Deadlock Control Research Articles

Correction to “On Algebraic Identification of Critical States for Deadlock Control in Automated Manufacturing Systems Modeled With Petri Nets”

Correction to “On Algebraic Identification of Critical States for Deadlock Control in Automated Manufacturing Systems Modeled With Petri Nets”

Deadlock control and hybrid social spider scheduling algorithm for two-stage assembly permutation flowshop with limited buffers

This paper focuses on the deadlock control and scheduling problem of two-stage assembly permutation flowshop with limited buffers. In such a system, all parts are first processed in a permutation flowshop, then assembled into final products. The objective is to find a feasible schedule, including a manufacturing subschedule and an assembly subschedule, to minimize makespan. Owing to limited buffers, not only may the blocking phenomenon appear in the system operation, but also some manufacturing subschedules may lead to deadlock states, making them unavailable. To obtain a feasible schedule, this work first proposes a deadlock control or an availability detection and amendment (ADA) algorithm to determine whether a manufacturing subschedule is available, and convert unavailable ones to available ones. Then by embedding ADA into a social spider algorithm (SSA), a hybrid social spider algorithm (HSSA) is developed for computing feasible schedules. In HSSA, an improved heuristic search algorithm is proposed to generate a better initial population, and a simplified variable neighborhood search algorithm is designed and incorporated into HSSA to enhance its searching ability. Finally, HSSA is tested on instances, showing its superiority over SSA in performance. The effect of buffer size on the scheduling objective is discussed.

Enhancement of Computational Efficiency for Deadlock Recovery of Flexible Manufacturing Systems Using Improved Generating and Comparing Aiding Matrix Algorithms

After the fourth industrial evolution, precision and automatic manufacturing have become increasingly widely accepted in production. With highly variable productivity and flexibility, flexible manufacturing systems (FMS) lower production costs and increase efficiency. Due to its resource shareability, unexpected system deadlock may occur in some specific situations. Many existing works use deadlock prevention as the primary control methodology in research on system deadlock control, while this type of control policy would constrain the transportation resources and reduce the system’s liveness. This paper adopts a new transition-based deadlock recovery policy as the direct control strategy, which uses generating and comparing aiding matrix (GCAM) to determine the optimal control transition. We also improve the existing GCAM-based method by reducing the computational redundancy. This kind of control strategy and its benefit could be demonstrated through two typical systems of simple sequential processes with resource (S3PR) nets and their Petri nets model.

Robust Deadlock Control for Reconfigurable Printing Manufacturing System Based on Process Algebra

The competition for shared resources in printing manufacturing system may lead to deadlock, which could cause unnecessary downtime and bring vast economic loss for enterprises. Supervisor is widely studied in the literature to solve the deadlock control problem. With the objective of improving the robustness of reconfigurable printing manufacturing system (RPMS), this paper designs a new Agent-Resource- Workstation (ARW) model with a supervisor. A new reconfiguration of workstation models (NRWMs) is proposed based on ARW model. The supervisors can control reconfiguration behavior of NRWMs by limiting the time and frequency of interaction between workstation models. Then, formal verification is performed by process algebra to show its external behavior. We use the mCRL2 tool to carry out simulation experiments on NRWMs and provide the experimental results. The results show that robust deadlock control policy for the RPMS is secure and effective.

A Refined Siphon-Based Deadlock Prevention Policy for a Class of Petri Nets

Resource allocation systems (RASs) exist in various fields of modern society. The deadlock control problem is a crucial issue in control theory of RAS. This work is concentrated on a special class of shared resource and process-oriented Petri nets whose initial marking can have only a token in every resource place. Using mixed-integer programming (MIP) and iterative siphon control, we present a two-stage deadlock prevention policy. In particular, a modified MIP technique is developed for the first stage to compute a specific type of emptiable siphons and a siphon control method introducing monitors with related arcs whose weights all equal to one is established in the second stage. This policy leads to a maximally permissive liveness-enforcing supervisor and such an obtained controlled net is ordinary. Moreover, it avoids the exhaustive enumeration of siphons and the reachability analysis. Examples are provided to explain the policy.

Robust liveness enforcement of Petri nets with uncontrollable and unobservable transitions based on structural analysis

This paper concentrates on robust deadlock control problems for an automated manufacturing system with uncontrollable, unobservable events and resource failures, which is modeled by a subclass of Petri nets. A recovery subnet is added to the holder of each unreliable resource to model resource failure and recovery. In order to prevent a strict minimal siphon in a Petri net model from being emptied, an extended constraint set is constructed based on the complementary set of a strict minimal siphon to obtain a robust liveness constraint. Due to the uncontrollability and unobservability of the transitions, an automated manufacturing system cannot enforce inadmissible robust liveness constraints. It is necessary to decide the admissibility of robust liveness constraints and transform the inadmissible constraints into admissible ones. To this end, a monitor is designed for each admissible robust liveness constraint such that it can be enforced. Finally, an iterative algorithm is developed to perform the above steps and a robust liveness controlled system is obtained. The feasibility of the control strategy is demonstrated by examples.

Robust deadlock control in automated manufacturing systems with unreliable resources based on an algebraic way

In automated manufacturing systems (AMSs), because of unpredictable failures, resources can lose functions such that the deadlock control methods, in existence, are invalidated. In this paper, a robust deadlock control approach is proposed for AMSs with multiple unreliable resources. The considered AMSs modelled by Petri nets (PNs) allow to acquire different types of resources at each processing stage. In order to visualise the fact that resource failures occur in AMSs, recovery subnets are designed for the modelling AMSs to depict the failures and recoveries of resources. Based on a siphon detection method performed by a set of integer linear programming formulations, a control specification is proposed. Control places (monitors) with their control variables are designed for the detected unmarked siphons at a marking to guarantee that they are always marked even if some unreliable resources break down. Iteratively, all unmarked siphons are detected and controlled. Therefore, a robust deadlock supervisor is synthesised to ensure the controlled system's liveness no matter there exist resource failures or not. The theoretical analyses and proof are given to verify the correctness of the proposed method. Finally, the comparative studies are presented to expound the proposed method's effectiveness and efficiency.

Petri‐net‐based deadlock detection and recovery for control of interacting equipment in automated container terminals

In automated container terminals (ACTs), quay cranes (QCs), automated guided vehicles (AGVs), and automated yard cranes (AYCs) interact intensively to handle containers at seaside and yard side. This work investigates interacting equipment in ACTs that employ AGVs with the capability of lifting a container temporarily buffered at the transfer area in front of a storage block. By establishing and using the Petri net model of equipment interaction system (EIS) for container transportation, deadlock control problem is studied for handling operations in ACTs, where all QCs, AYCs, and transport vehicles are considered as system resources. Deadlock is characterized as maximal special circuits (MSCs) that are saturated at a system state. After a deadlock detection method through MSC enumeration in the system Petri net model is developed, a procedure is proposed to resolve deadlock situations where an AYC is involved in the corresponding circular waiting relations. By modifying the operation sequence of AYCs, the procedure can resolve the conflicts among concurrent processes so as to eliminate deadlocks. Examples are presented to illustrate the effectiveness of the deadlock handling method, which is also tested in a simulation study. Results show that the EIS can recover from detected deadlocks involving AYCs to ensure smooth transport operations of container jobs.

Computation of Minimal Siphons in Petri Nets Using Problem Partitioning Approaches

A large amount of research has shown the vitality of siphon enumeration in the analysis and control of deadlocks in various resource-allocation systems modeled by Petri nets (PNs). In this paper, we propose an algorithm for the enumeration of minimal siphons in PN based on problem decomposition. The proposed algorithm is an improved version of the global partitioning minimal-siphon enumeration (GPMSE) proposed by Cordone et al. (2005) in IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, which is widely used in the literature to compute minimal siphons. The experimental results show that the proposed algorithm consumes lower computational time and memory compared with GPMSE, which becomes more evident when the size of the handled net grows.

An Improved Synthesis Method Based on ILPP and Colored Petri Net for Liveness Enforcing Controller of Flexible Manufacturing Systems

Petri nets are used to design deadlock control strategies for flexible manufacturing systems (FMS), which typically involve the addition of monitors and the associated arcs to the FMS. The addition of several monitors and associated arcs to first constructed Petri net model significantly complicates the Petri net controller. This paper develops a two-step method for preventing deadlocks based on a colored Petri net and a structurally minimal approach that significantly reduces the number of monitors. In the first step, a vector covering technique is applied to generate a minimal covered sets of first-met bad markings (FBMs) and legal markings that are respectively smaller than the sets of FBMs and legal markings. At one iteration, place invariants (PIs) corresponding to monitors are constructed by solving an integer linear programming problem (ILPP) to prohibit the maximum number of FBMs, while allowing all legal markings in the minimal covering set. The purpose of the ILPP is to maximize the number of FBMs forbidden by the PIs. Then, based on a colored Petri net, all generated monitors are combined into a global control place. Therefore, a supervisor with minimal structural complexity can be constructed. The obtained net model is controlled after the addition of the designed supervisor. Two instances from the literature are considered to illustrate the proposed approach.

Deadlock Prevention Controller for Automated Manufacturing Systems Modeled by S4PR

This article focuses on the problem of deadlock for sequential automated manufacturing systems (AMSs) that allow for the general resource allocation and flexible routings. A class of Petri nets, systems of sequential systems with shared resources (S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> PR), are used to model these considered AMSs. Our previous work has showed that deadlocks in S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> PR are characterized by saturated perfect activity-circuit (PA-circuit). In this article, we divide all saturable PA-circuits into two categories: 1) dependent and 2) independent. An algorithm is proposed to compute all independent saturable PA-circuits. We prove that by adding a monitor for each independent PA-circuit to ensure that it is not saturated, all dependent PA-circuits cannot be saturated either and deadlocks in S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> PR are successfully prevented. The presented method simplifies the structure of the deadlock controller without imposing tight constraints on the system. Finally, the proposed controller is illustrated by some examples.

Control Strategy of RGV Operation Blockage and Deadlock in Plane Mobile Stereo Garage

Aiming at the safety requirements of multi-RGV and multi-lift planar mobile stereo garage access vehicles, a time window-based system RGV operation blocking and deadlock control strategy is proposed. Combining the improved banker algorithm with the time window principle, the banker algorithm is used to evaluate the security of the RGV running path. If an unsafe state is detected, the RGV operation blocking and deadlock control strategy based on the time window algorithm is given. The verification is detailed through specific cases. The results show that the RGV operation blocking and deadlock control strategy proposed in this paper can improve the RGV operation efficiency while increasing the system security.

Adaptive Deadlock Control for a Class of Petri Nets With Unreliable Resources

In an automated manufacturing system (AMS), resources are, in general, subject to unpredictable failures, which invalidate many existing deadlock control strategies. In this article, we propose an adaptive deadlock control policy for an AMS with multiple types of unreliable resources. The considered AMS is modeled with a system of simple sequential processes with resources. First, based on an elementary siphon control method, monitors are added for elementary siphons and some particular dependent siphons to ensure the liveness of a system if there are no resource failures. By considering the fact that an unreliable resource may fail in a system, recovery subnets are added to describe the resource failures and recoveries. Since a monitor added for a siphon may not be able to guarantee that the corresponding siphon is always marked if the failure of a resource in the siphon occurs, the concept of switch controllers is presented so as to make the siphon always remarked if it is emptied by resource failures. It is verified that the adaptive controller proposed in this article can guarantee the liveness of the controlled system no matter whether unreliable resources break down or not. More importantly, if there is no resource failure, the system can maintain predefined production without degrading planned system performance. Finally, examples are presented to illustrate the validity of the proposed method.

Deadlock Control and Fault Detection and Treatment in Reconfigurable Manufacturing Systems Using Colored Resource-Oriented Petri Nets Based on Neural Network

A reconfigurable manufacturing system (RMS) means that it can be reconfigured and become more complex during its operation. In RMSs, deadlocks may occur because of sharing of reliable or unreliable resources. Various deadlock control techniques are proposed for RMSs with reliable and unreliable resources. However, when the system is large-sized, the complexity of these techniques will increase. To overcome this problem, this paper develops a four-step deadlock control policy for the detection and treatment of faults in an RMS. In the first step, a colored resource-oriented timed Petri net (CROTPN) is designed for rapid and effective reconfiguration of the RMS without considering resource failures. In the second step, “sufficient and necessary conditions” for the liveness of a CROTPN are introduced to guarantee that the model is live. The third step considers the problems of failures of all resources in the CROTPN model and guarantees that the model is reliable by designing a common recovery subnet and adding it to the obtained CROTPN model at the second step. The fourth step designs a new hybrid method that combines the CROTPN with neural networks for fault detection and treatment. A simulation is performed using the GPenSIM tool to evaluate the proposed policy under the RMS configuration changes and the results are compared with the existing approaches in the literature. It is shown that the proposed approach can handle any complex RMS configurations, solve the deadlock problem in an RMS, and detect and treat failures. Furthermore, is simpler in its structure.

Colored Resource-Oriented Petri Nets for Deadlock Control and Reliability Design of Automated Manufacturing Systems

Reliability modeling and deadlock control have become important issues in automated manufacturing systems (AMSs) with reliable and unreliable resources. Therefore, this paper develops a reliability modelling approach and deadlock control based on colored resource-oriented timed Petri net (CROTPN) and neural networks to find crucial reliability measures in AMSs. In the first step, a CROTPN with considering resource failures is developed to obtain “sufficient and necessary conditions” for the CROTPN liveness. In the second step, a fault diagnosis and treatment approach is proposed that integrates the obtained unreliable net with neural networks to ensure that the system is reliable. Furthermore, a neural unreliable CROTPN is used to analyze the system reliability. A simulation is carried out to illustrate the approach and compare the results to those found in the literature. The developed approach has been proved to be simpler in structure and can solve the deadlock problem and model AMS reliability.

Event Circular Waits and Their Analysis via Petri Nets

Deadlock control of automated manufacturing systems has been widely investigated in recent decades. According to classical Coffman theory, resource circular wait (RW) is viewed as a necessary condition for deadlocks to occur. However, the fact is not as simple as so. Counterexamples are presented to show that RWs do not necessarily appear together with deadlocks. Event circular waits (EWs) are proposed as an alternative to represent a fundamental necessary condition of deadlocks. First, we present the formal definitions of EWs in a type of Petri nets, i.e., weighted augmented marked graphs (WAMGs), and show that EWs are more general and essential than RWs in describing the cause of deadlocks. Second, we show a new classification of siphons, i.e., types I, II, III, and IV, and illustrate the relationship between undermarked siphons and EWs in the WAMGs. Third, we show that EWs are more efficient than RWs for deadlock avoidance since deadlocks can be avoided earlier at a specified marking by using EWs rather than RWs. Several examples are given to clarify the theory throughout this paper.

Fault-Recovery and Robust Deadlock Control of Reconfigurable Multi-Unit Resource Allocation Systems Using Siphons

A multi-unit resource allocation system usually contains several processes and a number of resources with multiple units. Due to the competition for shared resources in these systems, deadlocks may occur. Recently, researchers have shown an increased awareness in deadlock control strategies for such a kind of systems without considering the dynamic changes such as processing failures and rework by using the Petri net paradigm. This article reports a new strategy for deadlock analysis and control in reconfigurable multi-unit resource systems (MRSs). We discuss a generalized class of Petri nets in which each stage of a process may require a number of units of different types of resources to perform a task. In this way, we can model more complex real systems. Thanks to a generalized class of Petri nets, i.e., the system of sequential systems with shared resources (S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> R), this article proposes an effective integrated strategy for designing robust supervisors for reconfigurable MRSs, and improves an S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> R model to achieve a new model, namely a system of sequential systems with shared resources and part-re-entry (S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> RP), which represents the procedure that a flawed product re-enters a system and is re-processed. We use a siphon-based max-controllability deadlock prevention policy (DPP) to supervise the evolution of the S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> RP, and present a comprehensive analysis to demonstrate that the controlled S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> RP is free of deadlocks. A net analysis tool (INA) is used to test and validate the resulting S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> RP.

Discrete Event Approach to Robust Control in Automated Manufacturing Systems

In recent decades, deadlock control for automated manufacturing systems has been an active area. Most researchers have assumed that allocated resources, such as sensors, actuators, and controllers never fail. However, this case is not prevalent in practice due to the unexpected failure of resources. Thus, the objective of robust control is presented in this article. Several methods have been developed along this direction, such as methods that combine neighborhood constraints and the modified Banker’s algorithm, as well as methods based on critical places. To explore their effectiveness and performance, we not only conduct a comparison investigation but also develop new theoretical results. According to the experimental results, critical place-based approaches are simpler, more efficient, and more comprehensive than the Banker’s algorithm-based approaches in response to resource failures. This article is motivated by the control of production Petri nets; however, the results are also applicable to other more complex systems.

AB&amp;B: An Anytime Branch and Bound Algorithm for Scheduling of Deadlock-Prone Flexible Manufacturing Systems

This work investigates a scheduling problem of deadlock-prone flexible manufacturing systems modeled by place-timed Petri nets. It proposes an anytime branch and bound (AB&B) algorithm for it to minimize system makespan based on the branch tree of a net model and a highly permissive deadlock controller. The proposed algorithm searches a sequence of transitions in the branch tree that evolves the model from the initial marking to the final one. In order to prune the branch tree and increase search speed, this work develops two pruning rules, a lower bound of makespan, and a novel branching strategy. Their usage ensures AB&B’s high search efficiency. Experimental results demonstrate that the proposed algorithm surpasses the state-of-the-art ones. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In practice, scheduling is one of the most important issues for production managers to address. Existing approaches to deadlock-prone flexible manufacturing system (FMS) scheduling have multiparameters. Their settings can impact the scheduling results greatly. Since their turning is a challenging task, it is difficult to find the best parameter settings. This article proposes an anytime branch and bound (AB&B) algorithm for minimizing the makespan of deadlock-prone FMSs. It has only one parameter, i.e., maximal CPU time, which needs no turning. When it is highly tight, AB&B can output a feasible and decent schedule. If it is larger and larger, AB&B can output a better and better schedule. Comparison studies show that AB&B outclasses existing ones significantly. It is suitable for real-time scheduling cases in which satisfied schedules must be offered in a very short time.

Robust Deadlock Detection and Control of Automated Manufacturing Systems With Multiple Unreliable Resources Using Petri Nets

In recent years, the research on robust deadlock control has become increasingly popular in automated manufacturing systems (AMSs) because resource failures may lead any system to stagnation, e.g., deadlock. In this article, we study robust supervisory control issues in AMSs with multiple unreliable resources. Petri nets are used to model the considered AMSs that allow multi-quantity and multi-type of resource acquisitions. A set of integer linear programming formulations are introduced to detect a class of deadlocks that have the maximal number of dead transitions. By analysis, a deadlock is characterized by a saturated circuit, which only consists of a set of unmarked resources and a set of critical transitions. Based on the circuit, a linear marking constraint is developed to prevent such circuits from being saturated. A control place (monitor) with its control variable is thus designed for the constraint to prevent the deadlock from appearing even if some resource failures occur. Therefore, we can synthesize a robust deadlock supervisor, which can guarantee that the controlled system can implement the continual operations even if some unreliable resources fail. Finally, the theoretical analysis and comparative study are provided to elucidate the effectiveness and efficiency of our proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In practice, resource failures in automated manufacturing systems (AMSs) are common. Deadlock prevention control in AMSs allowing resource failures has gained more and more attention from researchers and practitioners. Most prior research is based on the enumeration of either siphons or perfect resource transition circuits whose number exponentially increases with the system scale. This means that the synthesized supervisor has a much complex structure. In this article, based on a special kind of circuits at a deadlock marking detected by using a set of mathematical formulations, we develop an effective and efficient method for AMSs with multiple unreliable resources to iteratively control deadlocks such that the controlled system can continue to operate smoothly even if some unreliable resources fail. The computational and comparative results show that our proposed approach can acquire more permissive states with a simpler supervisor.