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.     

Markov regenerative stochastic Petri nets with general execution policies: supplementary variable analysis and a prototype tool

Stochastic Petri nets (SPNs) with general firing time distributions are considered. Generally timed transitions can have general execution policies: the preemption policy may be preemptive repeat different (prd) or preemptive resume (prs) and the firing time distribution can be marking-dependent. A stationary analysis method covering all possible combinations is presented by means of supplementary variables. The method is implemented in a prototype tool SPNica which is based on Mathematica. The use of the general execution policies is illustrated by a WWW server model.     

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.     

Configuration structures, event structures and Petri nets

In this paper the correspondence between safe Petri nets and event structures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary nets without self-loops, under the collective token interpretation. To this end we propose a more general form of event structure, matching the expressive power of such nets. These new event structures and nets are connected by relating both notions with configuration structures, which can be regarded as representations of either event structures or nets that capture their behaviour in terms of action occurrences and the causal relationships between them, but abstract from any auxiliary structure.A configuration structure can also be considered logically, as a class of propositional models, or—equivalently—as a propositional theory in disjunctive normal from. Converting this theory to conjunctive normal form is the key idea in the translation of such a structure into a net.For a variety of classes of event structures we characterise the associated classes of configuration structures in terms of their closure properties, as well as in terms of the axiomatisability of the associated propositional theories by formulae of simple prescribed forms, and in terms of structural properties of the associated Petri nets.     

Real time identification of discrete event systems using Petri nets

The paper defines the identification problem for Discrete Event Systems (DES) as the problem of inferring a Petri Net () model using the observation of the events and the available output vectors, that correspond to the markings of the measurable places. Two cases are studied considering different levels of the system knowledge. In the first case the place and transition sets are assumed known. Hence, an integer linear programming problem is defined in order to determine a modelling the DES. In the second case the transition and place sets are assumed unknown and only an upper bound of the number of places is given. Hence, the identification problem is solved by an identification algorithm that observes in real time the occurred events and the corresponding output vectors. The integer linear programming problem is defined at each observation so that the can be recursively identified. Some results and examples characterize the identified systems and show the flexibility and simplicity of the proposed technique. Moreover, an application to the synthesis of supervisory control of systems via monitor places is proposed.     

Fault detection for discrete event systems using Petri nets with unobservable transitions

In this paper we present a fault detection approach for discrete event systems using Petri nets. We assume that some of the transitions of the net are unobservable, including all those transitions that model faulty behaviors. Our diagnosis approach is based on the notions of basis marking and justification, that allow us to characterize the set of markings that are consistent with the actual observation, and the set of unobservable transitions whose firing enable it. This approach applies to all net systems whose unobservable subnet is acyclic. If the net system is also bounded the proposed approach may be significantly simplified by moving the most burdensome part of the procedure off-line, thanks to the construction of a graph, called the basis reachability graph.     

Real-time scheduling of batch systems using Petri nets and linear logic

This paper presents an approach to model, design and verify scenarios of real-time systems used in the scheduling and global coordination of batch systems. The initial requirements of a system specified with sequence diagrams are translated into a single p-time Petri net model representing the global behavior of the system. For the Petri net fragments involved in conflicts, symbolic production and consumption dates assigned to tokens are calculated based on the sequent calculus of linear logic. These dates are then used for off-line conflict resolution within a token player algorithm used for scenario verification of real-time specifications and which can be seen as a simulation tool for UML interaction diagrams.     

Multiobjective scheduling algorithm for flexible manufacturing systems with Petri nets

In this work, we focus on general multi-objective scheduling problems that can be modeled using a Petri net framework. Due to their generality, Petri nets are a useful abstraction that captures multiple characteristics of real-life processes.To provide a general solution procedure for the abstraction, we propose three alternative approaches using an indirect scheme to represent the solution: (1) a genetic algorithm that combines two objectives through a weighted fitness function, (2) a non dominated sorting genetic algorithm (NSGA-II) that explicitly addresses the multi-objective nature of the problem and (3) a multi-objective local search approach that simultaneously explores multiple candidate solutions. These algorithms are tested in an extensive computational experiment showing the applicability of this general framework to obtain quality solutions.     

Distributed dynamic programming using concurrent object-orientedness with actors visualized by high-level Petri nets

This paper deals with application of concurrent object-oriented programming with Actors to solve dynamic programming problems in a distributed computing environment. This area of research is often called distributed artificial intelligence. Using a dynamic programming example of chained matrix multiplication, a method of managing dynamic programming searches in a distributed programming environment with Actors is presented. Distributed computations with Actors are visualized by means of Time-Varying Automata (for cases with no intra-actor concurrency) or using a class of high-level nets called Hierarchical Colored Petri Nets (for cases with intra-actor concurrency). Design and implementation features of the specific Actor-based programming environment, using a concurrent extension of C++, are also discussed.     

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。     

Queueing Petri nets with product form solution

The product form results recently published for stochastic Petri nets are combined with the well-known product form results for queueing networks in the model formalism of queueing Petri nets yielding the class of product form queueing Petri nets. This model class includes stochastic Petri nets with product form solution and BCMP queueing networks as special cases. We introduce an arrival theorem for the model class and present an exact aggregation approach extending known approaches from queueing networks.     

面向对象Petri网继承性的研究

面向对象Petri网(OOPN)利用面向对象的封装性解决了Petri网不能用于大型系统建模的问题.针对大型系统建模中的面向对象Petri网建模的便捷性进行研究,将面向对象的继承性以及与之紧密联系的多态性引入到OOPN中,以其在更大程度上实现模型的复用,使大型系统建模过程更加便捷、灵活.     

Verification of bounded Petri nets using integer programming

Model checking based on the causal partial order semantics of Petri nets is an approach widely applied to cope with the state space explosion problem. One of the ways to exploit such a semantics is to consider (finite prefixes of) net unfoldings—themselves a class of acyclic Petri nets—which contain enough information, albeit implicit, to reason about the reachable markings of the original Petri nets. In [19], a verification technique for net unfoldings was proposed, in which deadlock detection was reduced to a mixed integer linear programming problem. In this paper, we present a further development of this approach. The essence of the proposed modifications is to transfer the information about causality and conflicts between the events involved in an unfolding, into a relationship between the corresponding integer variables in the system of linear constraints. Moreover, we present some problem-specific optimisation rules, reducing the search space. To solve other verification problems, such as mutual exclusion or marking reachability and coverability, we adopt Contejean and Devie's algorithm for solving systems of linear constraints over the natural numbers domain and refine it, by taking advantage of the specific properties of systems of linear constraints to be solved. Another contribution of this paper is a method of re-formulating some problems specified in terms of Petri nets as problems defined for their unfoldings. Using this method, we obtain a memory efficient translation of a deadlock detection problem for a safe Petri net into an LP problem. We also propose an on-the-fly deadlock detection method. Experimental results demonstrate that the resulting algorithms can achieve significant speedups.