An Efficient Deadlock Prevention Policy for Noncyclic Scheduling of Multicluster Tools

A multi-cluster tool is composed of a number of individual cluster tools linked by buffering modules (BMs). The capacity of a BM can be one or two. Aiming at finding an optimal one-wafer cyclic schedule, this paper explores the effect of two-space BMs on the performance of a multi-cluster tool. A Petri net (PN) model is developed to model it by extending resource-oriented PNs. The dynamic behavior of robot waiting and tasks, process modules, and buffers is well described by the model. This paper shows that there is always a one-wafer cyclic schedule that reaches the lower bound of the cycle time of a process-bound tool. Furthermore, a closed-form algorithm is revealed to find such a schedule for the first time for such multi-cluster tools. Illustrative examples are given to show the application and power of the proposed method.

There are wafer fabrication processes in cluster tools that require wafer revisiting. If a swap strategy is applied to dual-arm cluster tools handling wafer revisiting, a three-wafer periodical process is formed with three wafers completed in each period. Such a period contains three cycles in a revisiting process and three cycles in a nonrevisiting one. Hence, analysis and scheduling of such tools become very complicated. In this paper, a Petri net (PN) model is developed to describe their operations. Based on it, it is found that, if a swap strategy is applied, such tools are always in a transient state. A systematic method is then presented to analyze their performance. With the help of the proposed PN model, this work, for the first time, derives the optimality conditions of three-wafer period scheduling. Industrial application examples are given to show the results.

A treelike hybrid multi-cluster tool is composed of both single-arm and dual-arm cluster tools with a treelike topology. Scheduling such a tool is challenging. For a hybrid treelike multi-cluster tool whose bottleneck individual tool is process-bound, this work aims at finding its optimal one-wafer cyclic schedule. It is modeled with Petri nets such that a onewafer cyclic schedule is parameterized as its robots’ waiting time. Based on the model, this work proves the existence of its onewafer cyclic schedule that features with the ease of industrial implementation. Then, computationally efficient algorithms are proposed to find the minimal cycle time and optimal onewafer cyclic schedule. Multi-cluster tool examples are given to illustrate the proposed approach. The use of the found schedules enables industrial multi-cluster tools to operate with their highest productivity.

Petri nets have been recognized as one of the most powerful tools for modeling flexible manufacturing systems (FMSs). Deadlock prevention policies are used to solve the deadlock problems of FMSs. It is well known that theory of regions is the efficient method for obtaining maximally permissive controllers. All legal and live maximal behavior of Petri net models can be preserved by using marking/transition-separation instances (MTSIs) or event-state-separation-problem (ESSP) methods. However, computing all sets of inequalities are an extremely time consuming problem due to the reachability graph of the deadlocked system. In our previous works, we proposed CMTSI method to improve the computational cost. In this paper, the selective siphon method is merged in our new deadlock prevention policy. The merit of the proposed policy is that the number of two types CMTSIs can then be simplified. Experimental results indicate that it is the most efficient policy to obtain maximal permissive behavior of Petri net models.

A PN-based approach to the high-level synthesis of digital systems

Due to the trend towards 450 mm diameter wafers and customisation, an increase in wafer diversity and transient operation are anticipated for multi-cluster tools in wafer fabrication. While most previous studies focus on steady state scheduling problem of cluster tools, research on multi-cluster tools scheduling problems with transient operations is still at early stage. This article addresses the dual-armed multi-cluster tools scheduling problem with transient operations and multiple wafer types. The problem is subject to residency constraints and makespan is adopted as the performance metrics. A non-linear mathematical model of the problem is established. To solve this problem, a time constraint sets-based heuristic algorithm, called the TB algorithm, is proposed in this article. Based on SWAP strategy, this article proposed the conception of virtual buffer modules, thus the TB algorithm converts the dual-armed multi-cluster tool scheduling problem into single-armed multi-cluster tools scheduling problem equivalently. Experimental results indicate that the proposed algorithm is feasible and efficient.

ABSTRACTTo improve the efficiency of wafer fabrication, this work addresses the scheduling and control problems of mixed-processing with multiple wafer types in cluster tools. Then, based on a developed Petri net (PN) model, it presents a general model for cluster tools with multiple wafer types and the conventional swap strategy. By analyzing the coordination mechanism between wafers processing and robot tasks, necessary and sufficient conditions are established to check the schedulability of the system that is operated by using the conventional swap strategy. If the system is not schedulable checked by such schedulability conditions, a constraint-guided heuristic algorithm and a conflicts-avoiding algorithm are developed to obtain a reasonable schedule. Finally, illustrative examples are presented to show the applications of the proposed method.

Based on elementary siphons of Petri nets and the mixed integer programming approach, an improved deadlock prevention policy is developed for S/sup 3/PR. Siphons in such a plant Petri net model are divided into elementary and dependent ones. Our policy consists of two stages: siphon control and control-induced siphon control. At first stage, a monitor (control place) is added for each elementary siphon such that it is invariant-controlled. Due to the addition of monitors to plant model, control-induced siphons are possibly generated in the augmented S/sup 3/PR, which is an RCN-merged net. The second stage sees that monitors are added to make always marked control-induced siphons in the resultant RCN-merged net without generating new control-induced siphons. Compared with our previous work, the deadlock prevention policy developed in this paper can lead to a structurally simple liveness-enforcing Petri net supervisor by adding only a small number of monitors and arcs. An FMS example is utilized to illustrate the proposed methods.

The main challenge in scheduling multi-cluster tools in semiconductor manufacturing is the interactions among clusters. These interactions create a k-unit optimal production that do not exist in single-cluster tools. This paper analyzes optimal scheduling of k-unit cycle production of multi-cluster tools with single-blade robots. A resource-based method is used to analytically derive closed-form expressions for the minimal cycle time of a multi-cluster tool. Conditions for decoupling multi-cluster tools and optimality conditions for the widely used pull schedule are also presented. An example from industry production is used to illustrate the derived formula and decoupling conditions.

Deadlocks in automated flexible manufacturing systems (FMS)is a crucial problem in production process. This paper presents an effective deadlock prevention policy for a special class of Petri nets, S3PR. Based on siphon method, a set of generalized mutual exclusion constraints (GMEC) expressed by the marking vector can be found. Then monitors based on the GMEC are added to the plant model such that the siphons in the resultant net are all invariant-controlled and no emptiable siphon is generated due to the addition of the monitors. This novel deadlock prevention policy can usually lead to a maximally permissive supervisor by adding a number of monitors and arcs, the number of monitors is decided by the number of emptiable siphon in the net system, the proposed policy can work excellently in proper size petri net system. Finally two manufacturing examples are utilized to illustrate the proposed method.

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.

Modelling and analysis of kanban-controlled (just-in-time) production systems under realistic assumptions presents a number of challenges, including the ability to conduct both qualitative and quantitative analysis, and the ability to model control policies. These challenges are due, in part, to station interdependence, blocking and starvation due to limited buffer spaces, and the necessity of modelling both material and kanban flows. Petri nets (PNs) have recently emerged as a promising approach for modelling manufacturing systems. PNs are a graphical and mathematical technique useful for modelling concurrent, asynchronous, distributed, parallel, non-deterministic and stochastic systems. PN models can be analysed to determine both their qualitative and quantitative properties. In this paper, we develop stochastic, coloured PN (SCPN) models of a JIT system utilizing two different kanban control policies: a traditional kanban system (TKS) policy and a flexible kanban system (FKS) policy. The resulting models can be used to represent JIT systems of arbitrary size, producing single or multiple types of products, with fixed order points 1. The models are shown to be live and bounded, and can be simulated to produce quantitative results. Sample simulation results are presented to illustrate the models' capabilities.

Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.INDEX TERMS Flexible manufacturing systems (FMS), deadlock, deadlock prevention, Petri Nets (PN), liveness enforcing supervisor (LES), PN computation tools.

In the above paper, it proposes a deadlock prevention policy for a flexible manufacturing system (FMS), which needs the complete state enumeration of the FMS that is modeled with Petri nets. The reachability graph of a Petri-net model is divided into two parts: the live zone (LZ) and the deadlock zone (DZ). The states in the LZ of the reachability graph of a Petri net constitute the legal behavior of the net from the viewpoint of deadlock prevention. The concept of first-met bad markings is proposed. A first-met bad marking is a node in DZ, whose father nodes are in LZ. The deadlock prevention policy is used in an iterative way. At each iteration, a first-met bad marking is identified from the reachability graph of a Petri net to be controlled. The reachability of a first-met bad marking is prohibited by adding a monitor, establishing a marking invariance relationship between the additional monitor and the activity places that are marked under the first-met bad marking. To achieve this, without a formal proof, [Lemma 1] is developed as shown in this article.

Some methods for deriving protocol specifications from given service specifications with time constraints have been proposed. However, existing methods cannot treat the class of service specifications with both parallel synchronization and data values. They also assume that all clocks in the distributed system are synchronized. We propose an algorithm to derive a correct protocol specification automatically from a given service specification described in an extended model of time Petri nets where the above restrictions are eliminated. Using our method, we will be free from considering the details of communication delays on the design of real-time distributed systems.