Optimal petri-net-based polynomial-complexity deadlock- avoidance policies for automated manufacturing systems

  • Authors:

  • Keyi Xing;MengChu Zhou;Huixia Liu;Feng Tian

  • Affiliations:

  • The State Key Laboratory for Manufacturing Systems Engineering and the Systems Engineering Institute, Xi'an Jiaotong 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;The State Key Laboratory for Manufacturing Systems Engineering and the Systems Engineering Institute, Xi'an Jiaotong University, Xi'an, China;The State Key Laboratory for Manufacturing Systems Engineering and the Systems Engineering Institute, Xi'an Jiaotong University, Xi'an, China

  • Venue:
  • IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans - Special section: Best papers from the 2007 biometrics: Theory, applications, and systems (BTAS 07) conference
  • Year:
  • 2009

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Abstract

Even for a simple automated manufacturing system (AMS), such as a general single-unit resource allocation system, the computation of an optimal or maximally permissive deadlock-avoidance policy (DAP) is NP-hard. Based on its Petri-net model, this paper addresses the deadlock-avoidance problem in AMSs, which can be modeled by systems of simple sequential processes with resources. First, deadlock is characterized as a perfect resource-transition circuit that is saturated at a reachable state. Second, for AMSs that do not have one-unit resources shared by two or more perfect resource-transition circuits that do not contain each other, it is proved that there are only two kinds of reachable states: safe states and deadlock. An algorithm for determining the safety of a new state resulting from a safe one is then presented, which has polynomial complexity. Hence, the optimal DAP with polynomial complexity can be obtained by a one-step look-ahead method, and the deadlock-avoidance problem is polynomially solved with Petri nets for the first time. Finally, by reducing a Petri-net model and applying the design of optimal DAP to the reduced one, a suboptimal DAP for a general AMS is synthesized, and its computation is of polynomial complexity.