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。     

基于随机Petri网的性能与可靠性评价

近年来,随机Petri网在柔性制造系统、计算机及通信系统等领域的性能与可靠性评价中得到了广泛的应用。文章首先介绍了性能与可靠性评价,然后回顾了广义随机Petri网及其状态空间爆炸问题,最后讨论了非马尔科夫随机Petri网。     

生化网络的随机Petri网建模与分析

细胞的行为是随机性的,学习细胞中的随机性有助于理解细胞的组织,设计和进化。建立、确认和分析随机的生化网络模型是当前计算系统生物学领域的一个重要研究主题。当前,标准的Petri网模型已经成为生化网络模拟和定性分析的有力工具。尝试使用随机Petri网对生化网络进行建模与分析,简单描述了随机Petri网理论对标准Petri网的扩充,通过对二聚作用和肌动蛋白这两个典型例子的建模与演化模拟,介绍、论证了随机Petri网理论的新应用。     

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。     

随机Petri网理论在GSM-R通信系统中的仿真应用

列车和无线闭塞中心在多数情况下通信处于正常状态,但在实际通信过程中可能出现以下几种引发故障因素：传输数据出错、连接丢失、越区切换、端到端传输延时。应用仿真主要考虑高速列车在移动闭塞区间条件下GSM-R无线通信系统的可靠性,结合随机Petri网理论对GSM-R铁路无线通信系统故障恢复事件进行建模和分析,给出了随机Petri网表示的列车与无线闭塞中心通信的故障恢复模型,并采用TimeNET仿真工具对GSM-R通信系统的可靠性进行分析得出相应结论。     

基于随机Petri网模型的网络协议性能测试

分析了协议性能测试需要解决的主要问题,并以随机Petri网为形式化工具,描述了网络协议的服务质量.提出从随机Petri网模型到TTCN(tree and tabular combined notation)测试集的转换规则,并根据随机Petri网模型生成了协议性能测试例.     

无界Petri网的可达树的综述

Petri网自提出以来得到了学术界和工业界的广泛关注. Petri网系统的可达性是最基本性质之一.系统的其他相关性质都可以通过可达性进行分析.利用等价的有限可达树来研究无界Petri网可达性,依然是一个开放性问题.该研究可以追溯到40年前,但由于问题本身的复杂性和难度太大,直到最近20年,经过国内外诸多学者的不懈努力,才逐渐取得了一些阶段性的成果和部分突破.本文回顾了近40年来国内外学者为彻底解决该问题作出的贡献.重点对4种开创性的研究成果展开讨论,分别为有限可达树、扩展可达树、改进可达树及新型改进可达树.探讨了今后无界Petri网可达性问题的研究方向.     

一类受控Petri网的基于管程的广义互斥控制

本文讨论受控Ｐｅｔｒｉ网的广义互斥控制问题。首先，我们给出了此问题存在管程最小约束控制解的充要条件，然后，对一类其不可控 子网为有限状态机的受控Ｐｅｔｒｉ网，证明了其广义互斥控制问题总存在管程最小约束控制解，并给出了综合这一管程的控制的算法。     

Petri网的广义笛积运算

文[1]曾给出Petri网的两种合成方法，即Ｐ／Ｔ网的加法和笛积运算。本文再提出几种Ｐ／Ｔ网的广义笛积运算，这几种运算都较好地保持网的结构性质。对此给出实例，显示了它们在Ｐ／Ｔ网的合成与分析中的作用。     

Comparison of Hybrid Systems and Fluid Stochastic Petri Nets

Hybrid Systems are modelsof interacting digital and continuous devices with applicationsin the control of aircraft, computers, or modern cars for instance.Concurrently, Fluid Stochastic Petri Nets (FSPNs) have been introducedas an extension of stochastic Petri nets to model physical systemsthat contain continuous fluid quantities controlled by discretelogic, as well as a means to deal with the possible state explosionof discrete models. Of course, an FSPN is by definition a hybridsystem but in this paper, we compare a general hybrid systemsformalism with FSPN formalism. The conclusion of this paper,suplemented by some examples, is that fluid stochastic Petrinets and hybrid system formalism can be converted from one tothe other. Although there is a price to pay for such a conversion,the conversion can transfer the solution methods from one tothe other and thus help the development of both formalisms.     

Algebraic structure of some stochastic discrete event systems,with applications

Generalized semi-Markov processes (GSMPs) and stochastic Petri nets (SPNs) are generally regarded as performance models (as opposed to logical models) of discrete event systems. Here we take the view that GSMPs and SPNS are essentially automata (generators) driven by input sequences that determine the timing of events. This view combines the deterministic, logical aspects and the stochastic, timed aspects of the two models. We focus on two conditions, (M) and (CX) (which we previously developed to study monotonicity and convexity properties of GSMPs), and the antimatroid and lattice structure they imply for the language generated by a GSMP or SPN. We illustrate applications of these structural properties in the areas of derivative estimation, simulation variance reduction, parallel simulation, and optimal control.Research supported in part by NSF grant ECS-89-96230.     

Decentralised control of continuous Petri nets

This paper focuses on decentralised control of systems modelled by continuous Petri nets, in which a target marking control problem is discussed. In some previous works, an efficient ON/OFF strategy-based minimum-time controller was developed. Nevertheless, the convergence is only proved for subclasses like Choice-Free nets. For a general net, the pre-conditions of applying the ON/OFF strategy are not given; therefore, the application scope of the method is unclear. In this work, we provide two sufficient conditions of applying the ON/OFF strategy-based controller to general nets. Furthermore, an extended algorithm for general nets is proposed, in which control laws are computed based on some limited information, without knowing the detailed structure of subsystems.     

Stochastic Petri net models of Ca2+ signaling complexes and their analysis

Mathematical models of Ca²⁺ release sites derived from Markov chain models of intracellular Ca²⁺ channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic Ca²⁺ excitability (i.e., puffs and sparks). Ca²⁺ release site models are composed of a number of individual channel models whose dynamic behavior depends on the local Ca²⁺ concentration which is influenced by the state of all channels. We consider this application area to illustrate how stochastic Petri nets and in particular stochastic activity networks can be used to model dynamical phenomena in cell biology. We highlight how state-sharing composition operations as supported by the M?bius framework can represent both mean-field and spatial coupling assumptions in a natural manner. We investigate how state-of-the-art techniques for the numerical and simulative analysis of Markov chains associated with stochastic Petri nets scale when modeling Ca²⁺ signaling complexes of physiological size and complexity.     

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     

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.     

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.