An effective algorithm to find elementary siphons in a class of Petri nets

  • Authors:

  • AnRong Wang;ZhiWu Li;JianYuan Jia;MengChu Zhou

  • Affiliations:

  • School of Electro-Mechanical Engineering, Xidian University, Xi'an, China;School of Electro-Mechanical Engineering, Xidian University, Xi'an, China;School of Electro-Mechanical Engineering, Xidian University, Xi'an, China;Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ and School of Electro-Mechanical Engineering, Xidian University, Xi'an, China

  • Venue:
  • IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
  • Year:
  • 2009

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Abstract

As a structural object of Petri nets, siphons play a key role in the development of deadlock prevention policies for resource allocation systems. Elementary siphons are a novel concept in net theory. Based on graph theory, this paper proposes an effective algorithm with polynomial complexity to find a set of elementary siphons for a linear system of simple sequential processes with resources (LS3PR), a subclass of Petri nets, which can model many flexible manufacturing systems. The algorithm is established through the use of a resource directed graph and complementary sets of strict minimal siphons (SMS) of the net. The upper bound of the number of SMS in such a net is identified. A running example is used to demonstrate the proposed method.