Discrete Time Stochastic Petri Nets

Basic graph models of processes, such as Petri nets, have usually omitted the concept of time as a parameter. Time has been added to the Petri net model in two ways. The timed Petri net (TPN) uses a fixed number of discrete time intervals. The stochastic Petri net (SPN) uses an exponentially distributed random variable. In this paper, a discrete time stochastic Petri model is described. These discrete time SPN's fill the gap between TPN and normal SPN. However, the use of discrete time complicates the SPN model in that more than one transition may fire at a time step. Finally, an example of a live and bounded Petri net which has nonempty, disjoint, recurrent subsets of markings is given.     

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。     

协同服务中事务处理模型分析方法

提出一种基于随机Petri网的协同服务事务处理模型与分析方法,分析企业协同服务中几个最具代表性的事务处理流程。以电子商务系统中的物流系统为例,分别对加入事务处理前后的流程应用模型进行等价化简,从而得到2类流程模型,并利用随机Petri网的性能评价方法,对比分析加入事务处理前后系统业务响应时间和吞吐量。     

工作流系统模型的性能等价分析

讨论了基于随机Petri网的工作流系统的顺序、并行、选择、循环4种基本模型,并详细推导了这4种基本模型的性能等价公式.最后通过现实中的一个工作流实例来说明如何建立相应的随机Petri网模型,以及如何利用这些性能等价公式来计算工作流的性能参数.给出了定量分析工作流系统性能的通用方法,通过用这些等价公式不仅可以对复杂的系统进行性能等价化简,而且还可以得到性能参数的乘积解.     

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     

一种资源共享系统的模型和近似性能分析

本文提出一种随机Ｐｅｔｒｉ网（ＳＰＮ）的资源共享系统的模型，并给出了模型分解和子模型迭代近似求解的两种方法：标识概率交换和平均标志个数交换。例子显示了这两种方法的有效性和相对误差。本文还证明了主述两种方法在固定迭代求解中，固定点解的存在。本文的复杂模型近似性能求解方法可以应用到很多复杂系统的性能分析中。     

基于随机Petri网的柔性工作流可用性分析

提出一种基于随机Petri网的柔性工作流可用性分析方法。给出基本的异常处理模型,以电子商务配送系统(ELMS)为例,利用随机Petri网对系统进行SPN建模,分析ELMS系统的各种可用性参数。实验结果表明,该方法能准确、有效地对支持异常处理操作的柔性工作流进行可用性分析。     

用于软件可靠性分析的分解方法

随机Petri网(SPN)是一种有力的系统建模和分析工具.但SPN在应用中经常碰到状态空间爆炸问题.分解压缩技术是解决随机网状态空间指数性增长的有效方法之一.介绍了一种获得SPN可靠性模型瞬时状态的分解方法.该方法在保证评价和预测可靠性精确度的基础上,不仅能有效地降低可靠性描述与分析的复杂度,还扩大了分解压缩技术的适用范围.     

基于随机Petri网的SPN2软件建模方法研究

随机Petri网(SPN)在进行系统性能分析时,其状态空间随着系统规模的增大而呈指数性增长,造成系统建模复杂。针对该问题,结合面向对象Petri网理论(OOPN)提出一种SPN2方法,与传统SPN方法相比,SPN2方法可进行分层及面向对象网中网建模,并应用该方法仿真高速列车在移动闭塞区间条件下GSM-R铁路无线通信系统的可靠性。     

Exploring impact of time management services on HLA-based Petri Nets Simulation Engine

We describe a HLA-based Stochastic Petri Nets (SPN) Simulation Engine that has been developed in order to study distributed behaviour of SPN. We simulate a Federation constituted from SPN (sub) models. Two approaches are considered: (1) a single Petri Nets (PN) is decomposed into subnets which are executed on different heterogeneously connected computers (2) different PN which model different processes are combined into a single distributed simulation. We use a sender/receiver SPN-model to illustrate these approaches and to explore the impact of time management services applied in the implementation of the SPN distributed simulation engine.     

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.     

Estimation methods for nonregenerative stochastic Petri nets

When a computer, manufacturing, telecommunication, or transportation system is modeled as a stochastic Petri net (SPN), many long-run performance characteristics of interest can be expressed as time-average limits of the associated marking process. For nets with generally-distributed firing times, such limits often cannot be computed analytically or numerically, but must be estimated using simulation. Previous work on estimation methods for SPNs has focused on the case in which there exists a sequence of regeneration points for the marking process of the net, so that point estimates and confidence intervals for time-average limits can be obtained using the regenerative method for analysis of simulation output. This paper is concerned with SPNs for which the regenerative method is not applicable. We provide conditions on the clock-setting distributions and new-marking probabilities of an SPN under which time-average limits are well defined and the output process of the simulation obeys a multivariate functional central limit theorem. It then follows from results of Glynn and Iglehart (1990) that methods based on standardized time series can be used to obtain strongly consistent point estimates and asymptotic confidence intervals for time-average limits. In particular, the method of batch means is applicable. Moreover, the methods of Munoz and Glynn can be used to obtain point estimates and confidence intervals for ratios of time-average limits. We illustrate our results using an SPN model of an interactive video-on-demand system     

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.     

A distributed approach for fault detection and diagnosis based on Time Petri Nets

This paper proposes an algorithm for the model based design of a distributed protocol for fault detection and diagnosis for very large systems. The overall process is modeled as different Time Petri Net (TPN) models (each one modeling a local process) that interact with each other via guarded transitions that becomes enabled only when certain conditions (expressed as predicates over the marking of some places) are satisfied (the guard is true). In order to use this broad class of time DES models for fault detection and diagnosis we derive in this paper the timing analysis of the TPN models with guarded transitions. In this paper we also extend the modeling capability of the faults calling some transitions faulty when operations they represent take more or less time than a prescribed time interval corresponding to their normal execution. We consider here that different local agents receive local observation as well as messages from neighboring agents. Each agent estimates the state of the part of the overall process for which it has model and from which it observes events by reconciling observations with model based predictions. We design algorithms that use limited information exchange between agents and that can quickly decide “questions” about “whether and where a fault occurred?” and “whether or not some components of the local processes have operated correctly?”. The algorithms we derive allow each local agent to generate a preliminary diagnosis prior to any communication and we show that after communicating the agents we design recover the global diagnosis that a centralized agent would have derived. The algorithms are component oriented leading to efficiency in computation.     

A combined queueing network and stochastic Petri-net approach for evaluating the performability of fault-tolerant computer systems

In this paper the performability analysis of fault-tolerant computer systems using a hierarchical decomposition technique is presented. A special class of queueing network (QN) models, the so-called BCMP [4], and generalized stochastic Petri nets (GSPN) [1] which are often used to separately model performance and reliability respectively, have been combined in order to preserve the best modelling features of both.

A conceptual model is decomposed into GSPN and BCMP submodels, which are solved in isolation. Then, the remaining GSPN portion of the model is aggregated with flow-equivalents of BCMP models, in order to compute performability measures. The substitutes of BCMP models are presented by means of simple GSPN constructs, thereby preserving the 1st and 2nd moments of the throughput. A simple example of a data communication system where failed transmissions are corrected, is presented.     

Distributed simulation of modular time Petri nets: An approach and a case study exploiting temporal uncertainty

This paper proposes an approach to modular modelling and simulation of complex time-critical systems. The modelling language is represented by Merlin and Farber’s Time Petri Nets (TPNs) augmented with inhibitor arcs and modular constructs borrowed from the Petri Net Markup Language (PNML) interchange format. Analysis techniques depend on Temporal Uncertainty Time Warp (TUTW), a time warp algorithm capable of exploiting temporal uncertainty in general optimistic simulations over a networked context. A key feature of the approach is the fact that TPN models naturally exhibit a certain degree of temporal uncertainty which the TUTW control engine can exploit to achieve good speedup without a loss in the accuracy of the simulation results. The developed TUTW/TPN kernel is demonstrated by modelling and simulation of a real-time system example.A preliminary version of this paper was presented at 38th SCS Annual Simulation Symposium, April 4–6, 2005, San Diego (CA), IEEE Computer Society, pp. 233–240. Franco Cicirelli achieved a PhD in computer science from the University of Calabria (Unical), DEIS—department of electronics informatics and systems science. As a postdoc, he is making research on agent and service paradigms for the development of distributed systems, parallel simulation, Petri nets, distributed measurement systems. He holds a membership with ACM. Angelo Furfaro, PhD, is a computer science assistant professor at Unical, DEIS, teaching object-oriented programming. His research interests are centred on: multi-agent systems, modeling and analysis of time-dependent systems, Petri nets, parallel simulation, verification of real-time systems, distributed measurement systems. He is a member of ACM. Libero Nigro is a full professor of computer science at Unical, DEIS, where he teaches object-oriented programming, software engineering and real-time systems courses. He directs the Software Engineering Laboratory (www.lis.deis.unical.it). His current research interests include: software engineering of time-dependent and distributed systems, real-time systems, Petri nets, modeling and parallel simulation of complex systems, distributed measurement systems. Prof. Nigro is a member of ACM and IEEE.     

一种基于广义随机Petri网的分析器

广义随机Petri网在离散事件系统的性能分析中得到广泛应用.本文介绍了能对含禁止线、K有界的GSPN模型进行稳态分析的自动分析工具,此工具同样适用于SPN模型的稳态分析和PN模型的可达性分析.并给出使用本软件的例子.     

一种兼顾协议正确性验证和性能评估的Petri网方法

基于Petri网的协议形式化分析方法由于其精炼、简洁和无二义性逐步成为分析协议的一条可靠和准确的途径,但是协议的形式化分析目前研究还不够深入,协议分析的两个重点内容正确性验证和性能评估所需要的模型不同,一种模型只能解决一方面的工作。为了有效地解决这一问题,文中提出了一种用原型Petri网作为协议验证模型的思路和方法,在不改变原型Petri网结构的基础上对变迁赋予发生时延,解决了协议的性能评估问题。本文还给出了协议验证内容与Petri网分析方法的对应关系,并对0-1停止等待协议进行了详细的分析,最后把0-1停止等待协议的原型Petri网模型转化为时延Petri网,对协议的性能进行了评估。     

装备维修保障的随机Petri网模型及分析

建立了装备维修保障系统的随机Petri（SPN）模型，应用SPN与马尔可夫链理论相结合的分析方法。为维修保障系统性能评估提供了理论依据。最后，通过实例分析了系统状态空间、各状态在稳态下的期望概率、系统可靠性和维修人员的工作强度。实例表明，相比传统的Petri网建模方法，在分析装备维修保障各状态间的逻辑关系和系统动态过程中，SPN具有显著的有效性和优越性。     

A concurrency-preserving translation from time Petri nets to networks of timed automata

Several formalisms to model distributed real-time systems coexist in the literature. This naturally induces a need to compare their expressiveness and to translate models from one formalism to another when possible. The first formal comparisons of the expressiveness of these models focused on the preservation of the sequential behavior of the models, using notions like timed language equivalence or timed bisimilarity. They do not consider preservation of concurrency. In this paper we define timed traces as a partial order representation of executions of our models for real-time distributed systems. Timed traces provide an alternative to timed words, and take the distribution of actions into account. We propose a translation between two popular formalisms that describe timed concurrent systems: 1-bounded time Petri nets (TPN) and networks of timed automata (NTA). Our translation preserves the distribution of actions, that is we require that if the TPN represents the product of several components (called processes), then each process should have its counterpart as one timed automaton in the resulting NTA.