International Journal of Control, Automation, and Systems

  • 제1권4호
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  • Pages.431-443
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  • 2003
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  • 1598-6446(pISSN)
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  • 2005-4092(eISSN)
제어로봇시스템학회 (Institute of Control, Robotics and Systems)
권호 표지

Efficient Computations for Evaluating Extended Stochastic Petri Nets using Algebraic Operations

  • Kim, Dong-Sung (School of Electrical and Computer Engineering, Cornell University) ;
  • Moon, Hong-Ju (Piolink Inc.) ;
  • Bahk, Je-Hyeong (Photonics Research Center, Korea Institute of Science and Technology) ;
  • Kwon, Wook-Hyun (School of Electrical Engineering & Computer Science, Seoul National University) ;
  • Zygmunt J. Haas (School of Electrical and Computer Engineering, Cornell University)
  • 발행 : 2003.12.01
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초록

This paper presents an efficient method to evaluate the performance of an extended stochastic Petri net by simple algebraic operations. The reachability graph is derived from an extended stochastic Petri net, and then converted to a timed stochastic state machine, using a semi-Markov process. The n-th moments of the performance index are derived by algebraic manipulations with each of the n-th moments of transition time and transition probability. For the derivation, three reduction rules are introduced on the transition trajectories in a well-formed regular expression. Efficient computation algorithms are provided to automate the suggested method. The presented method provides a proficient means to derive both the numerical and the symbolic solutions for the performance of an extended stochastic Petri net by simple algebraic manipulations.

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참고문헌

  1. Proc. of the IEEE v.77 Petri nets: Properties, analysis and applications T. Murata https://doi.org/10.1109/5.24143
  2. Proc. PERFORMANCE’ 84, Models of Comput. System Performance Extended stochastic petri nets: Applications and analysis J. B. Dugan;K. S. Trivedi;R. M. Geist;V. M. Nicola,
  3. IEEE Trans. Comput. v.C-31 Performance analysis using stochastic Petri nets M. K. Molloy https://doi.org/10.1109/TC.1982.1676110
  4. IEEE Trans. on Robotics and Automation v.6 Performance evaluation of automated manufacturing systems using generalized stochastic Petri nets R. Y. Al-Jaar;A. A. Desrochers https://doi.org/10.1109/70.63259
  5. Stochastic Processes and their Applications 32 A fundamental matrix for regular semi-markov processes M. Fygenson
  6. IEEE Trans on Automatic Control v.38 no.2 A moment generating function based approach for evaluation extended stochastic petri nets D. Guo;F. DiCesare;Z. M. C. https://doi.org/10.1109/9.250484
  7. IEEE Trans On Control Systems Technology v.3 no.2 Automating mason’s rule and its application to analysis of stochastic petri nets M. C. Zhou;C. H. Wang;X. Zhao https://doi.org/10.1109/87.388133
  8. Performance Evaluation v.20 Markov regenerative stochastic Petri nets H. Choi;V. G. Kulkarina;K. S. Trivedi
  9. Lecture Notes in Computer Science; Quantitative Evaluation on Computing and Communication Systems v.977 Steady state analysis of Markov Regenerative SPN with age memory polic M. Telek;A. Bobbio;L. Jereb;A. Puliafito;K. S. Trivedi
  10. Performance Evaluation v.27 Numerical analysis of deterministic and stochastic Petri nets with concurrent deterministic transitions C. Lindemann;G. S. Shedler
  11. Performance Evaluation v.36 Transient analysis of deterministic and stochastic Petri nets with concurrent deterministic transition C. Lindemann;G. S. Shedler https://doi.org/10.1016/S0166-5316(99)00020-6
  12. Performance Evaluation v.32 Petri nets with k simultaneously enabled generally distributed timed transitions A. Puliafito;M. Scarpa;K. S. Trivedi https://doi.org/10.1016/S0166-5316(97)00013-8
  13. Proc. of the International Workshop on Discrete Event Systems Performance evaluation of a discrete event system via the regular expression of trajectories H. Moon;W. H. Kwon
  14. Introduction to Automata Theory, Languages, and Computation J. E. Hopcropt;J. D. Ullman
  15. Journal of Algebra 13 Rational sets in commutative monoids S. Eilenberg
  16. Advanced Engineering Mathematics E. Kreyszig
  17. IEICE Trans. on Communication v.E82-B no.12 Performance analysis of the Exhaustive Timercontrolled Network with Finite Buffer S. Y. Moon;H. S. Park;W. H. Kwon