and Simulation, pp. 311–316. Elsevier, Amsterdam (1988)Google Scholar
  65. 65.
    Viswanadham, N., Narahari, Y.: Performance Modeling of Automated Manufacturing Systems. Prentice-Hall, Englewood Cliffs (1992)Google Scholar
  66. 66.
    Zhou, M., Venkatesh, K.: Modeling, Simulation, and Control of Flexible Manufacturing Systems: A Petri Net Approach. Series in Intelligent Control and Intelligent Automation, vol. 6. World Scientific, Singapore (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Laura Recalde
    • 1
  • Manuel Silva
    • 1
  • Joaquín Ezpeleta
    • 1
  • Enrique Teruel
    • 1
  1. 1.Dep. Informática e Ingeniería de Sistemas, I3AUniversidad de ZaragozaZaragozaSpain

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