Petri Net Toolbox in Control Engineering Education

Stochastic Petri Net Package (SPNP) is a software package whose goal is to compute performance, availability or performability measures from Stochastic Petri Nets (SPN) and Fluid Stochastic Petri nets (FSPN). This software can use either analytic numeric methods, or simulation methods. Unfortunately, the standard discrete event simulation is inefficient to estimate the probabilities of rare events. For such rare event simulations, importance splitting technique is a good method to speedup the simulation. In the literature, two diffierent importance splitting techniques are known: RESTART and splitting. In this paper, we describe the application of these methods to (both fluid and discrete) Petri nets, their implementation in SPNP and we give some illustrations of the speed-up. The RESTART technique has already been applied in another Petri net package, TimeNet, but here we implement both RESTART and splitting, and we apply them to a more general class of Petri nets including the fluid ones.

The focus area of this work is integrating reliability, availability, and maintainability (RAM) aspects into the conceptual process design of a real industrial system. Quantitative performance analysis has been carried out using Petri nets (PN) approach. In the present study, availability is considered as a performance measure which has been used as an indicator of the reliability and maintainability of the plant. The availability is considered in the process design stage for sorting different design alternatives. The proposed technique suggested in this paper provides a better way of understanding the behaviour of a system under varying operating conditions. It will also help practitioners in deciding upon maintenance strategy so that operation and maintenance cost can be optimised. Stochastic Petri nets (SPN) has been used to model the possible interactions among all active or parallel equipments in the system. Performance parameters have been evaluated using modelling and simulation software GRIF of Petri module.

Petri net modelling of biological regulatory networks

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.

The paradigm of Petri nets offers a rich modeling power that has been successfully exploited in many different application domains as manufacturing, logistic, traffic, computer and biological domains. In order to develop and analyze Petri models in an efficient and systematic way, appropriate software tools are required. Among the existing software platforms for scientific software development, MATLAB places at the user's disposal a large set of toolboxes with an inutitive graphical interface. This paper describes some of the existing Petri net toolboxes that have been developed on MATLAB, and that cover the needs for the modeling and analysis of discrete, continuous and hybrid systems.

Most studies employing Petri nets in semiconductor manufacturing model only one specific area (e.g. etching) in detail, and model the rest of the manufacturing process, e.g. by abstract input/output behavior. In our study, we show the feasibility of using Petri nets for modeling the complete production process. We use the first set of test data provided by the MASM-LAB, Arizona State University. It is a process of a two-product system making non-volatile memory chips. For modeling, we use our own tool PSim, which is based on a combined queuing and Petri net formalism. The integration of queues makes the modeling of parts waiting in front of a machine quite concise and intuitive. PSim offers a hierarchical and modular modeling approach, which is especially feasible for large and complex systems. We use the modular approach by once defining the structure of a machine as Petri net and then instantiating as many machines as needed. Then we model the operators, resources and the movement of parts between the machines as specified in the production plan. As a result, we can state that Petri nets are feasible for modeling a complete semiconductor manufacturing process.

The presented review analyzes the approaches and methods of using simulation models in the maintenance and repair organization of the complex technical objects and systems. The development of the concept of "Industry 4.0" and the Internet of things involves the transition from periodic and preventive maintenance to predictive maintenance based on the study of processes during the object operation. It is shown that system models based on Petri nets are convenient for describing and analyzing technological processes and equipment maintenance. The effectiveness of timed stochastic colored Petri nets for virtual tests in the design of maintenance and repair procedures in complex systems is revealed. The use of hierarchical Petri nets allows building complex models that describe interrelated processes. A general model based on a hierarchical network is proposed to study the processes of deterioration and degradation of the technical object aggregates and elements and to form a predictive maintenance strategy. The model includes a Gantt chart of production tasks, a set of active and reserve units, maintenance and repair modules. The examples of simulation models on Petri nets for various technical systems are considered. Solutions for flexible production systems, railway bridges, offshore wind turbines, an aircraft fleet, a group of robotic vehicles, and a complex of computer equipment of an enterprise are given. The models of various maintenance strategies are considered and the generality of the models based on hierarchical Petri nets is shown. The article formulates methodological principles for constructing hierarchical networks to simulate the operation and maintenance of technical systems. The article analyzes known software tools for the implementation of timed stochastic colored Petri nets. The summary concludes that the use of simulation models on Petri nets is promising for organizing maintenance and repair of complex technical objects and systems.

International audience

Performance analysis can be carried out in several ways, especially in case of Markovian models. In order to interpret high level of abstraction, we often use modeling tools like timed Petri nets (TPNs). Although some subclasses of TPNs (e.g. stochastic Petri nets (SPNs) [17, 19]) can be handled analytically, a general timed Petri net is hard to evaluate via numerical analysis. However, the simulation of SPNs or deterministic and stochastic Petri nets (DSPNs) [16] are supported by many known tools (see, e.g. [3, 20]), it is hard to find a simulation tool for timed Petri nets with generally distributed (i.e., particular but arbitrarily chosen) firing times. In this paper, we present TiPeNeSS (Timed Petri Net Simulator Software) which supports the simulation of timed Petri nets containing transitions with generally distributed firing delays. The input of the software (the Petri net and the parameters) is defined in an XML file, what allows us to generate results in batch mode. Besides, we describe a case study in which we optimize the frequency of the regular maintenance in a manufacturing process.

The emergence of Supply Chains (SCs) is an outcome of the recent advances in logistics and information technology. SCs are complex networks interconnecting different independent manufacturing and logistics companies integrated with material, information and financial flows (Viswanadham & Raghavan, 2000). Typically, SC management decisions are classified into three hierarchical levels according to the time horizon of decisions: strategic (longterm), tactical (medium-term), and operational (short-term, real-time) (Chopra & Meindl, 2001; Shapiro, 2001). Accordingly, different models have to be defined at each level of the decision hierarchy to describe the multiple aspects of the SC. While the development of formal models for SC design at strategic and tactical levels was addressed in the related literature (Dotoli et al., 2005; Dotoli et al., 2006; Gaonkar & Viswanadham, 2001; Luo et al., 2001; Vidal & Goetschalckx, 1997; Viswanadham & Gaonkar, 2003), research efforts are lagging behind in the subject of modeling and analyzing the SC operational performance. At the operational level, SCs can be viewed as Discrete Event Dynamical Systems (DEDSs), whose dynamics depends on the interaction of discrete events, such as customer demands, departure of parts or products from entities, arrival of transporters at facilities, start of assembly operations at manufacturers, arrival of finished goods at customers etc (Viswanadham & Raghavan, 2000). Among the available DEDS analytical formalisms, Petri Nets (PNs) may be singled out as a graphical and mathematical technique to model systems concurrency and synchronization. Moreover, PNs are able to capture precedence relations and structural interactions and may be executed in standard engineering software packages simply implementing their dynamics via the corresponding matrix equations. However, most SC models based on PNs proposed in the related literature share the limitation that products are modelled by means of discrete quantities, called tokens (Desrochers et al., 2005; Dotoli & Fanti, 2005; Elmahi et al., 2003; Viswanadham & Raghavan, 2000; Von Mevius & Pibernik, 2004; Wu & O’Grady, 2005). This assumption is not realistic in large systems with a huge amount of material flow: the state space of the SC model generally turns out to be excessively large, so that inconveniences in the simulation and performance optimization often arise, leading to large computational efforts. Since SCs are DEDSs whose number of reachable states is very large, PN formalisms using fluid approximations provide an

This paper is about the incremental computation of control sequences for discrete event systems in uncertain environments where uncontrollable events may occur. Timed Petri nets are used for this purpose. The aim is to drive the marking of the net from an initial value to a reference one, in minimal or near-minimal time, by avoiding forbidden markings, deadlocks, and dead branches. The approach is similar to model predictive control with a finite set of control actions. At each step only a small area of the reachability graph is explored: this leads to a reasonable computational complexity. The robustness of the resulting trajectory is also evaluated according to a risk probability. A sufficient condition is provided to compute robust trajectories. The proposed results are applicable to a large class of discrete event systems, in particular in the domains of flexible manufacturing. However, they are also applicable to other domains as communication, computer science, transportation, and traffic as long as the considered systems admit Petri Nets (PNs) models. They are suitable for dynamical deadlock-free scheduling and reconfiguration problems in uncertain environments.

GreatSPN is a collection of tools for modelling and analysis of systems using (stochastic) Petri nets. It features a modern Java-based graphical interface. But being technologically advanced does not mean that the tool learning curve is significantly simplified. In the tool the simple features that are needed for educational purpose are intermixed with more advanced features that require a deeper understanding of the formalisms and of the solvers. This paper presents GreatTeach, a streamlined and enriched version of GreatSPN meant for teaching resulting from our experience in teaching Petri nets to master students.

In this work, we explore the applicability of Stoch astic Petri Nets (SPNs) to multi-state failure and survivability analyses, using space sys tems as examples. Multi-state failure analyses introduce degraded states, and thus provid e more insights than the traditional binary reliability analysis into the degradation be havior of a system and its progression towards complete failure. Survivability analysis fo cuses on, among other things, the failure propagation in a system or a network following node or component failure, and it assesses for example whether the system will experience graceful degradation or catastrophic failure. The potential complexity of multi-state failure and system survivability analyses requires powerful (and flexible) stochastic modeling and simulation tools. After a brief introduction to Petri Nets, we argue that SPNs are particularly well suited to these types of analyses, and they are better at the task than the commonly used Markov Chains. We then propose a general framework for system survivability analysis, and we illustrate its applicability using space systems examples. We compare the survivability of two space architectures, a monolith spacecraft and a space-based network (which allows for distributed redundancy of certain subsystems). Monte Carlo simulations are run to generate representative results of stochastic behavior of the two architectures with r espect to on-orbit anomalies and failures. Finally, a comparison of the outputs of the two SPN models indicate, and quantify, the survivability advantage of the space-based network over the monolith spacecraft with respect to on-orbit anomalies and failures.

The author proposes an approach to represent assembly by Petri nets and presents an algorithm of automatic robot assembly planning based on the Petri-net model. The Petri-net model of assembly is configured by the goal structures and initial constraints, both in the Petri-net formalism. Due to the Petri-net representation of assembly, the plan generation is quite straightforward and the planning algorithm can be easily and efficiently implemented with simple matrix manipulation. An example of how to plan an assembly by the Petri net model is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Service Failure model is described by Stochastic Petri nets. Some of the service failure precisely corresponds to the confusion. Confusion is one of very important concept in the Petri nets. Because it appears to be difficult to obtain a “correct” implementation when emerges confusion in the Petri net system, it is not a good model when exists confusion. When we build some service failure and recovery model based on Stochastic Petri nets, it is very important to avoid some structural design error such as useless service failure structure (siphon and confusion structure). In this paper, we discuss useless service failure structures which are precisely equivalent to structural confusion; an algorithm detection useless service failure structure is presented.