Reduction rules for time Petri nets

The goal of net reduction is to increase the effectiveness of Petri-netbased real-time program analysis. Petri-net-based analysis, like all reachabilitybased methods, suffers from the state explosion problem. Petri net reduction is one key method for combating this problem. In this paper, we extend several rules for the reduction of ordinary Petri nets to work with time Petri nets. We introduce a notion of equivalence among time Petri nets, and prove that our reduction rules yield equivalent nets. This notion of equivalence guarantees that crucial timing and concurrency properties are preserved.     

基于DTPN的时间Petri网的组件级化简规则

时间Petrl网(TPNs)是实时系统时间特性常用的描述和验证的Petri网模型.组件级化简方法是TPN模型常用的分析方法,在保持外部可观察时间特性的前提下,将组件TPN模型化简成一个很简单的TPN模型.然而它却失去了组件内部的性质,如冲突和并发等性质.文中引人延迟时间Petri网(DTPN),通过组件TPN模型向DTPN模型转化,使化简后模型既保持外部可观察时间特性,又保持组件内部的冲突和并发等性质.为了分析化简后的DTPN模型,文中还提出了一种新的DT-PN调度分析方法.最后通过对一个C2系统的组件TPN模型的分析实例,验证该方法的有效性.     

时间Petri网的ECS-class可达性分析方法

时间Petri网(TPNs)是实时系统时间特性常用的描述和验证的Petri网模型,可达性分析是Petri网模型最基本分析方法.基于"状态类(State-class)"的可达性分析方法不能正确计算并发情况下的时间延迟,而基于"带时间戳的状态类(CS-class)"的可达性分析方法不能正确处理冲突情况下的事件调度,因此提出了"扩展的带时间戳的状态类(ECS-class)"可达性分析方法.它不仅正确的计算时间延迟,而且合理地调度事件.并对一个时间Petri网模型进行可达性分析验证.     

Reachability analysis of real-time systems using time Petri nets

Time Petri nets (TPNs) are a popular Petri net model for specification and verification of real-time systems. A fundamental and most widely applied method for analyzing Petri nets is reachability analysis. The existing technique for reachability analysis of TPNs, however, is not suitable for timing property verification because one cannot derive end-to-end delay in task execution, an important issue for time-critical systems, from the reachability tree constructed using the technique. In this paper, we present a new reachability based analysis technique for TPNs for timing property analysis and verification that effectively addresses the problem. Our technique is based on a concept called clock-stamped state class (CS-class). With the reachability tree generated based on CS-classes, we can directly compute the end-to-end time delay in task execution. Moreover, a CS-class can be uniquely mapped to a traditional state class based on which the conventional reachability tree is constructed. Therefore, our CS-class-based analysis technique is more general than the existing technique. We show how to apply this technique to timing property verification of the TPN model of a command and control (C2) system.     

Reduction rules for time Petri nets

 The goal of net reduction is to increase the effectiveness of Petri-net-based real-time program analysis. Petri-net-based analysis, like all reachability-based methods, suffers from the state explosion problem. Petri net reduction is one key method for combating this problem. In this paper, we extend several rules for the reduction of ordinary Petri nets to work with time Petri nets. We introduce a notion of equivalence among time Petri nets, and prove that our reduction rules yield equivalent nets. This notion of equivalence guarantees that crucial timing and concurrency properties are preserved. Received September 12, 1994/July 4, 1995     

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。     

Compositional semantics of a real-time prototyping language

The formal semantics of a prototyping language for hard real-time systems, PSDL, is given. PSDL provides a data flow notation augmented by application-orientation timing and control constraints to describe a system as a hierarchy of networks of processing units communicating via data streams. The semantics of PSDL are defined in terms of algebraic high-level Petri nets. This formalism combines algebraic specifications of abstract data types with process and concurrency concepts of Petri nets. Its data abstraction facilities are used to define the meaning of PSDL data types, while high-level Petri nets serve to model the casual and timing behavior of a system. The net model exposes potential concurrency of computation and makes all synchronization needs implied by timing and control constraints explicit and precise. Time is treated as state of clocks, and clocks are modeled as ordinary system components. The net semantics provides the basis for applying analysis techniques and semantic tools available for high-level Petri nets     

模拟实时系统的点区间优先级时间Petri网与TCTL验证

时间Petri网为实时系统提供了一种形式化的建模方法, 时间计算树逻辑(TCTL)为描述实时系统与时间相关的设计需求提供了一种逻辑化的表达方式, 因此基于时间Petri网的TCTL模型检测广泛应用于实时系统的正确性验证.然而对于一些涉及优先级的实时系统, 例如多核多任务实时系统, 这里不仅需要考虑任务之间的时间约束还要考虑任务执行的优先级以及引入优先级带来的抢占式调度问题, 致使相应的建模和分析变得更加困难.为此, 本文提出了点区间优先级时间Petri网, 通过在时间Petri网上定义变迁发生的优先级以及变迁的可挂起性, 从而可以模拟实时系统的抢占式调度机制, 即首先高优先级的任务抢占低优先级的任务所占用的资源, 导致后者被中断, 然后前者执行完毕后释放资源, 最后后者再次获得资源从中断的地方恢复.本文通过点区间优先级时间Petri网来模拟多核多任务实时系统, 使用TCTL来描述它们的设计需求, 设计了相应的模型检测算法, 开发了相应的模型检测器以验证它们的正确性.我们通过一个实例来说明我们的模型和方法的有效性.     

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.     

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.     

基于变迁覆盖的制造系统死锁控制策略

基于系统Petri网模型,研究柔性制造系统的死锁控制问题.论文利用变迁覆盖为系统设计活性控制器.变迁覆盖是由一组极大完备资源变迁回路组成的集合,其变迁集覆盖了Petri网中所有极大完备资源变迁回路的变迁集.验证变迁覆盖的有效性,然后仅对有效变迁覆盖中的极大完备资源变迁回路添加控制位置,就得到系统的活性受控Petri网.这种受控Petri网包含的控制位置个数少,从而结构相对简单.最后通过一个例子说明了所提出的死锁控制策略的构成与特点.     

信标基底的可选择性在制造系统死锁控制中的应用

本文基于Petri网模型,讨论柔性制造系统的死锁控制问题.为了建立结构简单的Petri网控制器,本文在以前的工作中提出了信标基底的概念.信标基底是一组满足特定条件的严格极小信标集合.本文证明基于不同的信标基底,建立的受控系统其容许性能也不同.而容许性是评价死锁控制策略优劣的重要标准之一.故如何选择信标基底,提高受控系统的容许性能是值得研究的问题.本文讨论了使受控系统容许性能大大提高的信标基底的选择条件.基于该条件,为柔性制造系统建立有效的死锁控制策略.最后,通过两个例子解释该条件和策略.     

基于Petri网合成与化简的分布式数据库系统并发控制的死锁检测

利用模块化设计的思想，首先为分布式数据库系统中各事务的每一种操作(读锁、写锁、解锁)构造一个基本的加权Petri网模型，并给出了加权Petri网共享合成的概念、然后利用共享合成技术，动态地构造各站点的加权Petri网模型，以适应系统的动态变化．此外，本文利用Petri网的化简技术，极大地简化了各站点的Petri网模型，之后利用同步合成技术构造出整个系统的Petri网模型，较好地解决了Petri网的可达性分析中可能出现的状态“爆炸”问题．最后给出了判断整个系统是否出现死锁的充分必要条件．     

SAT-Solving the Coverability Problem for Petri Nets

Net unfoldings have attracted great attention as a powerful technique for combating state space explosion in model checking, and have been applied to verification of finite state systems including 1-safe (finite) Petri nets and synchronous products of finite transition systems. Given that net unfoldings represent the state space in a distributed, implicit manner the verification algorithm is necessarily a two step process: generation of the unfolding and reasoning about it. In his seminal work McMillan (K.L. McMillan, Symbolic Model Checking. Kluwer Academic Publishers, 1993) showed that deadlock detection on unfoldings of 1-safe Petri nets is NP-complete. Since the deadlock problem on Petri nets is PSPACE-hard it is generally accepted that the two step process will yield savings (in time and space) provided the unfoldings are small.In this paper we show how unfoldings can be extended to the context of infinite-state systems. More precisely, we show how unfoldings can be constructed to represent sets of backward reachable states of unbounded Petri nets in a symbolic fashion. Furthermore, based on unfoldings, we show how to solve the coverability problem for unbounded Petri nets using a SAT-solver. Our experiments show that the use of unfoldings, in spite of the two-step process for solving coverability, has better time and space characteristics compared to a traditional reachability based implementation that considers all interleavings for solving the coverability problem.     

On Hybrid Petri Nets

Petrinets (PNs) are widely used to model discrete event dynamic systems(computer systems, manufacturing systems, communication systems,etc). Continuous Petri nets (in which the markings are real numbersand the transition firings are continuous) were defined morerecently; such a PN may model a continuous system or approximatea discrete system. A hybrid Petri net can be obtained if onepart is discrete and another part is continuous. This paper isbasically a survey of the work of the authors' team on hybridPNs (definition, properties, modeling). In addition, it containsnew material such as the definition of extended hybrid PNs andseveral applications, explanations and comments about the timingsin Petri nets, more on the conflict resolution in hybrid PNs,and connection between hybrid PNs and hybrid automata. The paperis illustrated by many examples.     

Complex-valued token Petri nets

This paper presents a new extension to ordinary Petri nets (PNs) that uses complex-valued tokens. By allowing two kinds of tokens, "real" and "imaginary," each place marking contains both quantity and type information. Complex-valued token PNs were designed to integrate seamlessly with other popular Petri net extensions such as timed nets, stochastic nets, and colored nets. This simple and intuitive application of complex numbers and complex arithmetic to PNs provides a unique modeling tool. Some examples show the capabilities of this proposed class of PNs. Note to Practitioners-Discrete-event systems are often man-made systems such as transportation systems, computer communication networks, distributed software, and manufacturing systems. They typically involve the flow of information and physical goods through a network. The flow itself evolves in continuous time but the initiation or completion of the event happens at a discrete point in time. Analyzing the system's performance is key to their successful operation. This paper presents a new approach to performance analysis with application to supply-chain management.     

应用必需信标的Petri网死锁预防策略

本文提出了表征一个Petri网子类,即S4R网(system of sequential systems with shared resources)中死锁问题的必需信标的概念和一种将混合整数规划算法与必需信标控制相结合的死锁预防策略.在该策略的迭代过程中,混合整数规划算法发现被控的Petri网中是否存在最大的死标识信标,若存在,则通过库所分类和迭代式的信标提取,得到必需信标,添加相应的控制库所,满足必需信标的最大可控性,从而实现被控的Petri网活性的目的.理论分析和算例验证表明了该策略的正确性和有效性.     

On systematic methods to remove redundant monitors from liveness-enforcing net supervisors

Petri nets based deadlock prevention for flexible manufacturing systems has received much attention over the past decade, primarily due to the seminal work of Ezpeleta et al. in 1995. A Petri net based deadlock prevention mechanism is usually implemented by adding monitors or control places to a plant Petri net model such that liveness can be enforced. The significance of this methodology lies in that both a plant model and its supervisor are in a same formalism-Petri nets. Due to the inherent complexity of Petri nets, in theory, the number of additional monitors that have to been added to achieve liveness-enforcement purpose for an uncontrolled plant model is exponential with respect to the size of the model. This paper first proposes a systematic method to minimize the number of additional monitors in a liveness-enforcing Petri net supervisor such that the resultant net system has the same permissive behavior while liveness can still be preserved. Furthermore, for the liveness-enforcing Petri net supervisors of flexible manufacturing systems, which have some particular property, an algorithm is developed such that more permissive liveness-enforcing Petri net supervisors can be obtained after liveness-restrictive monitor removal. Compared with the existing techniques of eliminating redundant monitors in the literature, the complete state enumeration of a supervisor is avoided, which implies the high computational efficiency of the methods in this paper. Flexible manufacturing examples are used to demonstrate the proposed approaches.     

基于Petri网的柔性制造系统一种预防死锁方法

基于Petri网的结构特性分析,研究了FMS(柔性制造系统)一种预防死锁方法.提出了 Petri网的一种特殊拓扑结构--基本信标的概念.在Petri网中基本信标的集合是SMS(严格极 小信标)集合的一个真子集.尤其在大型Petri网系统中,基本信标的集合比SMS的集合要小得 多.对于Petri网的一个子类S3PR,只对每一个基本信标添加一个库所使其不被清空,就可实现 预防死锁,也就是说无须控制S3PR的所有SMS而达到无信标被清空的目的.此外,对于S3PR, 还提出了一种求取SMS和基本信标的方法.相对于现在普遍采用的控制所有SMS来预防死锁 的策略,其具三方面优势.1)只需控制少量的SMS即所谓的基本信标.相应地,添加少量的控制 库所和连接弧,就可得到无死锁或活的Petri网.2)不需要先行计算出极小信标的集合.3)明显 地,这种方法更适合大型Petri网系统.我们通过穿插在文中的一个例子来说明这些方法.