Scheduling analysis of FMS: An unfolding timed Petri nets approach

We are interested in Flexible Manufacturing Systems (FMS) scheduling problem. Different methods have been explored to solve this problem and mainly to master its combinatorial complexity: NP-hard in the general case. This paper presents an analysis of the cyclic scheduling for the determination of the optimal cycle time and the minimization of the Work In Process (WIP). Especially, the product ratio-driven FMS cyclic scheduling problem using timed Petri nets (TPN) unfolding is described. In addition, it has been proved that the Basic Unit of Concurrency (BUC) is a set of the executed control flows based on the behavioral properties of the net. Using our method, one could divide original system into some subnets based on machine's operations using BUC and analyze the feasibility time in each schedule. Herein, our results showed the usefulness of transitive matrix to slice off some subnets from the original net, and explained in an example.     

基于精炼操作的Petri网建模及其分析方法

针对复杂系统的Petri网建模及其分析问题,定义了Petri网的精炼操作及其相关的Petri网模型.基于序列投影,建立精炼Petri网与原网、子网间的动态行为关联关系,并分析了该精炼操作的相关动态性质,得到一组性质保持判据.最后,基于该方法实现了一个顺序资源共享系统的应用案例的建模及其分析.所提出的方法不仅为复杂系统的Petri建模提供了新的思路,而且有助于复杂Petri网模型的分析和验证.     

Timed petri nets in modeling and analysis of simple schedules for manufacturing cells

It is shown that a large class of flexible manufacturing cells can be modeled using timed Petri nets. Net models of simple schedules (i.e., schedules in which exactly one part enters and one leaves the cell during each cycle) are conflict-free nets. Two complementary approaches to analysis of such models are presented: invariant analysis and throughput analysis. Invariant analysis provides analytic (or symbolic) solutions for the cycle time of a cell analyzing (invariant) subnets of the original net. Throughput analysis performs a series of performance-preserving net reductions to simplify the original model. Several directions for further research are indicated.     

Decentralized supervisory controller design to avoid deadlock in Petri nets

A decentralized supervisory controller design approach, using overlapping decompositions, is proposed for discrete-event systems modelled by Petri nets to avoid deadlock. In this approach, the given original Petri net is first decomposed into overlapping Petri subnets. A controller for each disjoint Petri subnet is then designed. A controller for the expanded Petri net is next obtained by combining these controllers in a certain way. In the final phase, the controller obtained for the expanded Petri net is contracted in a certain way to obtain a controller for the original Petri net. It is proved that this final controller avoids deadlock in the original Petri net.     

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.     

Using Timed Petri Net to Model Instruction-Level Loop Scheduling with Resource Constraints

This paper uses timed petri net to model and analyze the problem of instructionlevel loop scheduling with resource constraints,which has been proven to be an NP complete problem.First,we present a new timed Petri net model to integrate functional unit allocation,register allocation and spilling into a unified theoretical framework.Then we develop a state subgraph,called Register Allocation Solution Graph,which can effectively describe the major behavior of our new model.the main property of this state subgraph is that the number of all its nodes is polynomial.Finally we present and prove that the optimum loop schedules can be found with polynomial computation complexity,for almost all practical loop programs.Our work lightens a new idea of finding the optimum loop schedules.     

Minimizing cycle time and group scheduling, using Petri nets a study of heuristic methods

The objective of this paper is a study of minimizing the maximum completion time min F _max, or cycle time of the last job of a given family of jobs using flow shop heuristic scheduling techniques. Three methods are presented: minimize idle time (MIT); Campbell, Dudek and Smith (CDS); and Palmer. An example problem with ten jobs and five machines is used to compare results of these methods. A deterministic t-timed colored Petri net model has been developed for scheduling problem. An execution of the deterministic timed Petri net allows to compute performance measures by applying graph traversing algorithms starting from initial global state and going into a desirable final state(s) of the production system. The objective of the job scheduling policy is minimizing the cycle time of the last job scheduled in the pipeline of a given family of jobs. Three heuristic scheduling methods have been implemented. First, a sub-optimal sequence of jobs to be scheduled is generated. Second, a Petri net-based simulator with graphical user interface to monitor execution of the sequence of tasks on machines is dynamically designed. A deterministic t-timed colored Petri net model has been developed and implemented for flexible manufacturing systems (FMS). An execution of the deterministic timed Petri net into a reachability graph allows to compute performance measures by applying graph traversing algorithms starting from initial global state to a desirable final state(s) of the production system.     

柔性制造系统的时间Petri网建模与分析

时间Petri网是描述和验证实时系统最常用的形式模型之一。建立基于时间 Petri网的典型柔性制造系统模型,利用状态类分析方法,定量计算所有可行调度及其执行时间,进而获得最优调度,为复杂柔性制造系统的建模与调度提供有效的模型支持。     

Hybrid heuristic search approach for deadlock-free scheduling of flexible manufacturing systems using Petri nets

Based on the Petri net models of flexible manufacturing systems (FMSs), this paper focuses on deadlock-free scheduling problem with the objective of minimizing the makespan. Two hybrid heuristic search algorithms for solving such scheduling problems of FMSs are proposed. To avoid deadlocks, the deadlock control policy is embedded into heuristic search strategies. The proposed algorithms combine the heuristic best-first strategy with the controlled backtracking strategy based on the execution of the Petri nets. The scheduling problem is transformed into a heuristic search problem in the reachability graph of the Petri net, and a schedule is a transition sequence from the initial marking to the final marking in the reachability graph. By using the one-step look-ahead method in the deadlock control policy, the safety of a state in the reachability graph is checked, and hence, deadlock is avoided. Experimental results are provided and indicate the effectiveness of the proposed hybrid heuristic search algorithms in solving deadlock-free scheduling problems of FMSs. Especially, the comparison against previous work shows that both new algorithms are promising in terms of solution quality and computing times.     

着色时间工作流网任务调度的时间约束分析

为实现工作流管理系统中的任务调度和时间管理,避免流程在多任务运转时产生溢出,提高流程的工作效率。采用不固定时延定义了着色时间Petri网,通过控制任务间的最小时距避免了溢出,并用任务监测器实现了相应的控制策略。以各任务间的时间间隔最小为优化目标,对串行、并行、条件选择和循环四种基本着色时间工作流网进行了时序分析和任务调度,推导出多任务在基本着色时间工作流网调度的数学模型和着色时间工作流网整体运行时间函数的计算公式。最后通过一个审批流程对论述的任务调度方法进行了验证。     

基于平行Petri网的制造系统调度与控制一体化方法

为了消除制造系统调度层与控制层之间的隔阂,实现对生产事件快速灵活响应,本文提出了一种调度与控制一体化的方法.首先,定义了一种新型Petri网模型,即平行Petri网,从而集成地描述了传感器、执行器、任务和资源信息,构建制造系统的信息物理系统模型;其次,提出了一种从平行Petri网到赋时Petri网的抽象简化方法,大规模压缩优化调度所需搜索的状态空间;再次,定义了策略Petri网以描述最优调度策略.最后,给出了平行Petri网与策略Petri网同步执行算法,使得平行Petri网与物理系统同步执行.     

Optimizing layer‐based scheduling algorithms for parallel tasks with dependencies

Programming with parallel tasks leads to task graphs with dependencies representing a parallel program. Scheduling algorithms are employed to find an efficient execution order of the parallel tasks. A large variety of scheduling algorithms exist, including layer‐based scheduling algorithms for homogeneous target platforms that build consecutive layers of independent parallel tasks and schedule each layer separately. Although these scheduling algorithms provide good results in terms of scheduling algorithm runtime and schedule execution time, the resulting schedules leave room for optimization. This article proposes an optimization for arbitrary layer‐based scheduling algorithms, which is called Move‐blocks algorithm. Given a layer‐based schedule of the parallel tasks, this algorithm moves blocks of parallel tasks into preceding layers in order to reduce the overall execution time of a task‐based application. Suitable blocks of parallel tasks are identified by the algorithm Find‐blocks, which is employed together with the Move‐blocks algorithm. The algorithm Move‐blocks is applied to four well‐known scheduling algorithms. A detailed evaluation for a wide range of test cases is given. Copyright © 2010 John Wiley & Sons, Ltd.     

一类受控Petri网的反馈控制

受控Petri网是离散事件动态系统(DEDS)的一种控制理论模型.通过模型来研究实现 禁止状态避免的最大允许反馈控制是DEDS控制理论中的一个重要课题.文中对受控Petri网 的一个子类(非受控变迁子集的外延子网为TC网)讨论控制综合问题,给出求这类受控网中实 现禁止状态避免的最大允许反馈控制的一个算法.     

A Petri net-based particle swarm optimization approach for scheduling deadlock-prone flexible manufacturing systems

This paper proposes an effective hybrid particle swarm optimization (HPSO) algorithm to solve the deadlock-free scheduling problem of flexible manufacturing systems (FMSs) that are characterized with lot sizes, resource capacities, and routing flexibility. Based on the timed Petri net model of FMS, a random-key based solution representation is designed to encode the routing and sequencing information of a schedule into one particle. For the existence of deadlocks, most of the particles cannot be directly decoded to a feasible schedule. Therefore, a deadlock controller is applied in the decoding scheme to amend deadlock-prone schedules into feasible ones. Moreover, two improvement strategies, the particle normalization and the simulated annealing based local search, are designed and incorporated into particle swarm optimization algorithm to enhance the searching ability. The proposed HPSO is tested on a set of FMS examples, showing its superiority over existing algorithms in terms of both solution quality and robustness.     

多处理器调度算法实现及其Petri网建模与仿真

多处理器调度算法在嵌入式实时系统领域中起着关键的作用。根据多处理器的特点,提出一种实时多处理器动态分割并行调度算法SPara。该算法解决了此前多处理器算法,如Myopic、EDPF等仅依据截止期对任务调度产生的问题,实现了增加任务紧迫度限制的调度策略,以及针对执行时间长、截止期紧迫任务的有效调度方法。同时算法结合高级颜色时间Petri网理论进行建模并仿真。测试结果表明,SPara算法在处理器利用率以及调度成功率方面较Myopic等算法有较大提高。     

基于变迁指标分解的Petri网性质分析

Petri网的分解技术是复杂网系统分析的一种重要手段,基于变迁指标的分解方法将系统分解为一组T-网。通过获得分解子网的结构性质以及子网与原网间的性质保持关系,得到了判定原网结构性质的一些方法和结论;同时给出了判定原网系统活性的一个条件。所得结果为结构复杂Petri网的性质分析提供了有效的方法。     

A decomposition approach to non-preemptive real-time scheduling

Consider the problem of scheduling a set ofn tasks on a uniprocessor such that a feasible schedule that satisfies each task's time constraints is generated. Traditionally, researchers have looked at all the tasks as a group and applied heuristic or enumeration search to it. We propose a new approach called thedecomposition scheduling where tasks are decomposed into a sequence of subsets. The subsets are scheduled independently, in the order of the sequence. It is proved that a feasible schedule can be generated as long as one exists for the tasks. In addition, the overall scheduling cost is reduced to the sum of the scheduling costs of the tasks in each subset.Simulation experiments were conducted to analyze the performance of decomposition scheduling approach. The results show that in many cases decomposition scheduling performs better than the traditional branch-and-bound algorithms in terms of scheduling cost, and heuristic algorithms in terms of percentage of finding feasible schedules over randomly-generated task sets.     

面向对象Petri网的约简和系统死锁的检测

提出一套保持面向对象Petri网性质的约简规则和检测方法。该方法运用面向对象的概念和技术,为对象子网进行分层,且在保持子网性质的前提下,利用约简规则依次简化每层对象子网,并同时检测对象子网以及相应对象子网间的死锁关系,直到所有对象处理完毕。最后通过实例对所提出的方法进行了验证,验证结果表明该方法的提出大大减少了网中的节点,有效降低了面向对象Petri网中死锁检测的复杂度。