Comparison and Evaluation of Deadlock Prevention Methods for Different Size Automated Manufacturing Systems

In automated manufacturing systems (AMSs), deadlocks problems can arise due to limited shared resources. Petri nets are an effective tool to prevent deadlocks in AMSs. In this paper, a simulation based on existing deadlock prevention policies and different Petri net models are considered to explore whether a permissive liveness-enforcing Petri net supervisor can provide better time performance. The work of simulation is implemented as follows. (1) Assign the time to the controlled Petri net models, which leads to timed Petri nets. (2) Build the Petri net model using MATLAB software. (3) Run and simulate the model, and simulation results are analyzed to determine which existing policies are suitable for different systems. Siphons and iterative methods are used for deadlocks prevention. Finally, the computational results show that the selected deadlock policies may not imply high resource utilization and plant productivity, which have been shown theoretically in previous publications. However, for all selected AMSs, the iterative methods always lead to structurally and computationally complex liveness-enforcing net supervisors compared to the siphons methods. Moreover, they can provide better behavioral permissiveness than siphons methods for small systems. For large systems, a strict minimal siphon method leads to better behavioral permissiveness than the other methods

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

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

Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems

Deadlock prevention policies are used to solve the deadlock problems of FMSs. It is well known that the theory of regions is the efficient method for obtaining optimal (i.e., maximally permissive) controllers. All legal and live maximal behaviors of Petri net models can be preserved by using marking/transition-separation instances (MTSIs) or event-state-separation-problem (ESSP) methods. However, they encountered great difficulties in solving all sets of inequalities that is an extremely time consuming problem. Moreover, the number of linear programming problems (LPPs) of legal markings is also exponential with net size when a plant net grows exponentially. This paper proposes a novel methodology to reduce the number of MTSIs/ESSPs and LPPs. In this paper, we used the well-known reduction approach Murata (1989) to simply the construct of system such that the problem of LPPs can then be reduced. Additionally, critical ones of crucial marking/transition-separation instances (COCMTSI) are developed and used in our deadlock prevention policy that allows designers to employ few MTSIs to deal with deadlocks. Experimental results indicate that the computational cost can be reduced. To our knowledge, this deadlock prevention policy is the most efficient policy to obtain maximal permissive behavior of Petri net models than past approaches

Verification of Nonblockingness in Bounded Petri Nets With Minimax Basis Reachability Graphs

This paper proposes a semi-structural approach to verify the nonblockingness of a Petri net. We construct a structure, called minimax basis reachability graph (minimax-BRG): it provides an abstract description of the reachability set of a net while preserving all information needed to test if the net is blocking. We prove that a bounded deadlock-free Petri net is nonblocking if and only if its minimax-BRG is unobstructed, which can be verified by solving a set of integer constraints and then examining the minimax-BRG. For Petri nets that are not deadlock-free, one needs to determine the set of deadlock markings. This can be done with an approach based on the computation of maximal implicit firing sequences enabled by the markings in the minimax-BRG. The approach we developed does not require the construction of the reachability graph and has wide applicability.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Modeling sequential resource allocation systems using Extended Finite Automata

Deadlock avoidance for resource allocation systems (RAS) is a well-established problem in the Discrete Event System (DES) literature. This paper is mainly concerned with modeling the class of Conjunctive / Disjunctive sequential resource allocation systems (C/D RAS) as finite automata extended with variables. The proposed modeling approach allows for modeling multiple instance execution, routing flexibility and failure handling. With an appropriate model of the system, a symbolic approach is then used to synthesize the optimal supervisor, in the least restrictive sense. Furthermore, a set of compact logical formulae can be extracted and attached to the original model, which results in a modular and comprehensible representation of the supervisor

On the Performance Estimation and Resource Optimisation in Process Petri Nets

Many artificial systems can be modeled as discrete dynamic systems in which resources are shared among different tasks. The performance of such systems, which is usually a system requirement, heavily relies on the number and distribution of such resources. The goal of this paper is twofold: first, to design a technique to estimate the steady-state performance of a given system with shared resources, and second, to propose a heuristic strategy to distribute shared resources so that the system performance is enhanced as much as possible. The systems under consideration are assumed to be large systems, such as service-oriented architecture (SOA) systems, and modeled by a particular class of Petri nets (PNs) called process PNs. In order to avoid the state explosion problem inherent to discrete models, the proposed techniques make intensive use of linear programming (LP) problems

A flexible control system for flexible manufacturing systems

A flexible workcell controller has been developed using a three level control hierarchy (workcell, workstation, equipment). The cell controller is automatically generated from a model input by the user. The model consists of three sets of graphs. One set of graphs describes the process plans of the parts produced by the manufacturing system, one set describes movements into, out of and within workstations, and the third set describes movements of parts/transporters between workstations. The controller uses an event driven Petri net to maintain state information and to communicate with lower level controllers. The control logic is contained in an artificial neural network. The Petri net state information is used as the input to the neural net and messages that are Petri net events are output from the neural net. A genetic algorithm was used to search over alternative operation choices to find a "good" solution. The system was fully implemented and several test cases are described