一种紧同步随机Petri网模型的性能分析方法

紧同步随机Petri网模型常用于对多个子系统构成的实际系统进行建模.由于状态空间爆炸问题,这种模型的性能分析目前还没有得到很好的解决.首先给出了随机Petri网中顺序、并行、循环、选择这4种基本结构的性能近似等价公式,然后提出了一种同步变迁等价分解(synchronous transition equivalent decomposition,简称STED)法对紧同步随机Petri网进行分解求解,有效地缓解了具有一个或多个同步变迁情况下的空间爆炸问题,该方法对于子模型同构的情况处理简便且十分有效.     

基于Petri网的PLC系统设计分析与远程监控

Petri网在离散事件的动态仿真中有着广泛的应用,而如何将Petri网应用到离散制造系统中具有重大的价值.以离散制造业中最常见的搬运机械手模型为基础,提出了它的Petri网模型设计方法,并且利用科学的转换方法将Petri网转化为梯形图,应用到在制造业中广泛使用的PLC系统中.利用这种设计方法,不仅能够轻松地将Petri网应用到实践当中,还能够对模型的死锁、生产周期和不变量进行定量的分析,给制造系统进行管理控制、故障诊断和现场监控带来方便.     

装配可靠性的模糊广义随机Petri网建模与分析

针对一般广义随机Petri网模型精度低的问题,将模糊数引入到广义随机Petri网,提出模糊广义随机Petri网的概念.结合模糊数包含信息多的优点,利用模糊广义随机Petri网对装配过程进行建模,通过同构的Markov链对模型进行定量分析.用模糊广义随机Petri网模型计算得到的装配可靠度与一般广义随机Petri网模型的装配可靠度进行分析比较,结果表明了模糊广义随机Petri网模型的精度更高.以数控磨床砂轮架为例,证明了上述方法的有效性.     

Petri网在可靠性分析中的研究综述

可靠性的相关研究在安全关键系统中具有重要意义,利用Petri网可以实现对可靠性的形式化建模以及动态行为的描述。首先对基于Petri网的可靠性分析与研究的基本方法进行分类。其次,着重分析了利用随机Petri网求解系统可靠性的基本方法和步骤,针对等价于Markov过程和非Markov过程的两类系统,重点讨论了基于随机Petri网的系统可靠性分析方法,并指出各类分析研究方法的优缺点。进一步,分析和比较了其他各种类型Petri网在可靠性分析中的应用方法及其优缺点。最后,总结了一些常见的Petri网计算机仿真软件,并针对基于Petri网的可靠性研究展望了几个有价值的研究方向。     

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。     

《随机 Petri网和系统性能评价》介绍

《随机 Petri网和系统性能评价》(作者 :林闯 )一书得到国家科学技术学术著作出版基金资助 ,已由清华大学出版社出版。它是一本随机 Petri网理论和技术方面的专著 ,主要内容包括各种随机 Petri网理论和分析技术 ;随机 Petri网的模型方法、模型的分解和压缩技术以及性能界限求解技术 ;随机 Petri网在通信协议、ATM网络、柔性制造系统、计算机系统和软件系统性能评价中的应用 ;随机 Petri网软件工具。本书内容基本上是自包含的 ,内容新颖 ,容易理解 ,便于应用。主要读者对象是计算机、自动控制等相关专业的大学高年级学生、研究生、工程技…     

基于PLC技术的机电设备作动系统协调控制仿真

传统方法在进行机电设备作动系统调控时,存在协调控制误差较大,执行效率差等问题.结合PLC技术,提出一种机电设备作动系统协调控制方法.结合PLC技术中的Petri网法,组建Petri网控制模型;分析Petri网控制模型和梯形图之间的转换关系,完成机电设备作动系统的Petri网建模.将控制模型转换为PLC协调控制程序,以达到机电设备作动系统协调控制的目的.为验证提出方法的有效性,设计对比实验.结果表明,所提方法能够有效降低机电设备作动系统协调控制误差,同时增强系统的执行效率.     

基于随机对象Petri网的柔性制造系统性能分析

为了增强传统对象Petri网的定量分析能力,提出随机对象Petri网模型。该模型具备随机性和层次特性,获得与随机Petri网的等价关系,从宏观和微观2个层面对系统进行性能分析,并将该模型应用到柔性制造系统中。实验结果表明,该系统保留了面向对象的建模能力,具有较强的定量分析能力。     

分布式功能块控制应用的性能分析

IEC61499功能块逐渐被工业采纳。本文针对分布式功能块控制应用（DFBCA）缺乏性能分析方法的情况，提出了一种基于随机Petri网的DFBCA性能分析方法。该方法以DFBCA的运行状态为着手点，利用Petri网易于表示系统中可能发生的各种状态变化及其关系的特点，将DFBCA转换为随机Petri网模型。再利用随机Petri网模型与马尔可夫链（MC）同构的特征，将随机Petri网模型转换为MC。得到的MC为DFBCA的性能分析提供了数学基础。最后基于MC的状态转移矩阵和稳态概率，对在每个状态中的驻留时间、变迁的利用率、变迁的标记流速、子系统延时时间等性能指标进行了分析。通过具体的示例说明了这种性能分析方法的可行性。     

Petri网在生物信息学中的应用

生物信息学是一门正在快速发展的使用数学和计算机技术来构造和分析生物学模型的学科.Petri网是近来被用于生物信息学的有效工具,但是应用的深度和广度还有待深入研究.文中综述了Petri网在生物信息学领域应用的最新研究进展,主要包括三个方面:应用位置/变迁网定性分析生物学对象的结构性质;应用随机Petri网将随机性加入到生物学建模和分析中;应用混合Petri网描述和分析同时具有离散特性和连续特性的生物系统.最后对Petri网在生物信息学领域的应用情况进行总结并展望了未来的研究方向.     

A unified view of product-form approximation techniques for general closed queueing networks

Two major approximate techniques have been proposed for the analysis of general closed queueing networks, namely the aggregation method and Marie's method. The idea of the aggregation technique is to replace a subsystem (a subnetwork) by a flow equivalent single-server with load-dependent service rates. The parameters of the equivalent server are obtained by analyzing the subsystem in isolation as a closed system with different populations. The idea of Marie's method is also to replace a subsystem by an equivalent exponential service station with load-dependent service rates. However, in this case, the parameters of the equivalent server are obtained by analyzing the subsystem in isolation under a load-dependent Poisson arrival process. Moreover, in Marie's case, the procedure is iterative.

In this paper we provide a general and unified view of these two methods. The contributions of this paper are the following. We first show that their common principle is to partition the network into a set of subsystems and then to define an equivalent product-form network. To each subsystem is associated a load-dependent exponential station in the equivalent network. We define a set of rules in order to partition any general closed network with various features such as general service time distributions, pupulation constraints, finite buffers, state-dependent routing. We then show that the aggregation method and Marie's method are two ways of obtaining the parameters of the equivalent network associated with a given partition. Finally, we provide a discussion pertaining to the comparison of the two methods with respect to their accuracy and computational complexity.     

Product-form and stochastic Petri nets: a structural approach

Stochastic Petri nets (SPNs) with product-form solution are nets for which there is an analytic expression of the steady-state probabilities with respect to place markings, as it is the case for product-form queueing networks with respect to queue lengths. The most general kind of SPNs with product-form solution introduced by Coleman et al. (and denoted here by -nets) suffers a serious drawback: the existence of such a solution depends on the values of the transition rates. Thus since their introduction, it is an open question to characterize -nets with product-form solution for any values of the rates. A partial characterization has been obtained by Henderson et al. However, this characterization does not hold for every initial marking and it is expressed in terms of the reachability graph. In this paper, we obtain a purely structural characterization of -nets for which a product-form solution exists for any value of probabilistic parameters of the SPN and for any initial marking. This structural characterization leads to the definition of -nets (Stochastic Parametric Product-form Petri nets). We also design a polynomial time (with respect to the size of the net structure) algorithm to check whether a SPN is a -net. Then, we study qualitative properties of -nets and -nets, the non-stochastic versions of -nets and -nets: we establish two results on the complexity bounds for the liveness and the reachability problems, which are central problems in Petri nets theory. This set of results complements previous studies on these classes of nets and improves the applicability of product-form solutions for SPNs.     

Product form solution for generalized stochastic Petri nets

In this paper, we show the structural characteristics that a particular class of generalized stochastic Petri nets must exhibit in order for their stationary probabilities to have a product-form. Sufficient conditions for identifying such a class are derived and proven with the development of a series of transformations that can also be used to construct, for any GSPN of the class, an equivalent SPN. These resulting SPNs represent the structures that can be analyzed with standard methods for product-form SPNs to establish whether the original GSPNs have product-form solutions and to compute their performance indices with effective approaches based on computationally efficient algorithms that avoid the generation of their underlying state spaces.     

Integrated Performance Models for Distributed Processing in Computer Communication Networks

This paper deals with the analysis of large-scale closed queueing network (QN) models which are used for the performance analysis of computer communication networks (CCN's). The computer systems are interconnected by a wide-area network. Users accessing local/remote computers are affected by the contention (queueing delays) at the computer systems and the communication subnet. The computational cost of analyzing such models increases exponentially with the number of user classes (chains), even when the QN is tractable (product-form). In fact, the submodels of the integrated model are generally not product-form, e.g., due to blocking at computer systems (multiprogramming level constraints) and in the communication subnet (window flow control constraints). Two approximate solution methods are proposed in this paper to analyze the integrated QN model. Both methods use decomposition and iterative techniques to exploit the structure of the QN model such that computational cost is proportional to the number of chains. The accuracy of the solution methods is validated against each other and simulation. The model is used to study the effect that channel capacity assignments, window sizes for congestion control, and routing have on system performance.     

Modeling parallel and distributed systems with finite workloads

In studying or designing parallel and distributed systems one should have available a robust analytical model that includes the major parameters that determine the system performance. Jackson networks have been very successful in modeling computer systems. However, the ability of Jackson networks to predict performance with system changes remains an open question, since they do not apply to systems where there are population size constraints. Also, the product-form solution of Jackson networks assumes steady-state and exponential service centers or certain specialized queueing discipline. In this paper, we present a transient model for Jackson networks that is applicable to any population size and any finite workload (no new arrivals). Using several non-exponential distributions we show to what extent the exponential distribution can be used to approximate other distributions and transient systems with finite workloads. When the number of tasks to be executed is large enough, the model approaches the product-form solution (steady-state solution). We also, study the case where the non-exponential servers have queueing (Jackson networks cannot be applied). Finally, we show how to use the model to analyze the performance of parallel and distributed systems.     

New performance sensitivity formulae for a class of product-form queueing networks

Perturbation analysis (PA) applies a dynamic point of view to the sample paths of stochastic systems; the realization factor, one of the main concepts of PA, measures the final effect of a perturbation on system performance and provides a novel approach in obtaining performance sensitivities. In this paper, we solve analytically the set of equations for realization factors of a two-server cyclic network. We prove an invariance property of the performance sensitivity for Norton's aggregation. Using the results, we derive closed-form formulae for the derivatives of performance measures in a closed queueing network with load-dependent exponential servers. The performance measures have two general forms: customer average and time average. In contrast with the usual approach based on product-form solutions, our results provide additional insights into the performance sensitivity of closed queueing networks and have immediate applications to problems of optimal control. The general formulae are expressed in terms of Buzen's algorithm with a computational complexity comparable to that of the formulae obtained by directly taking the derivatives of the product-form solutions.     

Markovian and analytical models for multiple bus multiprocessor systems with memory blockings

This paper deals with the performance evaluation of asynchronous multiple bus multiprocessor systems where memory modules are temporarily unavailable to processor requests. Such systems cannot be modelled with a product-form queueing network (QN) model because of memory blockings. In this context, we first propose an exact continuous-time Markovian QN model for analyzing small size systems. In order to study medium to large size systems, we also propose several approximate lumped Markovian models and two approximate analytical QN models. The robustness of these approximate models is studied when any memory module gets systematically blocked after each access to this memory module. Results are compared against those obtained either with the exact Markovian QN model or with a stochastic simulation model.     

改进同伦分析方法及推广Kuramoto Sivashinsky方程的近似解

首先介绍了带有两个辅助参数的改进同伦分析方法,然后用该方法得到了推广Kuramoto-Sivashin-sky方程的同伦近似解.所得近似解与精确孤立波解进行比较,发现本文得到的近似解更有效地逼近真实解.因为该解包含了两个辅助参数,所以能够更有效地调节和控制其收敛区域和速度.研究表明带有两个辅助参数的改进同伦分析方法对复杂非线性系统的研究更有它的优点.     

执行机构带宽对动态逆方法的影响及解决方案

本文从理论上分析了执行机构带宽对动态逆闭环控制系统动态特性影响, 发现较低的执行机构带宽会在伪线性系统中引入一个非线性干扰项, 为此提出了两种方法来消除这个非线性干扰项, 一个是采用参考模型的思想设计补偿器提高执行机构子系统的等效带宽, 另一个思路则是直接在非线性反馈项中引入补偿直接对消非线性干扰项. 仿真结果表明, 两类方法都能较好地消除非线性干扰项, 直接补偿方法能精确消除干扰项, 但需要准确动力学模型, 提高等效带宽的方法虽然是近似的, 但能方便地引入自适应算法, 可以抑制执行机构模型参数不确定的影响.     

基于相似度的粗糙集近似算子快速求解

由于经典粗糙集只能处理精确分类问题,基于相似度的粗糙集模型被提出并用于解决不完备信息系统的相关问题.粗糙集通过近似算子对某一给定的概念进行近似表示,科学的求解这些算子对粗糙集理论的发展具有重要意义.本文提出一种新的近似算子快速求解方法,分析证明了所提快速方法比经典方法具有更高的求解效率.文章定义了元素覆盖度、集合覆盖度等概念,使用覆盖度等价关系可以将覆盖粗糙集转化为经典粗糙集,从而简化覆盖粗糙集的相关问题的解决.