基于有色Petri网的SysML序列图的分析与验证

针对SysML序列图本身缺乏分析和验证手段的问题,提出了一种序列图到有色Petri网的转换方法:定义了将序列图的常用操作转换为等价有色Petri网的转换规则,重点是把序列图的常用结构如可选结构、条件结构、并行结构以及循环结构等映射为有色Petri网。这当中既包含结构元素,如库所、变迁、输入/输出弧,又包含逻辑元素,如全局声明中的颜色集和变量、颜色集与库所、弧表达式以及初始标志。应用这些规则可以将序列图转换为有色Petri网模型,进而对其进行仿真分析,并可通过有色Petri网工具验证模型的无死锁性、可达性、有界性和活性。最后通过数字证书更新的实例分析了映射前后两种模型的语义,验证了映射的正确性。     

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     

Synthesis of Controllers of Processes Modeled as Colored Petri Nets

This paper presents an adaptation of a supervisory control theory and a supervisor synthesis problem to a class of colored Petri nets. More specifically, the forbidden state control problem with full observation, in which a discrete-event system is modeled as a colored Petri net with a symmetry specification, is investigated. This problem is decidable if the colored Petri net has finite color sets and bounded places. A new algorithm for deriving a controller is presented in detail with a proof of correctness. Unlike conventional algorithms that explore the entire reachable set of states, our algorithm avoids an exhaustive search of the state space by exploiting a symmetry specification. It performs particularly well when applied to large but structured processes with similar components. Furthermore, this approach leads to a representation of controllers which are smaller than those obtained with automaton-based approaches.     

CPN tools-assisted simulation and verification of nested Petri nets

Nested Petri nets (NP-nets) is an extension of Petri net formalism within the “nets-within-nets” approach, when tokens in a marking are Petri nets wich have autonomous behavior and synchronize with the system net. The formalism of NP-nets allows modeling multi-level multi-agent systems with dynamic structure in a natural way. Currently there is no tool support for NP-nets simulation and analysis. The paper proposes translation of NP-nets into colored Petri nets and using CPN Tools as a virtual machine for NP-nets modeling, simulation and automatic verification.     

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.     

广义随机价格着色Petri网下不确定市场环境供应链建模问题

针对随机需求市场环境下企业利润变化分析的需要,在PCPN的基础上,与GSPN进行有机结合,本文提出广义随机价格着色Petri网,讨论了广义随机价格着色Petri网(GSPCPN)的变迁步规则,给出了不确定市场环境下供应链的模型。以一个不确定市场条件下供应链流程为实例演示了其应用,结论表明:广义随机价格着色Petri网对于解决供应链不确定市场环境下的利润和库存变化分析问题是有效的。     

Performance analysis of stochastic timed Petri nets using linearprogramming approach

Stochastic timed Petri nets are a useful tool in the performance analysis of concurrent systems such as parallel computers, communication networks and flexible manufacturing systems. In general, performance measures of stochastic timed Petri nets are difficult to obtain for practical problems due to their sizes. In this paper, we provide a method to efficiently compute upper and lower bounds for the throughputs and mean token numbers for a large class of stochastic timed Petri nets. Our approach is based on uniformization technique and linear programming     

A moment generating function based approach for evaluating extendedstochastic Petri Nets

A moment-generating-function (MGF)-based approach for performance analysis of extended stochastic Petri nets (ESPNs) is presented. The method integrates Petri nets, MGF and stochastic network concepts, and Mason's rule into a tool for evaluating various discrete-event dynamic systems. The ESPNs are modeled, given the specification of a system. Then, the state machine PN is derived, the transfer functions based on the MGFs of the related transitions are found, the network is reduced to a single transition with its transfer function for each performance measure, and system performance is calculated. Firing delays of transitions in ESPNs can be either deterministic or stochastic with an extended distribution. Three fundamental structures that can be reduced into a single transition are discussed. The machine-repairman model with a buffer is given as an example to illustrate the method for evaluating performance parameters     

Automatic construction of systems of distributed components from nested Petri nets models

Multi-level multi-agent systems (MASs) with dynamic structure are widely used in solving important applied problems in telecommunication, transportation, social, and other systems. Therefore, ensuring correct behavior of such systems is an actual and important task. One of the most error-prone stages of system development in the framework of model-oriented approach is the implementation stage, in the course of which a program code is constructed based on the model developed. This paper presents an algorithm for automated translation of MAS models represented as nested Petri nets into systems of distributed components. Nested Petri nets are the extension of Petri nets in the framework of the nets-within-nets approach, which assumes that tokens in a Petri net may themselves be Petri nets, possess autonomous behavior, and interact with other tokens of the net. This makes it possible to model MASs with dynamic structure in a natural way. The translation presented in this paper preserves distribution level and important behavioral properties (safety, liveness, and conditional liveness) of the original model and ensures fairness of the target system execution. The use of such translation makes it possible to automate construction of distributed MASs by models of nested Petri nets. As a test example, translation of nested Petri nets into systems of distributed components was implemented on the basis of the EJB component technology.     

Modeling of AGV networks in flexible manufacturing systems

It is shown that Petri nets are useful tool for modeling of AGV networks in flexible manufacturing systems. In this paper we concentrate on a part of AGV (automated guided vheicle) system that behaves as concurrently and asynchronizingly in FSM.

The main idea of this paper is based on combining of some fundamental parts modeled by colored Petri nets, which are called simply “parts”.

It is also shown that our computer system enables that using the concept of parts, we can construct any AGV model without much effort by operating a mouse, and provides a simulation result.     

Integration of Petri nets and moment generating function approaches for system performance evaluation

This article integrates arbitrary stochastic Petri nets (ASPN) and moment generating function approaches for performance evaluation of discrete event dynamic systems (DEDS). These systems include computer-integrated manufacturing systems, resource-shared distributed systems, and communication networks. ASPN can describe various DEDS in which the time duration for activities may be a random variable of arbitrary distributions. In ASPN models, transitions with firing delays of general distributions are used to model these activities. Using our proposed performance analysis methodology, we first represent a system as an ASPN model, then generate its reachability graph and convert it into a state machine Petri net, derive the transfer functions of interesting performance measures through stepwise reductions, and finally obtain the analysis results. This method makes it possible to obtain analytical solutions of important performance indices. We use a robotic assembly system to illustrate the method. We obtain several important performance measures of a closed-form. Finally, we discuss the limitations of this approach and future research.     

动态模糊Petri网模型及其应用研究

以模糊Petri网的基本定义，动态模糊集和动态模糊逻辑为基础，讨论了动态模糊Petri网的基本模型，建立了动态模糊Petri网与模糊Petri网之间的映射关系和转移算法，解决了与动态模糊知识的动态模糊Petri网表示相关的几个问题，最后给出了动态模糊Petri网中动态模糊性的计算方法和相应的推理方法。     

Modeling and performance evaluation of supply chains using batch deterministic and stochastic Petri nets

Batch deterministic and stochastic Petri nets are introduced as a tool for modeling and performance evaluation of supply chains. The new model is developed by enhancing deterministic and stochastic Petri nets (DSPNs) with batch places and batch tokens. By incorporating stochastic Petri nets (SPNs) with the batch features, inhibitor arcs, and marking-dependent weights, operational policies of supply chains such as inventory policies can be easily described in the model. Methods for structural and performance analysis of the model are developed by extending existing ones for DSPNs. As applications, an inventory system and an industrial supply chain are modeled and their performances are evaluated analytically and by simulation, respectively, using this BSPN model. The applications demonstrate that our model and associated methods can solve some important supply chain modeling and analysis issues. Note to Practitioners-This paper was motivated by the problem of performance analysis and optimization of supply chains but it also applies to other discrete event systems where materials are processed in finite discrete quantities (batches) and operations are performed in a batch way because of batch inputs and/or in order to take advantages of the economies of scale. Existing Petri net modeling and analysis tools for such systems ignore their batch features, making their modeling complicated. This paper suggests a new model called batch deterministic and stochastic Petri nets (BDSPNs) by enhancing deterministic and stochastic Petri nets with batch places and batch tokens. Methods for structural and performance analysis of the model are developed. We then show how an inventory system and a real-life supply chain can be modeled and their performances can be evaluated analytically and by simulation respectively based on the model. The model and associated analysis methods therefore provide a promising tool for modeling and performance evaluation of supply chains.     

基于Petri网的建设工程项目实施阶段资源建模与仿真*

基于分层赋时着色Petri网,构建了一个能够准确表达资源配置、任务持续时间及信息传递的资源模型,以便有效进行建设工程项目实施阶段的资源管理和优化配置.在建设工程项目实施阶段资源特点分析的基础上,对分层赋时着色Petri网中的非空颜色集合进行定义,并对资源管理中分层建模、资源分配和资源归还基础模型进行了研究,解决了基于分层赋时着色Petri网构建建设工程项目实施阶段资源模型的关键问题.最后,以某工业与民用建筑的实施阶段为例,进行资源管理模型的构建和仿真分析,验证了基于分层赋时着色Petri网构建建设工程项目实施阶段资源管理模型的正确性和有效性.     

土壤—植被混合地表红外辐射温度场的耦合建模方法*

目前混合地表温度场的数学模型忽略了地表内部各组分间的热通量交互,致使温度场模拟结果不够准确、真实.针对已有独立求解模型的不足,结合土壤-植被混合地表的材质组成及空间分布特点,建立温度场的耦合求解模型,通过在热平衡方程中引入组分间热通量的交互项,对土壤-植被-大气耦合的能量平衡过程进行描述.实验结果表明,利用耦合模型求解的混合地表的温度场分布和热图像特征与自然地表红外辐射特性的真实分布规律具有更好的一致性,从而验证了温度场耦合建模方法的有效性.     

Verifying functions in online stock trading systems

Temporal colored Petri nets, an extension of temporal Petri nets, are introduced in this paper. It can distinguish the personality of individuals (tokens), describe clearly the causal and temporal relationships betwee nevents in concurrent systems, and represent elegantly certain fundamental properties of concurrent systems, such as eventuality and fairness. The use of this method is illustrated with an example of modeling and formal verification of an online stock trading system. The functional correctness of the modeled system is formally verified based on the temporal colored Petri net model and temporal assertions. Also, some main properties of the system are analyzed. It has been demonstrated sufficiently that temporal colored Petri nets can verify efficiently some time-related properties of concurrent systems, and provide both the power of dynamic representation graphically and the function of logical inference formally. Finally. future work is described.     

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。     

Framework for modeling and analysis of distributed problem-solving systems

Petri nets have the basic concepts necessary to model distributed systems with asynchronous processes. Petri nets are not directly applicable to certain kinds of systems like distributed intelligent systems (DISs). These are complex systems where multiple intelligent agents cooperate through communication to achieve the solution to a problem. The paper identifies the limitations of ordinary Petri nets for modeling DISs and proposes extensions. The extended Petri net incorporates colored tokens, inhibition arcs, non-primitive places and transitions, multiple copies of tokens and cumulative places. It is called a distributed problem-solving Petri net. The definitions and analysis techniques are given and illustrated by means of an example.     

Possibilistic Petri nets

This paper presents the possibilistic Petri net model which combines possibility logic with Petri nets with objects. The main feature of this model is to allow one to reason about the aspects of uncertainty and change in dynamic discrete event systems. The paper presents relevant concepts of Petri nets with objects and possibility logic and how imprecision and vagueness are introduced in the marking of a Petri net with objects. The marking of a net is imprecise, or in a more general way, fuzzy, in order to represent an ill-known knowledge about a system state. A new marking updating according to the fuzzy marking such defined is also discussed. An example of shop door monitoring is presented that illustrates our approach.