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Integration of Petri nets and moment generating function approaches for system performance evaluation

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Journal of Systems Integration

Abstract

This article integrates arbitrary stochastic Petri nets (ASPN) and moment generating function approaches for performance evaluation of discrete event dynamic systems (DEDS). These systems include computer-integrated manufacturing systems, resource-shared distributed systems, and communication networks. ASPN can describe various DEDS in which the time duration for activities may be a random variable of arbitrary distributions. In ASPN models, transitions with firing delays of general distributions are used to model these activities. Using our proposed performance analysis methodology, we first represent a system as an ASPN model, then generate its reachability graph and convert it into a state machine Petri net, derive the transfer functions of interesting performance measures through stepwise reductions, and finally obtain the analysis results. This method makes it possible to obtain analytical solutions of important performance indices. We use a robotic assembly system to illustrate the method. We obtain several important performance measures of a closed-form. Finally, we discuss the limitations of this approach and future research.

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References

  1. T. Agerwala and Y. Choed-Amphai, “A synthesis rule for concurrent systems,”Proc. of 15th Design Automation Conference, Las Vegas, NV, 1978, pp. 305–311.

  2. J. Campos, J.M. Colom, M. Silva, “Performance evaluation of repetitive automated manufacturing systems”, inProc. of Second Rensselaer's Conf. on Computer Integrated Manufacturing, Troy, NY, 1990, pp. 74–81.

  3. P. Chen, S.C. Bruell, G. Balbo, “Alternative methods for incorporating nonexponential distributions into stochastic timed Petri nets,”Proc. the Third IEEE Int. Workshop on Timed Petri Nets and Performance Models, Tokyo. 1989, pp. 187–197.

  4. G. Chiola, “A software package for the analysis of generalized stochastic Petri net models,” inProc. IEEE Int. Workshop on Timed Petri Nets, Torino, Italy, July 1985, pp. 136–143.

  5. D.R. Cox, “A use of complex probabilities in the theory of stochastic process”,Proc. Cambridge Philosophical Society, vol. 51, pp. 313–319, 1955.

    Google Scholar 

  6. A. Cumani, “ESP — a package for the evaluation of stochastic Petri nets with phase-type distributed transition times,” inProc. IEEE Int. Workshop on Timed Petri Nets, Torino, Italy, 1985.

  7. A.A. Desrochers.Modeling and Control of Automated Manufacturing Systems. IEEE Computer Society Press: Washington, DC, 1990.

    Google Scholar 

  8. J.B. Dugan, K.S. Trivedi, R.M. Geist, and V.F. Nicola, “Extended stochastic Petri nets: application and analysis”, inProc. PERFORMANCE 84, Paris, France, December 1984, pp. 507–519.

  9. J.B. Dugan, A. Bobbio, A. Ciardo, and K.S. Trivedi, “The design of a unified package for the solution of stochastic Petri net models”1985 Int. Workshop on Timed Petri Nets, Torino, Italy, 1985, pp. 6–13.

  10. G. Florin and S. Natkin, “Evaluation based upon stochastic Petri nets of the maximum throughput of a full duplex protocol,” inInformatik Fachberichte C. Girault and W. Reisig (eds.), Springer-Verlag NY, 1982.

    Google Scholar 

  11. G. Florin and S. Natkin, “Necessary and sufficient ergodicity condition for open synchronized queueing networks,”IEEE Trans. on Software Engineering, vol. 15, no. 4, pp. 367–380, 1989.

    Article  Google Scholar 

  12. G. Florin and S. Natkin, “One-place unbounded stochastic Petri nets: ergodic criteria and steady-state solutions,”Journal of Systems and Software, vol. 1, no. 2, pp. 103–115, 1986.

    Article  Google Scholar 

  13. Y.C. Ho, “Performance evaluation and perturbation analysis of discrete event dynamic systems,”IEEE Trans. on Automatic Control, vol. 32, no. 7, pp. 563–572, July 1987.

    Article  Google Scholar 

  14. D.L. Guo, F. DiCesare, and M.C. Zhou, “A moment generating function based approach for evaluating extended stochastic Petri nets,”IEEE Transactions on Automatic Control, vol. 37., no. 12, 1992.

  15. D.L. Guo, F. DiCesare, and M.C. Zhou, “Moment generating function approach to performance analysis of extended stochastic Petri nets,”Proc. of IEEE Int. Conf. on Robotics and Automation, Sacramento, CA, 1991, pp. 1309–1314.

  16. Y.T. Leung and R. Suri, “Performance evaluation of discrete manufacturing systems,”IEEE Magazine Control Systems, vol. 10, no. 4, pp. 77–86, June 1990.

    Article  Google Scholar 

  17. H. Jungnith and A.A. Desrochers “Flow equivalent nets for the performance analysis of flexible manufacturing systems,” inProc. of IEEE Int. Conf. on Robotics and Automation, Sacramento, CA, 1991, pp. 122–127.

  18. L. Kleirock,Queueing Systems. Wiley-Interscience: NY, 1975.

    Google Scholar 

  19. M.A. Marsan, G. Balbo, and G. Conte, “A class of generalized stochastic Petri nets for performance analysis of multiprocessor systems,”ACM TOCS, vol. 2, no. 2, pp. 93–122, May 1984.

    Article  Google Scholar 

  20. M.A. Marsan and G. Chiola, “On Petri nets with deterministic and exponentially distributed firing times,”Lecture Notes in Computer Science, no. 254, pp. 132–145, 1986.

    Google Scholar 

  21. M.A. Marsan, G. Balbo, A. Bobbio, G. Chiola, G. Conte, A. Cumani, “The effects of execution policies on the semantics and analysis of stochastic Petri nets,”IEEE Trans. on Software Engineering, vol. 15, no. 7, pp. 832, 1989.

    Article  Google Scholar 

  22. S.J. Mason and H.J. Zimmermann,Electronic Circuits, Signal, and Systems, John Wiley & Sons: NY, 1960.

    Google Scholar 

  23. M.K. Molloy, “Performance analysis using stochastic Petri nets,”IEEE Trans. on Computers, vol. 3, no. 9, pp. 913–917, 1982.

    Google Scholar 

  24. T. Murata, “Petri nets: properties, analysis and application,”Proc of the IEEE, vol. 77, no. 4, pp. 541–579, 1989.

    Article  Google Scholar 

  25. J.L. Peterson,Petri Net Theory and the Modeling of Systems. Prentice-Hall: Englewood Cliffs, NJ, 1981.

    Google Scholar 

  26. A.A.B. Pritsker and W.W. Happ, “GERT: Graph Evaluation and Review Technique, Part 1, Fundamentals,”Journal of Industrial Engineering, vol. 17, no. 5, pp. 267–274, 1966.

    Google Scholar 

  27. A.A.B. Pritsker and G.E. Whitehouse, “GERT: Graph Evaluation and Review Technique, Part 2, Probabilistic and Engineering Applications,”Journal of Industrial Engineering, vol. 17, no. 6, pp. 293–303, 1966.

    Google Scholar 

  28. A.A.G. Pritsker,Modeling and Analysis Using Q-GERT Networks. John Wiley & Sons: NY, 1979.

    Google Scholar 

  29. W. Reisig,Petri Nets: An Introduction. Springer-Verlag: NY, 1985.

    Google Scholar 

  30. M. Silva,Las redes de Petri en la Automatica y la Informatica. Editorial AC Madrid, 1985.

    Google Scholar 

  31. G.E. Whitehouse,Systems Analysis and Design Using Network Techniques. Prentice Hall: Englewood Cliffs, NJ, 1973.

    Google Scholar 

  32. R. Valette, “Analysis of Petri nets by stepwise refinements,”J. of Compt. and Syst. Sci., vol. 18, pp. 35–46, 1979.

    Article  Google Scholar 

  33. R. Valette, “Nets in production systems,” W. Brauer, W. Reisig, and G. Rozenberg (eds.).Advance in Petri Nets 1986, vol. 255, part I, Springer-Verlag: NY, pp. 191–217, 1987.

    Google Scholar 

  34. N. Viswanadham and Y. Narahari, “Stochastic Petri net models for performance evaluation of automated manufacturing systems,”Information and Decision Technologies, vol. 14, pp. 125–142, 1989.

    Google Scholar 

  35. M.C. Zhou and F. DiCesare, “Adaptive design of Petri net controllers for error recovery in automated manufacturing systems,”IEEE Trans. on Systems, Man, and Cybernetics, vol. 19, no. 5, pp. 963–973, 1989.

    Google Scholar 

  36. M.C. Zhou, F. DiCesare, and D. Rudolph, “Control of a flexible manufacturing system using Petri nets,” in Reprints of1990 IFAC World Congress, Tallin Russia, vol. 9, pp. 43–48, August 1990.

  37. M.C. Zhou, F. DiCesare, and D. Guo, “Modeling and performance analysis of a resource-sharing manufacturing system using stochastic Petri nets,” inProc IEEE Int. Symp. on Intelligent Control, Philadelphia, PA, 1990, pp. 1005–1010.

  38. M.C. Zhou,A Theory for the Synthesis and Augmentation of Petri Nets in Automation. Doctoral Dissertation, ECSE Department, Rensselaer Polytechnic Institute, May 1990.

  39. M.C. Zhou and F. DiCesare, “A Petri net design method for automated manufacturing systems with shared resources,”Proc. of IEEE Conference Robotics and Automation. Cincinnati, OH, 1990, pp. 526–531.

  40. M.C. Zhou and F. DiCesare, “Hybrid synthesis of Petri nets for manufacturing systems: A case study,” in3rd Int. Symp. on Robotics & Manufacturing (ISRAM '90), Vancouver, Canada, July 1990, pp. 667–672.

  41. M.C. Zhou and F. DiCesare, “Parallel and sequential mutual exclusions for Petri net modeling for manufacturing systems,”IEEE Trans. on Robotics and Automation, vol. 7, no. 4, pp. 515–527, 1991.

    Article  Google Scholar 

  42. M.C. Zhou and M.C. Leu, “Modeling and performance analysis of a flexible PCB assembly station using Petri nets,” Trans. of the ASME,J. of Electronic packaging, vol. 113, no. 4, pp. 410–416, 1991.

    Google Scholar 

  43. M.C. Zhou, “Combination of Petri nets and intelligent decision makers for manufacturing systems control,” in6th IEEE International Symposium on Intelligent Control, Arlington, VA, 1991, pp. 146–151.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering and Center for Manufacturing Systems, New Jersey Institute of Technology, 07102, Newark, NJ

    Mengchu Zhou

  2. Department of Telecommunications Engineering, Changchun Institute of Post and Telecommunications, Changchung, Jilin, P.R.C.

    Dianlong Guo

  3. Department of Electrical, Computer, and Systems Engineering and Center for Manufacturing Productivity and Technology Transfer, Rensselaer Polytechnic Institute, 12180, Troy, NY

    Frank Dicesare

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  1. Mengchu Zhou
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  2. Dianlong Guo
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  3. Frank Dicesare
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Zhou, M., Guo, D. & Dicesare, F. Integration of Petri nets and moment generating function approaches for system performance evaluation. Journal of Systems Integration 3, 43–62 (1993). https://doi.org/10.1007/BF01974171

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  • DOI: https://doi.org/10.1007/BF01974171

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