Advertisement

Journal of Intelligent Manufacturing

, Volume 26, Issue 2, pp 321–330 | Cite as

Deadlock prevention policy for a class of petri nets based on complementary places and elementary siphons

  • ShouGuang Wang
  • WenHui Wu
  • Jing Yang
Article

Abstract

For a class of Petri nets called Systems of Simple Sequential Processes with Resources \((\mathrm{{S}}^{3}\mathrm{{PR}})\), this paper proposes a sufficient condition under which there exists a complementary-place supervisor to enforce their liveness. Moreover, an algorithm is proposed to design liveness-enforcing supervisors based on complementary places and elementary siphons. The significance of the proposed policy lies in its design simplicity. A flexible manufacturing system example shows that in some cases, the proposed policy can obtain a structurally simpler supervisor with 99.9 % maximal permissive behavior.

Keywords

Flexible manufacturing system Petri net Discrete event system Deadlock 

Notes

Acknowledgments

This work is in part supported by National Natural Science Foundation of China under Grant 61100056, Zhejiang Provincial Natural Science Foundation of China under Grant LY12F03020, the Zhejiang Provincial Education Department Foundation under Grant Y201018216, the Opening Project of Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University, Nanjing, Grant No. MCCSE2012A05, and the Opening Project of State Key Laboratory of Industrial Control Technology, Grant No. ICT1235.

References

  1. Abdallah, I. B., & ElMaraghy, H. A. (1998). Deadlock prevention and avoidance in FMS: A Petri net based approach. International Journal of Advanced Manufacturing Technology, 14(10), 704–715.CrossRefGoogle Scholar
  2. Bernardi, S., & Campos, J. (2009). Computation of performance bounds for real-time systems using time Petri nets. IEEE Transactions on Industrial Informatics, 5(2), 168–180.CrossRefGoogle Scholar
  3. Chao, D. Y., & Pan, Y.-L. (2013). Uniform formulas for compound siphons, complementary siphons and characteristic vectors in deadlock prevention of flexible manufacturing systems. Journal of Intelligent Manufacturing, 24(2), 1–11.Google Scholar
  4. Chen, Y., & Li, Z. (2011). Design of a maximally permissive liveness-enforcing supervisor with a compressed supervisory structure for flexible manufacturing systems. Automatica, 47(5), 1028–1034.CrossRefGoogle Scholar
  5. Chen, Y., Li, Z., Khalgui, M., & Mosbahi, O. (2011). Design of a maximally permissive liveness-enforcing Petri net supervisor for flexible manufacturing systems. IEEE Transactions on Automation Science and Engineering, 8(2), 374–393.CrossRefGoogle Scholar
  6. Ezpeleta, J., Colom, J. M., & Martinez, J. (1995). A Petri net based deadlock prevention policy for flexible manufacturing systems. IEEE Transactions on Robotics and Automation, 11(2), 173–184.CrossRefGoogle Scholar
  7. Fanti, M. P., & Zhou, M. C. (2004). Deadlock control methods in automated manufacturing systems. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 34(1), 5–22.CrossRefGoogle Scholar
  8. Ferrarini, L., Piroddi, L., & Alleqri, S. (1999). A comparative performance analysis of deadlock avoidance control algorithms for FMS. Journal of Intelligent Manufacturing, 10(6), 569–585.CrossRefGoogle Scholar
  9. Giua, A., & Seatzu, C. (2008). Modeling and supervisory control of railway networks using Petri nets. IEEE Transactions on Automation Science and Engineering, 5(3), 431–476.CrossRefGoogle Scholar
  10. Herrero-Perez, D., & Martinez-Barbera, H. (2010). Modeling distributed transportation systems composed of flexible automated guided vehicles in flexible manufacturing systems. IEEE Transactions on Industrial Informatics, 6(2), 166–180.CrossRefGoogle Scholar
  11. Hu, H., & Li, Z. (2009a). Liveness enforcing supervision in video streaming systems using siphons. Journal of Information Science and Engineering, 25(6), 1863–1884.Google Scholar
  12. Hu, H., & Li, Z. (2009b). Local and global deadlock prevention policies for resource allocation systems using partially generated reachability graphs. Computers and Industrial Engineering, 57(4), 1168–1181.CrossRefGoogle Scholar
  13. Hu, H., & Li, Z. (2010). Synthesis of liveness enforcing supervisor for automated manufacturing systems using insufficiently marked siphons. Journal of Intelligent Manufacturing, 21(4), 555–567.CrossRefGoogle Scholar
  14. Hu, H., Li, Z., & Al-Ahmari, A. (2011). Reversed fuzzy Petri nets and their application for fault diagnosis. Computers and Industrial Engineering, 60(4), 505–510.CrossRefGoogle Scholar
  15. Hu, H., Zhou, M., & Li, Z. (2009). Liveness enforcing supervision of video streaming systems using non-sequential Petri nets. IEEE Transactions on Multimedia, 11(8), 1446–1456.CrossRefGoogle Scholar
  16. Huang, Y. S., Jeng, M. D., Xie, X. L., & Chung, S. L. (2001). Deadlock prevention policy based on Petri nets and siphons. International Journal of Production Research, 39, 283–305.CrossRefGoogle Scholar
  17. Huang, Y. S., Jeng, M. D., Xie, X. L., & Chung, D. H. (2006). Siphon-based deadlock prevention policy for flexible manufacturing systems. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 36(6), 1248–1256.CrossRefGoogle Scholar
  18. Li, S. Y., An, A. M., Wang, Y., Wang, G., Hou, C. Q., & Cai, Y. (2012). Design of liveness-enforcing supervisors with simpler structures for deadlock-free operations in flexible manufacturing systems using necessary siphons. Journal of Intelligent Manufacturing. doi: 10.1007/s10845-012-0647-4.
  19. Li, Z. W., Hu, H. S., & Wang, A. R. (2007a). Design of liveness-enforcing supervisors for flexible manufacturing systems using Petri nets. IEEE Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews, 37(4), 517–526.CrossRefGoogle Scholar
  20. Li, Z. W., & Zhou, M. C. (2004). Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 34(1), 38–51.CrossRefGoogle Scholar
  21. Li, Z. W., & Zhou, M. C. (2006a). Clarifications on the definitions of elementary siphons of Petri nets. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 36(6), 1227–1229.Google Scholar
  22. Li, Z. W., & Zhou, M. C. (2006b). Two-stage method for synthesizing livenessenforcing supervisors for flexiblemanufacturing systems using Petri nets. IEEE Transactions on Industrial Informatics, 2(4), 313–325.CrossRefGoogle Scholar
  23. Li, Z. W., & Zhou, M. C. (2009). Deadlock resolution in automated anufacturing systems: A novel Petri net approach. London: Springer-Verlag.Google Scholar
  24. Li, Z. W., Zhou, M. C., & Uzam, M. (2007b). Deadlock control policy for a class of petri nets without complete siphon enumeration. IET Control Theory and Applications, 1(6), 1594–1605.CrossRefGoogle Scholar
  25. Liu, D., Li, Z. W., & Zhou, M. C. (2010a). Liveness of an extended \(\text{ S }^{3}\text{ PR }\). Automatica, 46(6), 1008–1018.CrossRefGoogle Scholar
  26. Liu, G. J., Jiang, C. J., Wu, Z. H., & Chen, L. J. (2009). A live subclass of Petri nets and their application in modeling flexible manufacturing systems. International Journal of Advanced Manufacturing Technology, 41, 66–74.CrossRefGoogle Scholar
  27. Liu, G. J., Jiang, C. J., & Zhou, M. C. (2010b). Two simple deadlock prevention policies for \(\text{ S }^{3}\text{ PR }\) based on key-resource/operation-place pairs. IEEE Transactions on Automation Science and Engineering, 7(4), 945–957.CrossRefGoogle Scholar
  28. Liu, G. J., Jiang, C. J., & Zhou, M. C. (2011). Improved sufficient condition for the controllability of dependent siphons in system of simple sequential processes with resources. IET Control Theory and Application, 5(9), 1059–1068.CrossRefGoogle Scholar
  29. Liu, G. Y., Li, Z. W., & Zhong, C. F. (2010c). New controllability condition for siphons in a class of generalized Petri nets. IET Control Theory and Applications, 4(5), 854–864.CrossRefGoogle Scholar
  30. Murata, T. (1989). Petri nets: Properties, analysis, and applications. Proceedings of the IEEE, 77(4), 541–580.CrossRefGoogle Scholar
  31. Piroddi, L., Cordone, R., & Fumagalli, I. (2008). Selective siphon control for deadlock prevention in Petri nets. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 38(6), 1337–1348.CrossRefGoogle Scholar
  32. Piroddi, L., Cordone, R., & Fumagalli, I. (2009). Combined siphon and marking generation for deadlock prevention in Petri nets. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 39(3), 650–661.CrossRefGoogle Scholar
  33. Pla, A., Gay, P., Meléndez, J., & López, B. (2012). Petri net-based process monitoring: A workflow management system for process modelling and monitoring. Journal of Intelligent Manufacturing, 23(5), 1–16.Google Scholar
  34. Reveliotis, S. A. (2005). Real-time management of resource allocation systems: A discrete-event systems approach. NY: Springer.Google Scholar
  35. Starke, P. H. (1992). INA: Integrated Net Analyzer. http://www2.informatik.hu-berlin.de/~starke/ina.html.
  36. Uzam, M. (2002). An optimal deadlock prevention policy for flexible manufacturing systems using Petri net models with resources and the theory of regions. International Journal of Advanced Manufacturing Technology, 19, 192–208.Google Scholar
  37. Uzam, M., & Zhou, M. C. (2007). An iterative synthesis approach to Petri net based deadlock prevention policy for flexible manufacturing systems. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 37(3), 362–371.CrossRefGoogle Scholar
  38. Valckenaers, P., & Van Brussel, H. (2003). Deadlock avoidance in flexible flow shops with loops. Journal of Intelligent Manufacturing, 14(1), 137–144.CrossRefGoogle Scholar
  39. Wang, S. G., Wang, C. Y., & Yu, Y. P., (2010). A method of computing strict minimal siphons in \(\text{ S }^{3}\text{ PR }\) based on resource circuits. In 49th IEEE Conference on Decision and, Control pp. 2785–2790.Google Scholar
  40. Wang, S. G., Wang, C. Y., & Yu, Y. P. (2011). Comments on “Siphon-based deadlock prevention policy for flexible manufacturing systems”. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 41(2), 338–340.CrossRefGoogle Scholar
  41. Wang, S. G., Wang, C. Y., & Zhou, M. C. (2012a). Controllability conditions of resultant siphons in a class of Petri nets. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 42(5), 1206–1215.Google Scholar
  42. Wang, S. G., Wang, C. Y., Zhou, M. C., & Li, Z. W. (2012b). A method to compute strict minimal siphons in S3PR based on loop resource subsets. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 42(1), 226–237.CrossRefGoogle Scholar
  43. Xing, K. Y., Zhou, M. C., Liu, H. X., & Tian, F. (2009). Optimal Petri net based polynomial complexity deadlock avoidance policies for automated manufacturing systems. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 39(1), 188–199.Google Scholar
  44. Yamalidou, K., Moody, J., Lemmon, M., & Antsaklis, P. (1996). Feedback control of petri nets based on place invariants. Automatica, 32, 15–28. Google Scholar
  45. Zhong, C. F., & Li, Z. W. (2010). On self-liveness of a class of Petri net models for fexible manufacturing systems. IET Control Theory and Applications, 4(3), 403–410.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Information and Electronic EngineeringZhejiang Gongshang UniversityHangzhouChina

Personalised recommendations