A novel continuous model to approximate time Petri nets: modelling and analysis

Tianlong Gu; Rongsheng Dong

International Journal of Applied Mathematics and Computer Science (2005)

  • Volume: 15, Issue: 1, page 141-150
  • ISSN: 1641-876X

Abstract

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In order to approximate discrete-event systems in which there exist considerable states and events, David and Alla define a continuous Petri net (CPN). So far, CPNs have been a useful tool not only for approximating discrete-event systems but also for modelling continuous processes. Due to different ways of calculating instantaneous firing speeds of transitions, various continuous Petri net models, such as the CCPN (constant speed CPN), VCPN (variable speed CPN) and the ACPN (asymptotic CPN), have been proposed, where the continuous flow is specified uniquely by maximal firing speeds. However, in applications such as chemical processes there exist situations where the continuous flow must be above some minimal speed or in the range of minimal and maximal speeds. In this paper, from the point of view of approximating a time Petri net, the CPN is augmented with maximal and minimal firing speeds, and a novel continuous model, i.e., the Interval speed CPN (ICPN) is defined. The enabling and firing semantics of transitions of the ICPN are discussed, and the facilitating of continuous transitions is classified into three levels: 0-level, 1-level and 2-level. Some policies to resolve the conflicts and algorithms to undertake the behavioural analysis for the ICPN are developed. In addition, a chemical process example is presented. sm

How to cite

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Gu, Tianlong, and Dong, Rongsheng. "A novel continuous model to approximate time Petri nets: modelling and analysis." International Journal of Applied Mathematics and Computer Science 15.1 (2005): 141-150. <http://eudml.org/doc/207722>.

@article{Gu2005,
abstract = {In order to approximate discrete-event systems in which there exist considerable states and events, David and Alla define a continuous Petri net (CPN). So far, CPNs have been a useful tool not only for approximating discrete-event systems but also for modelling continuous processes. Due to different ways of calculating instantaneous firing speeds of transitions, various continuous Petri net models, such as the CCPN (constant speed CPN), VCPN (variable speed CPN) and the ACPN (asymptotic CPN), have been proposed, where the continuous flow is specified uniquely by maximal firing speeds. However, in applications such as chemical processes there exist situations where the continuous flow must be above some minimal speed or in the range of minimal and maximal speeds. In this paper, from the point of view of approximating a time Petri net, the CPN is augmented with maximal and minimal firing speeds, and a novel continuous model, i.e., the Interval speed CPN (ICPN) is defined. The enabling and firing semantics of transitions of the ICPN are discussed, and the facilitating of continuous transitions is classified into three levels: 0-level, 1-level and 2-level. Some policies to resolve the conflicts and algorithms to undertake the behavioural analysis for the ICPN are developed. In addition, a chemical process example is presented. sm},
author = {Gu, Tianlong, Dong, Rongsheng},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {discrete event systems; continuous Petri nets; hybrid systems},
language = {eng},
number = {1},
pages = {141-150},
title = {A novel continuous model to approximate time Petri nets: modelling and analysis},
url = {http://eudml.org/doc/207722},
volume = {15},
year = {2005},
}

TY - JOUR
AU - Gu, Tianlong
AU - Dong, Rongsheng
TI - A novel continuous model to approximate time Petri nets: modelling and analysis
JO - International Journal of Applied Mathematics and Computer Science
PY - 2005
VL - 15
IS - 1
SP - 141
EP - 150
AB - In order to approximate discrete-event systems in which there exist considerable states and events, David and Alla define a continuous Petri net (CPN). So far, CPNs have been a useful tool not only for approximating discrete-event systems but also for modelling continuous processes. Due to different ways of calculating instantaneous firing speeds of transitions, various continuous Petri net models, such as the CCPN (constant speed CPN), VCPN (variable speed CPN) and the ACPN (asymptotic CPN), have been proposed, where the continuous flow is specified uniquely by maximal firing speeds. However, in applications such as chemical processes there exist situations where the continuous flow must be above some minimal speed or in the range of minimal and maximal speeds. In this paper, from the point of view of approximating a time Petri net, the CPN is augmented with maximal and minimal firing speeds, and a novel continuous model, i.e., the Interval speed CPN (ICPN) is defined. The enabling and firing semantics of transitions of the ICPN are discussed, and the facilitating of continuous transitions is classified into three levels: 0-level, 1-level and 2-level. Some policies to resolve the conflicts and algorithms to undertake the behavioural analysis for the ICPN are developed. In addition, a chemical process example is presented. sm
LA - eng
KW - discrete event systems; continuous Petri nets; hybrid systems
UR - http://eudml.org/doc/207722
ER -

References

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  4. David R. and Alla H. (2001): On hybrid Petri nets. - Discr. EventDynam. Syst. Theory Applic., Vol. 1, No. 1, pp. 9-40. Zbl0969.93024
  5. Dubois E., Alla H. and David R. (1994): Continuous Petri net with maximal speeds depending on time. - Proc. 5th Int. Conf. Application and Theory of Petri Nets, Zaragoza, Spain, pp. 32-39. 
  6. Gu T. and Bahri P.A. (2002): A survey of Petri-net applications in batch processes. - Comput. Ind., Vol. 47, No. 1, pp. 99-111. 
  7. Gu T., Bahri P.A. and Lee P.L. (2002): Development of hybrid time Petri nets for scheduling of mixed batch continuous process. - Proc. 15th IFAC World Congress, Barcelona, Spain, pp.1121-1126. 
  8. Merlin P.M. and Farber D.J. (1976): Recoverability of communication protocols-Implications of a theoretical study. - IEEE Trans. Commun., Vol. 24, No. 9, pp. 1036-1043. Zbl0362.68096
  9. Murata T. (1989): Petri nets: Properties, analysis and applications. - Proc. IEEE, Vol. 77, No. 1, pp. 541-580. 
  10. Ramchandani C. (1974): Analysis of asynchronous concurrent systems by timed Petri nets. - Massachusetts Inst. Technology, Techn. Rep., No. 120. 

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