Deadlock Prevention Policy Research Articles

Distributed Computation of Liveness-Enforcing Supervisory Control of Flexible Manufacturing Systems

This paper presents a modular deadlock prevention policy for large-scale flexible manufacturing systems. It can find maximally permissive liveness-enforcing supervisory control in an efficient computational complexity manner. A vector covering approach is used to minimize essential set of legal markings and first-met bad markings. Providing that modules of system interact using choice, we will prove that monitor-based supervisory control methods can be applied distributedly. Then, choice operator of Petri net will be used to synthesis subsystems. Even if such assumption limits the application of modular monitor-based supervisory control, the proposed results constitute a primary step towards a synthesis procedure that overcomes time and space complexity of monitor-based deadlock prevention policies.

Analysis of Flexible Manufacturing System using Petri Nets to design a Deadlock Prevention Policy

Analysis of Flexible Manufacturing System using Petri Nets to design a Deadlock Prevention Policy

An algorithm to evaluate implementation cost for liveness-enforcing supervisors designed by deadlock prevention policy

Deadlock prevention policy is widely used to design the liveness-enforcing supervisors because of its advantage that deadlocks are considered and solved in design and planning stages for flexible manufacturing systems modeled with Petri nets. However, how to evaluate the implementation cost of these liveness-enforcing supervisors is not done in the existing literature. This article proposes an algorithm to evaluate the implementation cost performance of different liveness-enforcing supervisors designed by deadlock prevention policy. By designing a multiple objective linear programming problem associated with two parameters (denoted as f1 and f2) to characterize the corresponding implementation costs for the added control places and the related input and out transitions and control arcs, the proposed algorithm first obtains the variable regions of f1 and f2 And then a satisfactory level coefficient (denoted as [Formula: see text]) concentrating on the optimal compromise solutions of f1 and f2 (denoted as f1* and f2*) is solved by a linear programming problem. As a result, the implementation cost performance of the corresponding liveness-enforcing supervisor can be indicated conveniently on the basis of the values of [Formula: see text], f1*, and f2*. The practical potential of the proposed algorithm is demonstrated via a theoretical analysis and several widely used examples from the existing literature.

Transition-based deadlock control policy using reachability graph for flexible manufacturing systems

Most existing deadlock prevention policies deal with deadlock problems arising in flexible manufacturing systems modeled with Petri nets by adding control places. Based on the reachability graph analysis, this article proposes a novel deadlock control policy that recovers the system from deadlock and livelock states to legal states and reaches the same number of states as the original plant model by adding control transitions. In order to reduce the structural complexity of the supervisor, a set covering approach is developed to minimize the number of control transitions. Finally, two flexible manufacturing system examples are presented to illustrate the proposed approach.

An Efficient Siphon-Based Deadlock Prevention Policy for a Class of Generalized Petri Nets

We propose a new deadlock prevention policy for an important class of resource allocation systems (RASs) that appear in the modeling of flexible manufacturing systems (FMSs). The model of this class in terms of generalized Petri nets is, namely, S4PR. On the basis of recent structural analysis results related to the elementary siphons in generalized Petri nets on one hand and an efficient deadlock avoidance policy proposed for the class of conjunctive/disjunctive (C/D) RASs on the other hand, we show how one can generate monitors to be added to a net system such that all its strict minimal siphons aremax′-controlled and no insufficiently marked siphon is generated. Thereby, a new, simple, and more permissive liveness-enforcing supervisor synthesis method for S4PR is established.

Think-globally-act-locally approach with weighted arcs to the synthesis of a liveness-enforcing supervisor for generalized Petri nets modeling FMSs

This paper proposes a general approach, called a think-globally-act-locally method with weighted arcs (TGALW), which can be used to compute a liveness-enforcing supervisor (LES) for the Petri net (PN) model of a flexible manufacturing system (FMS) prone to deadlocks. Compared with siphon-based deadlock prevention policies that are usually rather conservative, the method is especially effective for generalized PN classes such as S4R and S4PR and also leads to optimal or near optimal LESs while maintaining the necessary computations simple. An original PNM is first transformed into a net that is behaviorally equivalent to it. A global sink/source place (GP) is used temporarily in the design steps and is finally removed when the liveness of the system is achieved. At each iteration step, bad markings are identified and then controlled by monitors through an established place-invariant based method. A condition of the optimal controllability of a bad marking is proposed, i.e., if all bad markings are optimally controlled at each iteration step, the TGALW method can find an optimal LES. Redundancy of monitors is checked. Typical examples existing in the literature are used to demonstrate applicability and the effectiveness of the proposed method.

Synthesis of Monitor-Based Liveness-Enforcing Supervisors for $\rm{S}^{3}$ PR With ${\boldsymbol{\xi }}$ -Resources

Deadlocks are a rather undesirable phenomenon in flexible manufacturing systems (FMSs). This work, by adding monitors, develops a deadlock prevention policy for FMSs that can be modeled by a class of Petri nets called α-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PR with i-resources. First, an algorithm is presented to reduce an S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PR via a i-resource. Based on the algorithm, i-resources in α-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PRs are classified into two types: 1) A-ξ-resources and 2) B-ξ-resources. Next, for an α-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PR with only B-ξ-resources, it is proved that a maximally permissive liveness-enforcing supervisor can be designed by controlling all emptied strict minimal siphons. For an α-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PR containing A-ξ-resources, a liveness-enforcing supervisor can be designed by iteratively reducing the net via A-ξ-resources and adding the corresponding monitors. Finally, a deadlock prevention algorithm for α-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PRs is presented. Two FMS examples are used to illustrate its application. Its comparison results with other state-of-the-art deadlock prevention policies validate its overall advantages in terms of computational complexity, structural complexity, and behavior permissiveness.

Further reduction of minimal first-met bad markings for the computationally efficient synthesis of a maximally permissive controller

To date, research on the supervisor design for flexible manufacturing systems focuses on speeding up the computation of optimal (maximally permissive) liveness-enforcing controllers. Recent deadlock prevention policies for systems of simple sequential processes with resources (S3PR) reduce the computation burden by considering only the minimal portion of all first-met bad markings (FBMs). Maximal permissiveness is ensured by not forbidding any live state. This paper proposes a method to further reduce the size of minimal set of FBMs to efficiently solve integer linear programming problems while maintaining maximal permissiveness using a vector-covering approach. This paper improves the previous work and achieves the simplest structure with the minimal number of monitors.

Deadlock Prevention for Flexible Manufacturing Systems via Controllable Siphon Basis of Petri Nets

Siphons are a kind of special structural objects in a Petri net, and plays a key role in synthesizing a live Petri net controller for flexible manufacturing systems. In order to obtain a small size Petri net controller, this paper introduces the concept of a controllable siphon basis. It then proves that a live Petri net controller can be established by adding a control place and related arcs to each strict minimal siphon (SMS) in a controllable siphon basis. The initial markings of control places are determined by an integer linear program. The number of control places in the obtained controllers is the same as the number of SMSs in the controllable siphon basis, while the latter is no more than that of the activity places in a Petri net model. An algorithm for constructing a controllable siphon basis is proposed, and a new deadlock prevention policy based on it is established. A few examples are provided to demonstrate the proposed concepts and policy and used to compare them with the state-of-the-art methods.

Elementary Siphons of Petri Nets and Deadlock Control in FMS

For responsiveness, in the Petri nets theory framework deadlock prevention policies based elementary siphons control are often utilized to deal with deadlocks caused by the sharing of resources in flexible manufacturing system (FMS) which is developing the theory of efficient strict minimal siphons of an S3PR. Analyzer of Petri net models and their P-invariant analysis, and deadlock control are presented as tools for modelling, efficiency structure analysis, control, and investigation of the FMSs when different policies can be implemented for the deadlock prevention. We are to show an effective deadlock prevention policy of a special class of Petri nets namely elementary siphons. As well, both structural analysis and reachability graph analysis and simulation are used for analysis and control of Petri nets. This work is successfully applied Petri nets to deadlock analysis using the concept of elementary siphons, for design of supervisors of some supervisory control problems of FMS and simulation of Petri net tool with MATLAB.

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.

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 Control for a Class of Generalized Petri Nets Based on Proper Resource Allocation

AbstractThis article develops a deadlock prevention policy for a class of generalized Petri nets, namely G‐systems, which can model flexible manufacturing systems with machining, assembly, and disassembly operations. In this research, a polynomial complexity control policy for non‐blocking supervisors is established by properly adjusting resource allocation. First, a set of linear inequality constraints is derived with respect to different resource requirements such that the allocation of the system resources to various requesting processes can be appropriately restricted, that is, the resulting system has no deadlock state by imposing monitors on operation places. Moreover, an algorithm is proposed to identify the redundant constraints such that structurally simple liveness‐enforcing net supervisors can be obtained. Compared with existing polices, the proposed method can usually lead to a suboptimal supervisor with high computational efficiency. Finally, a flexible manufacturing system example is utilized to demonstrate the proposed method.

On deadlock-free control of automated manufacturing systems with flexible routes and assembly operations using Petri nets

In order to design Petri net (PN)-based liveness-enforcing supervisors to deal with flexible routes and assembly operations in automated manufacturing systems (AMS), a deadlock prevention policy was proposed in Hu et al. (IEEE Trans Ind Inf 9:109–121, 2013). The proposed policy exploits the structural analysis of PN models of AMS in the sense that the liveness of a PN model is attributed to the absence of undermarked siphons. To demonstrate the applicability and effectiveness of this method, a few examples were utilized. Some liveness-enforcing supervisors computed in Hu et al. (IEEE Trans Ind Inf 9:109–121, 2013) to enforce liveness on the considered Petri net models do not provide live system behaviors. The purpose of this paper is to report these facts and to provide the correct results.

On a deadlock prevention policy for a class of Petri nets S3PMR

In Yan et al. (J Inf Sci Eng 25(1): 167–183, 2009), a deadlock prevention policy is proposed for a subclass of Petri nets, S3PMR, that can well model a large class of flexible manufacturing systems (FMS) where deadlocks are caused by unmarked siphons in their Petri net models. To validate the effectiveness and efficiency of the proposed approach, two examples were demonstrated in Yan et al. (J Inf Sci Eng 25(1): 167–183, 2009). This paper shows that there is a problem with one of the control places computed for one of the examples. In Yan et al. (J Inf Sci Eng 25(1): 167–183, 2009), for another example, two different deadlock prevention supervisors were proposed. It is also shown in this paper that, for these two supervisors, it is possible to obtain two subsets of control places. Thus, the structures of the two supervisors are further simplified with the same permissive system behaviours.

A Deadlock Prevention Policy Based on Complementary Places

For Petri net models of flexible manufacturing systems,this work proposes a method to design liveness-enforcing supervisors based on complementary places.Firstly,a finite-capacity net珦Nis obtained from a given Petri net N by adding a capacity function K.Then,by increasing K to Kmax,the maximal reachability set of live finite-capacity net珦Nis computed and the complementary-place transformation is used to obtain the live system N′.Finally,an example of S3PR net is provided to compare with some other approaches proposed in prior work.Comparison results show that the liveness-enforcing supervisor obtained by the proposed method has simpler structure and more permissive behavior in some cases.Furthermore,another example of S3PGR2net shows that the proposed method can be applied to the general Petri nets.

Design of a Maximally Permissive Liveness‐enforcing Supervisor with Reduced Complexity for Automated Manufacturing Systems

AbstractThis paper deals with the problems of computational and structural complexity in designing maximally permissive liveness‐enforcing supervisors for a class of Petri nets called Systems of Simple Sequential Processes with Resources (S3PR) without ξ‐resources. The supervisor consists of two parts: the first part proposes an algorithm to extract a desired emptied strict minimal siphon (SMS) from a given emptied siphon based on loop resource subsets. This is faster than the existing ones. The second part proposes a siphon‐based deadlock prevention policy, which can obtain a maximally permissive liveness‐enforcing supervisor with reduced structural complexity and no weighted monitors, owing to the contribution of the first part, which can compute a desired SMS such that one with the smallest number of resource places is selected first for control. Several flexible manufacturing systems are used to show the proposed method and its superior performance over the previous ones.

Comments on “Efficient deadlock prevention policy in automated manufacturing systems using exhausted resources”

As reported by Hu and Li (International Journal of Advanced Manufacturing Technology 40:566-571, 2009), in order to design liveness-enforcing supervisors for automated manufacturing systems (AMS), a deadlock prevention policy was proposed based on the exhausted resources. The proposed policy exploits a special structure of Petri nets for the liveness of a specific system. In order to show the applicability of this method, two examples were considered. One of the examples involves an AMS with a large-state space. Unfortunately, the liveness-enforcing supervisor containing seven monitors (control places) computed as reported by Hu and Li (International Journal of Advanced Manufacturing Technology 40:566-571, 2009) to enforce liveness on this system does not provide a live behaviour. This paper reports this fact.

Maximally Permissive Petri Net Supervisors for Flexible Manufacturing Systems with Uncontrollable and Unobservable Transitions

AbstractThis paper presents a deadlock prevention policy to obtain behaviorally optimal supervisors for flexible manufacturing systems with uncontrollable and unobservable transitions. The conditions of uncontrollability and unobservability of transitions are revealed in the sense of the implementation of a Petri net supervisor. Then, integer linear programming models are designed to obtain a Petri net supervisor such that all legal markings are reachable and the number of control places is reduced. We also show that a controllable transition can be unobservable and self‐loops can be used to disable the transition but do not observe its firing. Finally, examples are provided to illustrate the proposed approach.

Deadlock prevention policy for a class of petri nets based on complementary places and elementary siphons

For a class of Petri nets called Systems of Simple Sequential Processes with Resources $$(\mathrm{{S}}^{3}\mathrm{{PR}})$$ ( S 3 PR ) , this paper proposes a sufficient condition under which there exists a complementary-place supervisor to enforce their liveness. Moreover, an algorithm is proposed to design liveness-enforcing supervisors based on complementary places and elementary siphons. The significance of the proposed policy lies in its design simplicity. A flexible manufacturing system example shows that in some cases, the proposed policy can obtain a structurally simpler supervisor with 99.9 % maximal permissive behavior.