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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 579623, 15 pages
http://dx.doi.org/10.1155/2015/579623
Research Article

Deadlock Prevention Policy with Behavioral Optimality or Suboptimality Achieved by the Redundancy Identification of Constraints and the Rearrangement of Monitors

1College of Electronics and Information, Xi’an Polytechnic University, No. 19 South Jinhua Road, Xi’an 710048, China
2School of Electro-Mechanical Engineering, Xidian University, No. 2 South Taibai Road, Xi’an 710071, China
3Faculty of Telecommunication Networks, Odessa National Academy of Telecommunications Named after A.S. Popov, Koval’ska Street 1, Odessa 65029, Ukraine

Received 22 May 2015; Accepted 20 September 2015

Academic Editor: Kamel Barkaoui

Copyright © 2015 Liang Hong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This work develops an iterative deadlock prevention method for a special class of Petri nets that can well model a variety of flexible manufacturing systems. A deadlock detection technique, called mixed integer programming (MIP), is used to find a strict minimal siphon (SMS) in a plant model without a complete enumeration of siphons. The policy consists of two phases. At the first phase, SMSs are obtained by MIP technique iteratively and monitors are added to the complementary sets of the SMSs. For the possible existence of new siphons generated after the first phase, we add monitors with their output arcs first pointed to source transitions at the second phase to avoid new siphons generating and then rearrange the output arcs step by step on condition that liveness is preserved. In addition, an algorithm is proposed to remove the redundant constraints of the MIP problem in this paper. The policy improves the behavioral permissiveness of the resulting net and greatly enhances the structural simplicity of the supervisor. Theoretical analysis and experimental results verify the effectiveness of the proposed method.