基于Gillespie算法的生化随机Petri网演化分析

Petri网既有严格的数学表达方式,又有直观的图形描述形式,是当前生物化学系统模拟和定性分析的一个有力工具。作为标准Petri网的一个重要扩展,随机Petri网使得可以定量地分析生物化学系统。建立了两个典型的生物化学系统的随机Petri网模型：Schlogl系统和转录调控系统,并使用Gillespie随机仿真算法模拟了这些生化随机Petri网模型的状态演化。     

流体随机Petri网与混合Petri网的比较分析

流体随机Petri网和混合Petri网作为传统Petri网的拓展,可以建模离散成分和连续成分并存的混合系统,也可用于解决离散模型的状态空间爆炸问题.由于这两种建模机制远未发展成熟,分析比较它们的异同点有助于机制本身的进一步发展完善,有助于为特定的应用选择合适的建模方法.本文讨论了流体随机Petri网和混合Petri网的定义、连续标识、分析方法、以及相互转换的可能性.结论是这两种建模机制是互补的,各自适合于特定的应用场合.     

随机时间Petri网综述

随机时间Petri网作为一种灵活有力的建模机制,被广泛应用于计算机和通信系统的性能与可靠性评价。综述了随机时间Petri网各主要予类的发展历程与研究现状。首先介绍了随机时间Petrl网的一些基本概念,然后回顾了广义随机Petri网,简要总结了处理状态空间爆炸问题的主要途径,讨论了非马尔科夫随机Petri网及其分析技术,最后详细分析了流体随机Petri网。     

代谢网络结构与功能的Petri网分析

发展基因组尺度代谢网络模型的模拟和分析方法有助于学习这些网络的结构与功能关系,是当前计算系统生物学领域的一个重要研究主题。由于具备严格的数学描述,直观的图形表达,外加存在众多的算法和工具,Petri网可能成为代谢网络模拟和分析的有力工具。应用位置/变迁网来分析代谢网络的结构与功能特征,首先建立了巴斯德毕赤酵母代谢的Petri网模型,随后计算了该模型中的P、T不变量,并讨论了它们的生物学意义。     

随机Petri网在性能分析中的应用

本文介绍一种随机Ｐｅｔｒｉ网及其在性能分析中的应用，这种网的可达图同构于马尔柯夫链，从而可依据马氏理论求解一些性能指标。     

基于价格随机Petri网的服务协同建模与分析

针对一个企业不仅重视系统性能,也重视系统成本的问题,提出了价格随机Petri网,用于系统的价格和性能分析。价格随机Petri网既具有随机Petri网在性能分析方面的优势,又能计算系统的成本,对系统的建立和改进具有宏观指导作用。基于价格随机Petri网对服务协同典型模型提出了等价化简方法,并进行了相应的证明,此方法在一定程度上提高了系统分析的效率。     

混合Petri网的流体随机Petri网模型

混合Petri网和流体随机Petri网作为混合系统的建模方法,其内在的建模机制和分析方法不尽相同,而且这两种机制远未发展成熟.分析并建立它们之间相互转换的方法有助于机制本身的发展完善,并利用对方的建模原语和分析方法对系统进行多角度的分析.提出了一阶混合Petri网转换成流体随机Petri网的形式化方法及转换后变迁合并的方法,并给出了转换和合并方法的正确性证明,最后结合实例简要阐述了这两种方法的实现过程.     

基于延迟特性的改进随机Petri网建模与分析

随机Petri网能够分析过程中的随机特性,但是不能有效地描述延迟和花费问题.为了解决上述问题,提出了一种基于延迟特性的随机Petri网模型.该模型能根据延迟时间和过程的随机性得到总的时间和花费特性.给出了状态类延迟时间和延迟花费的串联及并联化简方法.最后,通过首都机场的实例说明该方法能更好地表示出应急救援的时间和花费特性.     

基于广义随机Petri网的装备维修保障建模与分析

信息化条件下,传统的装备维修保障已经不适应现代战场的需要.通过BPR(Business Process Reengineering)可以有效提高其效率,而对改造效果的评价成为是否实施BPR的关键问题.研究了如何利用广义随机Petri网对装备维修保障流程进行建模,对模型进行化简求出可达图构建与模型同构的马尔科夫链(MC),并基于MC的稳定状态概率进行所要求的系统性能分析,获得流程系统的主要性能指标可以为重新设计业务流程提供支持和依据.     

基于随机着色Petri网的RUDP协议建模与分析

鉴于传输层传输协议TCP的低效率和UDP的不可靠性,本文提出一种新型的多帧无线传输RUDP协议,同时引入广义随机着色Petri网（GSCPN）,并利用GSCPN对本RUDP进行建模和分析,为以后更好地研究RUDP协议提供模型参考,具有很好的理论价值。     

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.     

Performance analysis using Petri nets

The purpose of this paper is to focus on the implementation issues associated with using Petri nets for the performance analysis of discrete event dynamic systems while demonstrating several applications in manufacturing systems. Practical modeling issues will be discussed and several applications will be presented that illustrate the advantages and limitations of this methodology. These issues lead to the definition of several research problems in Petri nets for performance analysis.     

基于随机Petri网的机群系统可信赖性研究

随机Petri网(SPN)是一种灵活有力的建模工具,在可信赖性研究方面已形成较为成熟的理论体系.采用SPN网对机群系统前端分配器及后端服务器进行建模,通过在系统建模时对前端分配器给予必要的修复保证,给出整个机群系统的SPN模型,在模型分析的基础上给出了机群系统的可信赖性参数,并对模型进行了仿真分析.仿真结果表明,在对关键系统前端分配器给予修复保证后,系统模型的稳态可用性将大大提高.     

Adaptive decomposition and approximation for the analysis of stochastic Petri nets

We present a new approximate solution technique for the numerical analysis of stochastic Petri nets and related models. The approach combines numerical iterative solution techniques and fixed point computations using the complete knowledge of state space and generator matrix. In contrast to other approximation methods, the proposed method is adaptive by considering states with a high probability in detail and aggregating states with small probabilities. Probabilities are approximated by the results derived during the iterative solution. Thus, a maximum number of states can be predefined and the presented method automatically aggregates states such that the solution is computed using a vector of a size smaller or equal to the maximum. By means of non-trivial examples it is shown that the approach computes good approximations with a low effort for many models.     

Discrete event diagnosis using labeled Petri nets. An application to manufacturing systems

In this paper an approach to on-line diagnosis of discrete event systems based on labeled Petri nets is presented. The approach is based on the notion of basis markings and justifications and it can be applied both to bounded and unbounded Petri nets whose unobservable subnet is acyclic. Moreover it is shown that, in the case of bounded Petri nets, the most burdensome part of the procedure may be moved off-line, computing a particular graph called Basis Reachability Graph.Finally, the effectiveness of the proposed procedure is analyzed applying a MATLAB diagnosis toolbox we developed to a manufacturing example taken from the literature.     

Modeling and scheduling of ratio-driven FMS using unfolding time Petri nets

In this paper, we focus on the analysis of a cyclic schedule for the determination of the optimal cycle time and minimization of the Work in Process (WIP for short). Especially, this paper deals with product ratio-driven FMS cyclic scheduling problem with each other products and ratios using Timed Petri nets unfolding (TPN for short). TPN slicing and unfolding are applied to analyze this FMS model. We can divide original system into subsystem using TPN slices and change iterated cycle module into acyclic module without any loss of other behavior properties.     

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.