Comparing digraph and Petri net approaches to deadlock avoidance inFMS

Flexible manufacturing systems (FMSs) are modern production facilities with easy adaptability to variable production plans and goals. These systems may exhibit deadlock situations occurring when a circular wait arises because each piece in a set requires a resource currently held by another job in the same set. Several authors have proposed different policies to control resource allocation in order to avoid deadlock problems. These approaches are mainly based on some formal models of manufacturing systems, such as Petri nets (PNs), directed graphs, etc. Since they describe various peculiarities of the FMS operation in a modular and systematic way, PNs are the most extensively used tool to model such systems. On the other hand, digraphs are more synthetic than PNs because their vertices are just the system resources. So, digraphs describe the interactions between jobs and resources only, while neglecting other details on the system operation. The aim of this paper is to show the tight connections between the two approaches to the deadlock problem, by proposing a unitary framework that links graph-theoretic and PN models and results. In this context, we establish a direct correspondence between the structural elements of the PN (empty siphons) and those of the digraphs (maximal-weight zero-outdegree strong components) characterizing a deadlock occurrence. The paper also shows that the avoidance policies derived from digraphs can be implemented by controlled PNs.     

Deadlock avoidance policy for Petri-net modeling of flexiblemanufacturing systems with shared resources

Multiple products through a flexible manufacturing system (FMS) with limited resources can lead to deadlock. In this paper, the authors study the problem of deadlock avoidance by using the Petri net (PN) model for FMSs and introducing the concept of deadlock structure. The necessary and sufficient conditions to prevent deadlock are characterized. The authors use a state feedback restriction policy which prevents some enabled transitions from firing for avoiding deadlock in the system. In particular, when the number of any key kind of resources is greater than one, this policy is minimally restrictive and allows the maximal use of resources in the system. The authors present the PN realization of these restriction policies when the closed-loop system can be modeled by a live PN. The restriction policies can be easily implemented. An example is provided for illustration     

部分可控Petri网分布式死锁监控器设计

研究了部分可控Petri网柔性制造系统中的死锁避免的问题。为了保证死锁避免和资源最大允许利用,提出了基于分支定界法的Petri网死锁监控器的优化设计方法,采用多个子控制节点对全局状态建立分布式监控器,通过行为可行和分布可行对分布式监控器下合法状态空间进行检测,对最大行为可行子集建立线性规划模型求解最大分布可行合法状态集,得到分布式监控器下的最大合法状态子空间。最后,建立了柔性制造系统的部分可控Petri网模型,针对系统的死锁避免等多个行为特性要求,分别设计了集中式监控器和分布式监控器,分布式监控器能有效地避免死锁。     

柔性制造系统中多路径条件下的死锁避免第二部分:控制策略

在第一部分推导出的面向资源的着色Ｐｅｔｒｉ的基础上讨论ＦＭＳ中多路径条件下的死锁避免控制策略问题，给出了无死锁运行的充要条件及其相应的控制策略。     

On the Optimality of Randomized Deadlock Avoidance Policies

This paper revisits the problem of selecting an optimal deadlock resolution strategy, when the selection criterion is the maximization of the system throughput, and the system is Markovian in terms of its timing and routing characteristics. This problem was recently addressed in some of our previous work, that (i) provided an analytical formulation for it, (ii) introduced the notion of randomized deadlock avoidance as a generalization of the more traditional approaches of deadlock prevention/avoidance, and detection and recovery, and (iii) provided a methodology for selecting the optimal randomized deadlock avoidance policy for a given resource allocation system (RAS) configuration. An issue that remained open in the problem treatment of that past work, was whether the proposed policy randomization is essential, i.e., whether there exist any RAS configurations for which a randomized deadlock avoidance policy is superior to any other policy that does not employ randomization. The work presented in this paper establishes that for the basic problem formulation where the only concern is the (unconstrained) maximization of the system throughput—or the other typical performance objectives of minimizing the system work-in-process and mean sojourn time—randomization of the deadlock resolution strategy is not essential. However, it is also shown that, sometimes, it can offer an effective mechanism for accommodating additional operational constraints, like the requirement for production according to a specified product mix. Furthermore, the undertaken analysis provides an analytical characterization of the dependence of the aforementioned performance measures on the transition rates relating to the various events of the underlying state space, which can be useful for the broader problem of synthesizing efficient scheduling policies for the considered class of resource allocation systems.     

Controller design and performance evaluation for deadlock avoidance in automated flexible manufacturing cells

In this paper, the design of a deadlock avoidance controller is described. The uncontrolled system is modeled using colored Petri nets. The system controller is based on a restrictive (not maximally permissive) deadlock avoidance policy to resolve deadlocks and control the real-time resource allocation decisions in the system. Performance evaluation of systems controlled by not maximally permissive algorithms is essential in determining the applicability and effectiveness of the control algorithms. The performance of the controlled system is compared with performance of optimal control policies to quantify the effects of the restrictiveness of the deadlock avoidance policy on system performance.     

一类FMS的最佳活Petri网模型的综合

利用Petri网为一类柔性制造系统建模,并讨论避免系统死锁问题.通过Petri网模 型的结构分析,证明了系统产生死锁的一个充分必要条件.给出了避免死锁的最佳控制器,它 可以通过给系统的Petri网模型增加一些新的位置与相应的弧来实现.从而导出了这类制造 系统的最佳活Petri网模型.     

A divide-and-conquer-method for the synthesis of liveness enforcing supervisors for flexible manufacturing systems

In this paper a divide-and-conquer-method for the synthesis of liveness enforcing supervisors (LES) for flexible manufacturing systems (FMS) is proposed. Given the Petri net model (PNM) of an FMS prone to deadlocks, it aims to synthesize a live controlled Petri net system. For complex systems, the use of reachability graph (RG) based deadlock prevention methods is a challenging problem, as the RG of a PNM easily becomes unmanageable. To obtain the LESs from a large PNM is usually intractable. In this paper, to ease this problem the PNM of a system is divided into small connected subnets. Each connected subnet prone to deadlocks is then used to compute the LES for the original PNM. Starting from the simplest subnet prone to deadlocks to make the subnet live, monitors (control places) are computed. The RG of each subnet is considered and split into a dead-zone (DZ) and a live-zone. All states in the DZ are prevented from being reached by means of a well-established invariant-based control method. Next, the computation of monitors is followed for bigger subnets. Previously computed monitors are included within the bigger subnets based on a criterion. This process keeps the DZ of the bigger subnets smaller compared with the original uncontrolled subnets. When all subnets are live we obtain a set of monitors that are included within the PNM to obtain a partially controlled PNM (pCPNM). A new set of monitors is also computed for the pCPNM. Finally, a live controlled Petri net system is obtained. The proposed method is generally applicable, easy to use, effective and straightforward although its off-line computation is of exponential complexity in theory. Its use for FMS control guarantees deadlock-free operation and high performance in terms of resource utilization and system throughput. Two FMS deadlock problems from the literature are used to illustrate the applicability and the effectiveness of the proposed method.     

避免FMS死锁的控制策略

本文利用ＦＭＳ的Ｐｅｔｒｉ网模型讨论系统的死锁问题，给出了系统死锁的必要充分条件，提出了避免系统死锁的反馈控制策略，这种策略对系统的限制小，在许多情形下是最优的。     

Design of a maximally permissive liveness-enforcing supervisor with a compressed supervisory structure for flexible manufacturing systems

In this paper, a deadlock prevention policy for flexible manufacturing systems (FMS) is proposed, which can obtain a maximally permissive liveness-enforcing Petri net supervisor while the number of control places is compressed. By using a vector covering approach, the sets of legal markings and first-met bad markings (FBM) are reduced to two small ones, i.e., the minimal covering set of legal markings and the minimal covered set of FBM. A maximally permissive control purpose can be achieved by designing control places such that all markings in the minimal covered set of FBM are forbidden and no marking in the minimal covering set of legal markings is forbidden. An integer linear programming problem is designed to minimize the number of control places under an assumption that a control place is associated with a P-semiflow. The resulting net has the minimal number of control places on the premise that the assumption holds, and possesses all permissive states of a plant. The only problem of the proposed method is its computational complexity that makes it inapplicable to large-scale Petri net models. An FMS example from the literature is presented to illustrate the proposed method.     

Modeling and deadlock avoidance of automated manufacturing systems with multiple automated guided vehicles.

An automated manufacturing system (AMS) contains a number of versatile machines (or workstations), buffers, an automated material handling system (MHS), and is computer-controlled. An effective and flexible alternative for implementing MHS is to use automated guided vehicle (AGV) system. The deadlock issue in AMS is very important in its operation and has extensively been studied. The deadlock problems were separately treated for parts in production and transportation and many techniques were developed for each problem. However, such treatment does not take the advantage of the flexibility offered by multiple AGVs. In general, it is intractable to obtain maximally permissive control policy for either problem. Instead, this paper investigates these two problems in an integrated way. First we model an AGV system and part processing processes by resource-oriented Petri nets, respectively. Then the two models are integrated by using macro transitions. Based on the combined model, a novel control policy for deadlock avoidance is proposed. It is shown to be maximally permissive with computational complexity of O (n2) where n is the number of machines in AMS if the complexity for controlling the part transportation by AGVs is not considered. Thus, the complexity of deadlock avoidance for the whole system is bounded by the complexity in controlling the AGV system. An illustrative example shows its application and power.     

感知范围受限的群机器人自主围捕算法

针对在有障碍物场地中感知范围受限的群机器人协同围捕问题,本文首先给出了机器人个体、障碍物、目标的模型,并用数学形式对围捕任务进行描述,在此基础上提出了机器人个体基于简化虚拟速度和基于航向避障的自主围捕控制律.基于简化虚拟速度模型的控制律使得机器人能自主地围捕目标同时保持与同伴的距离避免互撞;基于航向的避障方法提升了个体...     

具有多项式时间复杂性的避免制造系统死锁控制策略

基于系统 Petri 网模型, 研究自动制造系统的避免死锁问题. 对不含中心资源的制造系统, 证明了它只包含安全和死锁两类可达状态. 通过一步向前看的方法, 给出了系统多项式时间复杂性的最佳避免死锁策略. 对一般系统定义了一种辅助 Petri 网. 利用辅助网的最佳避免死锁策略, 提出了综合一般制造系统多项式复杂性的避免死锁策略的方法.     

基于混合法的叶片FMS控制系统研究

本文基于Ｐｅｔｒｉ网建模的混合法，建立了叶片ＦＭＳ控制系统活的、安全和可逆的Ｐｅｔｒｉ网模型，应用该模型开发了叶片ＦＭＳ控制系统仿真器，可成功地避免叶片ＦＭＳ的死锁产生。     

Fault-tolerant deadlock avoidance algorithm for assembly processes

Unreliable resources pose challenges in design of deadlock avoidance algorithms as resources failures have negative impacts on scheduled production activities and may bring the system to dead states or deadlocks. This paper focuses on the development of a suboptimal polynomial complexity deadlock avoidance algorithm that can operate in the presence of unreliable resources for assembly processes. We formulate a fault-tolerant deadlock avoidance controller synthesis problem for assembly processes based on controlled assembly Petri net (CAPN), a class of Petri nets (PNs) that can model such characteristics as multiple resources and subassembly parts requirement in assembly production processes. The proposed fault-tolerant deadlock avoidance algorithm consists of a nominal algorithm to avoid deadlocks for nominal system state and an exception handling algorithm to deal with resources failures. We analyze the fault-tolerant property of the nominal deadlock avoidance algorithm based on resource unavailability models. Resource unavailability is modeled as loss of tokens in nominal Petri Net models to model unavailability of resources in the course of time-consuming recovery procedures. We define three types of token loss to model 1) resource failures in a single operation, 2) resource failures in multiple operations of a production process and 3) resource failures in multiple operations of multiple production processes. For each type of token loss, we establish sufficient conditions that guarantee the liveness of a CAPN after some tokens are removed. An algorithm is proposed to conduct feasibility analysis by searching for recovery control sequences and to keep as many types of production processes as possible continue production so that the impacts on existing production activities can be reduced.     

Avoidance versus detection and recovery problem in buffer-spaceallocation of flexibly automated production systems

Motivated by recent developments in the semiconductor manufacturing industry, this paper undertakes an analytical investigation of the problem of selecting optimally the deadlock resolution strategy for buffer space allocation in flexibly automated production systems. In the process, it extends the behavioral models for the aforementioned systems currently considered in the literature, to account for probabilistic uncontrollable effects like the requirement for extra finishing steps and/or rework, and it introduces a new deadlock resolution scheme, characterized as randomized deadlock avoidance. The combination of these two extensions brings the considered system behavior(s) to the realm of probabilistic automata, an area of increasing academic interest. For the resulting model, and under the assumption of Markovian timings, it develops an analytical methodology for selecting the optimal deadlock resolution strategy that maximizes the steady-state system throughput, and it demonstrates its effectiveness through application to a "prototype" system configuration. The obtained results provide an interesting analytical expression of the need to assess the gains obtained by the increased concurrency supported by the deadlock detection and recovery strategy versus the productivity losses experienced under this approach due to increased system blocking, and/or additional material handling overheads. It turns out that, for the considered system configuration, the optimal selection scheme switches between detection and recovery and pure deadlock avoidance, every time that the time cost of deadlock recovery, tau(d), crosses a threshold Theta, which is a function of the remaining system behavioral and timing parameters. Beyond its own theoretical merit, this last result raises also the question of whether the policy randomization introduced in this work will ever enhance the performance of any configuration in the considered class of Resource Allocation Systems (RAS); this issue will be investigated in a sequel paper.     

NECESSARY AND SUFFICIENT CONDITIONS FOR DEADLOCKS IN FLEXIBLE MANUFACTURING SYSTEMS BASED ON A DIGRAPH MODEL

As typical discrete event systems, flexible manufacturing systems have been extensively studied in such aspects as modeling, control and performance analysis. One important topic in the study of such systems is the deadlock detection, prevention and avoidance. In the past decade, two major modeling formalisms, i.e., Petri nets and digraphs, have been adopted for developing deadlock control policies for flexible manufacturing systems. In this paper, the concepts of slack, knot, order and effective free space of circuits in the digraph are established and used to concisely and precisely quantify the sufficient conditions for a system state to be live. Necessary conditions for this liveness is quantified for a special class of system states ‐ called evaluation states. The significance of the result is that the conditions are true for avoiding both primary deadlocks and impending deadlocks that are arbitrary steps away from a primary one, whereas only second level deadlocks have been studied in the literature. Examples are provided to illustrate the method.     

Fault-tolerant and maximally-permissive FMS controllers right out of the box—an automatic design approach

This paper presents a comprehensive, all-in-one approach to automatic generation of high-level coordination controllers for flexible manufacturing systems (FMS). The approach comprises an intuitive graphical world wide web (WWW) user interface to specify the FMS layout and the desired production sequences. It also includes algorithms (a) to generate a proper Petri Net model for the specified plant, (b) to set up optimal (i.e. minimally restrictive) collision and deadlock avoidance policies together with a proper supervisory controller to enforce these policies, and (c) to react to disturbances such as machine breakdowns. These algorithms run in the design (offline) phase without user interaction. During online operation the operator only needs to indicate the arrival of new raw materials and the removal of finished products using the same user interface as mentioned before. An example implementation demonstrates the applicability and efficiency of the proposed approach.     

On Siphon Computation for Deadlock Control in a Class of Petri Nets

As a structural object, siphons are well recognized in the analysis and control of deadlocks in resource allocation systems modeled with Petri nets. Many deadlock prevention policies characterize the deadlock behavior of the systems in terms of siphons and utilize this characterization to avoid deadlocks. This paper develops a novel methodology to find interesting siphons for deadlock control purposes in a class of Petri nets, i.e., a system of simple sequential processes with resources . Resource circuits in an are first detected, from which, in general, a small portion of emptiable minimal siphons can be derived. The remaining emptiable ones can be found by their composition. A polynomial-time algorithm for finding the set of elementary siphons is proposed, which avoids complete siphon enumeration. It is shown that a dependent siphon can always be controlled by properly supervising its elementary siphons. A computationally efficient deadlock control policy is accordingly developed. Experimental study shows the efficiency of the proposed siphon computation approach.     

DEADLOCK AVOIDANCE FOR FLEXIBLE MANUFACTURING SYSTEMS WITH CHOICES BASED ON DIGRAPH CIRCUIT ANALYSIS

Due to existence of concurrent part flows and resource sharing in modern automated flexible manufacturing systems (FMS), deadlock is a common problem and its occurrence causes loss of productivity. When a manufacturing system is modeled by a digraph, existence of circuits in such a graph is a necessary condition for deadlock. Our previous work further showed that the knot and order of a circuit is closely related to impending deadlocks — a type of deadlock that is more difficult to detect. In this paper, we extend our previous work on deadlock avoidance for flexible manufacturing systems to allow choices in process flows (a.k.a., flexible part routing). Due to introduction of choices, part flow dynamics become more sophisticated and our previous results are no longer valid. A systematic circuit analysis is performed in this paper. New concepts such as broken circuit, basic circuit, choice circuit and supremal circuit are introduced to reduce significantly the number of circuits thus improving efficiency of our approach. The extended method is highly permissive with the adjusted effective free space calculation to capture more necessary parts flow dynamics, especially when multiple knots exist in the digraph model. The online policy runs in polynomial time once the set of basic circuits of the digraph is computed offline. Simulation results on selected examples are given.