基于Petri网和并发调度标识图的并发任务调度的建模与分析

在云计算及网格计算环境下,由于资源具有分布、异构、动态、自治等特点,其并发任务的调度更加复杂,迫切需要强有力的图形与数学工具对其进行建模与分析。Petri网是描述与分析并发、异步、动态等事件的理想的图形与数学工具。给出了并发任务调度的加权时延Petri网模型。可达标识图是分析Petri网动态特性的一个重要工具,但它不能表达Petri网中变迁的并发关系,尤其是不便于分析被描述系统的时间特性。提出了并发调度标识图的概念,给出了构造时延Petri网的并发调度标识图的算法。最后,利用并发调度标识图分析了并行下载的时间特性。     

基于T-图的复杂Petri网约简算法研究

为了解决Petri网并行控制和模拟运行的问题,提出基于T-图的复杂Petri网并行约简方法。根据Petri网的并发性,给出基于T-图的Petri网模型的子网划分原理,提出子网划分的条件,并给出理论证明和实例验证;在此基础上,提出基于T-图的Petri网的子网划分算法,并对其子网划分过程相关概念进行形式化;最后,给出一个银行存取款系统的应用示例,对其Petri网模型的子网划分进行理论分析和算法的编程验证,实验结果与理论分析相一致。实验结果表明,该算法是对复杂结构Petri网进行划分、化简、分析的一种有效方法。     

基于带标记的并发可达标识图的关键路径的求解方法

将AOE 网转换成有色时延Petri网模型,在模型转换过程中同时计算出各位置所对应的事件的最早开始时间,给出了模拟AOE 网的有色时延Petri网模型的带标记的并发可达标识图的构建算法;利用并发可达标识图中的标记序列直接得到关键路径并计算出完成所有活动所需的最短时间。实例与仿真实验结果表明,当AOE网中平均存在3个以上的并发活动时,所提方法执行效率优于传统的求解关键路径的算法,并发活动越多,所提算法效率越高。     

网格计算资源调度的层次Petri网建模与分析

本文给出了网格计算资源的三层调度方案,并利用层次颜色Petri网对这一调度方案进行了建模与分析。对不同层次的资源调度建立了相应的颜色时延Petri网模型,不同层次的颜色时延Petri网模型可以有不同的行为表现,体现了网格计算资源的异构、自治等特点。给出了层次颜色Petri网的可迭任务图的概念及构造算法,并利用可达任务图,对网格计算资源调度系统的运行状态进行了分析。     

基于Petri网的工作流过程模型及资源分布分析

针对工作流系统的特点对时延Petri网模型进行扩展,提出了一种新的工作流建模方法,即扩展时延Petri网。给出了扩展时延Petri网的定义,并用该方法分析了工作流四种基本模型;给出了利用排队论和随机Petri网理论计算工作流模型时间性能指标的新方法,用这种方法可求得与实例到达率相关的工作流模型平均完成时间。最后应用上述方法讨论了工作流资源分布的几种模式,并与模拟结果加以对比,计算结果的最大误差在3%左右,说明基于扩展时延Petri网的方法是分析工作流系统时间性能的有效方法。     

基于时延Petri网数据并行问题的分析

Petri网作为一种直观的图形建模工具和一种具有丰富数学基础的形式模型,非常适合描述具有并发、异步和分布特征的系统。数据并行即将相同的操作同时作用于不同的数据,利用时延变迁Petri网来分析数据并行问题,可以找出具有相同操作的结构,这对于数据并行问题在并行机上进行模拟有很大好处。     

基于P-不变量的Petri网并行化方法的研究

为使Petri网系统能够并行执行或模拟运行,提出了基于P-不变量的Petri网并行化方法.根据Petri网系统具有同步与并发的特点,给出基于P-不变量的Petri网模型分割、进程创建条件与并行化分析.在此基础上,提出并行进程创建条件拓展定理并给予证明和实例验证.给出实现并行化所需要解决的Petri网模型行为规范的形式化、P-不变量求解与基于P-不变量的Petri网并行化方法.实验结果表明,基于P-不变量的Petri网系统的并行化方法是可行和有效的.     

Petri网的硬件实现

Petri网是异步并发现象建模的重要工具,Petri网的硬件实现将为并行控制器的设计提供有效的途径.给出了几种Petri网系统的硬件实现方法,包括带抑制弧和允许弧的C/E系统、P/T系统、T-时延Petri网系统;给出了硬件实现中非纯网的处理方法.首先讨论实现各种Petri网的逻辑电路;然后用ABEL语言对逻辑电路进行描述;最后给出了一个用解释Petri网描述的服务系统的例子,说明如何使用硬件(CPLD)实现的方法.实验结果表明了上述方法的正确性.这对于离散事件动态系统控制器的设计,尤其是片上并行控制器、多处理器芯片的设计都具有十分重要的意义.     

多功能流水线调度的Petri网分析

在单功能流水线的Petri网模型[1]基础上，给出了一种基于时延Petri网的多功能流水线建模方法。并给出其资源状态转换图来反映其运行过程中资源的使用状况，利用这种资源状态转换图可求出其任意输入序列的最佳调度方案。     

时间Petri网模拟能力的研究

模型的模拟能力一直是系统建模方面的一个重要研究课题。本文先用一个直观的“零检验”例子说明时间Petri网的模拟能力比传统Petri网要强,并首次证明了时间Petri网与计算科学的最高模型——图灵机有相等的模拟能力;最后给出了另外一种含时间因素的时延Petri网向时间Petri网的转换方法,这说明了时间Petri网虽然形式上较为简单,但其模拟能力却并不比其它含时间因素的Petri网逊色,同时为时延Petri网的研究提供了另外一种有效方法。     

New NP-Complete Problems in Performance Evaluation of Concurrent Systems Using Petri Nets

Timed Petri nets are useful in performance evaluation of concurrent systems. The maximum computation rate is achieved for minimal cycle time of timed Petri net. It is known that minimal cycle time problem for P-invariant Petri nets is NP-complete. In this paper we prove that the minimal cycle time problem, for non-P-invariant Petri nets and for a small subclass of P-invariant Petri nets called free-choice nets having live and safe marking, is NP-complete.     

一种基于代数语义的软件体系结构求精方法

软件体系结构是引导需求到实现的桥梁,目前在软件体系结构建模方法中主要分为形式化和非形式化两种。针对大型分布式系统的体系结构采用Petri网进行建模,兼顾了可视化操作和形式化的准确性,同时利用细化求精操作建立体系结构的层次模型,有效解决了状态空间爆炸问题。此外,在求精过程中为了保证用于下层求精的子网能准确表达上层行为规约,引入了进程代数来刻画Petri网的行为语义。最后,给出了进程项构造子网的算法及案例研究,并通过开源工具验证上述内容的正确性。     

Relating SPO and DPO graph rewriting with Petri nets having read, inhibitor and reset arcs

It belongs to the folklore that graph grammars can be seen as a proper generalisation of Petri nets. In this paper we show how this intuitive relationship can be made formal. The double-pushout approach to graph rewriting turns out to be strictly related to Petri nets with read and inhibitor arcs, while the single-pushout approach has strong connections to Petri nets with read and reset arcs.     

A new methodology for analyzing distributed systems modeled by petri nets

Distributed computing systems can be modeled adequately by Petri nets. The computation of invariants of Petri nets becomes necessary for proving the properties of modeled systems. This paper presents a two-phase, bottom-up approach for invariant computation and analysis of Petri nets. In the first phase, a newly defined subnet, called the RP-subnet, with an invariant is chosen. In the second phase, the selected RP-subnet is analyzed. Our methodology is illustrated with two examples viz., the dining philosophers' problem and the connection-disconnection phase of a transport protocol. We believe that this new method, which is computationally no worse than the existing techniques, would simplify the analysis of many practical distributed systems.     

A characterization of the stochastic process underlying astochastic Petri net

Stochastic Petri nets (SPN's) with generally distributed firing times can model a large class of systems, but simulation is the only feasible approach for their solution. We explore a hierarchy of SPN classes where modeling power is reduced in exchange for an increasingly efficient solution. Generalized stochastic Petri nets (GSPN's), deterministic and stochastic Petri nets (DSPN's), semi-Markovian stochastic Petri nets (SM-SPN's), timed Petri nets (TPN's), and generalized timed Petri nets (GTPN's) are particular entries in our hierarchy. Additional classes of SPN's for which we show how to compute an analytical solution are obtained by the method of the embedded Markov chain (DSPN's are just one example in this class) and state discretization, which we apply not only to the continuous-time case (PH-type distributions), but also to the discrete case     

Checking system boundedness using ordinary differential equations

Boundedness is one of the most important properties of discrete Petri nets. Determining the boundedness of a Petri net is usually done through building coverability graph or coverability tree. However, the computation is infeasible for complex applications because the size of the coverability graph may increase faster than any primitive recursive functions. This paper proposes a new technique to check the boundedness without causing this problem. Let a concurrent system be represented by a (discrete) Petri net. By relaxing the (discrete) Petri net to a continuous Petri net, we can model the concurrent system by a family of ordinary differential equations. It has been shown that the boundedness of the discrete Petri net is equivalent to the boundedness of the solutions of the corresponding ordinary differential equations. Hence, we can check the boundedness of a (discrete) Petri net by analyzing the solutions of a family of ordinary differential equations. A case study demonstrates the benefits of our technique.     

Homomorphisms between models of parallel computation

To better understand the relationships between different models of parallel computation, we introduce a new computation system formulation and develop general notions of homomorphisms and isomorphisms between computation systems. This allows us to study relations between vector addition systems, vector replacement systems, Petri nets, and generalized Petri nets. Results in this paper that may be of particular interest include a long list of properties preserved under homomorphism, and constructions that show that vector replacement systems can be simulated by vector addition systems, and that generalized Petri nets can be emulated by Petri nets.     

Fuzzy rule base systems verification using high-level Petri nets

In this paper, we propose a Petri nets formalism for the verification of rule-based systems. Typical structural errors in a rule-based system are redundancy, inconsistency, incompleteness, and circularity. Since our verification is based on Petri nets and their incidence matrix, we need to transform rules into a Petri nets first, then derive an incidence matrix from the net. In order to let fuzzy rule-based systems detect above the structural errors, we are presenting a Petri-nets-based mechanism. This mechanism consists of three phases: rule normalization, rules transformation, and rule verification. Rules will be first normalized into Horn clauses, then transform the normalized rules into a high-level Petri net, and finally we verify these normalized rules. In addition, we are presenting our approach to simulate the truth conditions which still hold after a transition firing and negation in Petri nets for rule base modeling. In this paper, we refer to fuzzy rules as the rules with certainty factors, the degree of truth is computed in an algebraic form based on state equation which can be implemented in matrix computation in Petri nets. Therefore, the fuzzy reasoning problems can be transformed as the liner equation problems that can be solved in parallel. We have implemented a Petri nets tool to realize the mechanism presented fuzzy rules in this paper.