Control Algorithm Using a Revised MIP Method to Deal with Livelocks in S4R of Petri Nets

  • Shaoyong Li (李绍勇)Email author
  • Zongli Wu (吴宗礼)
  • Hailin Li (李海林)
  • Xianhong Wei (魏先宏)
  • Ying Cai (蔡颖)
  • Caiqin Hou (厚彩琴)


Livelocks, like deadlocks, can result in serious results in running process of flexible manufacturing systems (FMSs). Current deadlock control policies (DCPs) based on mixed integer programming (MIP) cannot detect siphons that cause and cope with livelocks in Petri nets. This study proposes a revised mixed integer programming (RMIP) method to directly solve the new smart siphons (NSSs) associated with livelocks in a system of sequential systems with shared resources (S4R), a typical subclass of generalized Petri net models. Accordingly, the solved NSSs are max’-controlled by adding the corresponding control places (CPs). As a result, an original S4R system with livelocks can be converted into the live controlled Petri net system. The related theoretical analysis and an example are given to demonstrate the proposed RMIP and the corresponding control algorithm (CA).

Key words

flexible manufacturing system (FMS) Petri nets revised mixed integer programing (RMIP) livelocks live controlled Petri net system 

CLC number

U 292.18 

Document code


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Copyright information

© Shanghai Jiao Tong University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Shaoyong Li (李绍勇)
    • 1
    Email author
  • Zongli Wu (吴宗礼)
    • 1
  • Hailin Li (李海林)
    • 1
  • Xianhong Wei (魏先宏)
    • 1
  • Ying Cai (蔡颖)
    • 1
  • Caiqin Hou (厚彩琴)
    • 1
  1. 1.School of Civil EngineeringLanzhou University of TechnologyLanzhouChina

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