Problematic configurations and choice-join pairs on Mono-T-Semiflow nets: towards the characterization of behavior-structural properties


This work is concerned with the computation of problematic configurations and problematic choice-join pairs in timed continuous Petri nets under the infinite server semantics; those net structural objects explain possible bad/counter-intuitive behaviors of systems, such as non-monotonicities and discontinuities of the equilibrium throughput. The calculation of problematic configurations is a computationally complex task since their number grows exponentially with the input cardinality of join transitions. In order to alleviate this inconvenience, four type of reduction rules preserving the set of problematic configurations are addressed. Reduction rules are weighted versions of the macroplace, macrotransition, and fusion of transitions rules, the elimination of implicit places rule is also provided. Reduced nets are useful to better understand the net substructures leading to unexpected behaviors in the equilibrium throughput. They help to highlight that the structural objects named problematic choice-join pairs, defined in this work, are the actual responsible of these counter-intuitive throughput behaviors. The great advantage over the set of problematic configurations is that the set of problematic choice-join pairs grows polynomially in the size of the net.

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  1. Angeli D, Leenheer PD, Sontag ED (2007) A Petri net approach to the study of persistence in chemical reaction networks. Math Biosci 210(2):598–618

    MathSciNet  Article  Google Scholar 

  2. Berthelot G (1986) Checking properties of nets using transformations. In: Rozenberg G (ed) Advances in Petri Nets 1985. Springer, Berlin, pp 19–40

  3. David R, Alla H (2010) Discrete, continuous, and hybrid Petri nets, 2nd edn. Springer, Berlin

    Google Scholar 

  4. Dicesare F, Harhalakis G, Proth J, Silva M, Vernadat F (1993) Practice of Petri nets in manufacturing. Chapman and Hall

  5. Esparza J, Silva M (1991) On the analysis and synthesis of free choice systems. In: Rozenberg G (ed) Advances in Petri nets 1990, LNCS 483. Springer, Berlin, pp 243–286

  6. Fanti M, Mangini A, Dotoli M, Ukovich W (2013) A three-level strategy for the design and performance evaluation of hospital departments. IEEE TransSyst Man Cybern: Syst 43(4):742–756

    Google Scholar 

  7. Fraca E, Júlvez J, Silva M (2014) On the fluidization of Petri nets and marking homothecy. Nonlinear Anal: Hybrid Syst 12:3–19

    MathSciNet  MATH  Google Scholar 

  8. Júlvez J, Boel R (2010) A continuous Petri net approach for model predictive control of traffic systems. IEEE Trans Syst Man Cybernet Part A: Syst Humans 40 (4):686–697

    Article  Google Scholar 

  9. Júlvez J, Recalde L, Silva M (2005) Steady-state performance evaluation of continuous mono-t-semiflow Petri nets. Automatica 41(4):605–616

    MathSciNet  Article  Google Scholar 

  10. Mahulea C, Recalde L, Silva M (2009) Basic server semantics and performance monotonicity of continuous Petri nets. Discret Event Dyn Syst 19(2):189–212

    MathSciNet  Article  Google Scholar 

  11. Marsan MA, Balbo G, Conte G, Donatelli S, Franceschinis G (1994) Modelling with generalized stochastic Petri nets, 1st edn. Wiley, New York

    Google Scholar 

  12. Molloy (1982) Performance analysis using stochastic Petri nets. IEEE Trans Comput C-31(9):913–917

    Article  Google Scholar 

  13. Navarro-Gutiérrez M, Ramírez-Treviño A, Silva M (2017) Homothecy, bifurcations, continuity and monotonicity in timed continuous Petri nets under infinite server semantics. Nonlin Anal: Hybrid Syst 26:48–67

    MathSciNet  MATH  Google Scholar 

  14. Navarro-Gutiérrez M, Ramírez-Treviño A, Silva M (2018) On monotonicity and continuity: computing problematic configurations in timed continuous Petri nets. In: WODES’18: 14th international workshop on discrete event systems, Sorrento

  15. Recalde L, Teruel E, Silva M (1999) Autonomous continuous P/T systems. In: Donatelli S, Kleijn J (eds) Application and theory of Petri Nets 1999, proceedings. Springer, Berlin, pp 107–126

  16. Recalde L, Mahulea C, Silva M (2006) Improving analysis and simulation of continuous Petri nets. In: 2006 IEEE International conference on automation science and engineering, pp 9–14

  17. Silva M (1985) Las redes de Petri en la automática y la informática. Ed. AC, Madrid

    Google Scholar 

  18. Silva M, Júlvez J, Mahulea C, Vázquez CR (2011) On fluidization of discrete event models: observation and control of continuous Petri nets. Discret Event Dyn Syst 21(4):427–497

    MathSciNet  Article  Google Scholar 

  19. Silva M, Fraca E, Wang L (2014) Performance evaluation and control of manufacturing systems: a continuous Petri nets view. In: Campos J, Seatzu C, Xie X (eds) Formal methods in manufacturing. CRC Press Taylor & Francis, pp 409–452

  20. Vázquez CR, Silva M (2011) Timing and liveness in continuous Petri nets. Automatica 47(2):283–290

    MathSciNet  Article  Google Scholar 

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Correspondence to Antonio Ramírez-Treviño.

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Navarro-Gutiérrez, M., Fraustro-Valdez, J.A., Ramírez-Treviño, A. et al. Problematic configurations and choice-join pairs on Mono-T-Semiflow nets: towards the characterization of behavior-structural properties. Discrete Event Dyn Syst 30, 175–209 (2020).

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  • Petri nets
  • Problematic configurations
  • Choice-join pairs
  • Structural properties