Performance modelling and availability analysis of a milk pasteurising system using Petri nets formalism

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 Petri Net Toolbox (PN Toolbox) for MATLAB is a software package that offers instruments for the simulation, analysis and design of untimed, deterministic and stochastic P-/T-timed and stochastic Petri nets (PNs). The facilities available in this toolbox are appropriate for studying the dynamics of many classes of discrete-event systems. The Petri Net Simulink Block (PNSB) allows the modeling and analysis of hybrid systems whose event-driven part(s) is (are) modeled based on the PN formalism. The current paper focuses on the exploitation of the PN Toolbox for illustrating the usage of the PN theory in Control Engineering from the pedagogic point of view, the discussion being supported by example problems and comments on the teaching goals. The PN Toolbox is included in the Connections Program of The MathWorks Inc., as a third party product.

PurposeThe purpose of this paper is to examine the potential of applying Petri nets to improve construction material logistics analysis and modelling.Design/methodology/approachThe characteristics of construction logistics are unveiled by analysing the existing practices of logistics management. In views of the dynamic nature of construction logistics problem, a stochastic Petri nets (SPNs) approach is proposed to tackle the time‐evolution property. Using a simulation package called PetriTool™ a simulation model is developed. Finally, a case example is applied to illustrate the way in which SPNs is used for analysing and modelling construction material logistics problems.FindingsThe results indicate that the impacts triggered by variations in delivery lead‐time and changes in delivery quantities can be approximated thereby facilitating decision makers to devise a more reliable and optimal materials management plan for construction projects.Research limitations/implicationsThe complex routing patterns in demand analysis and materials procurement methods that results in the enlarged supply chains have not been considered in this paper.Practical implicationsThe lack of a simple but powerful formalism to analyse and model the decision process under a dynamic environment hinders the implementation of efficient logistics systems in the construction industry. The SPNs model presented in this paper can support planners and managers in making construction logistics management decisions under dynamic environment.Originality/valueThis paper demonstrates that the time‐based SPNs can offer more enriched solutions especially when modelling the time‐evolution behaviours of construction logistics.

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.

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 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

International audience

The four papers in this special issue apply tools and techniques from computer performance evaluation in the very different domain of modelling biological systems. This might seem to be a very odd thing to do but the practice of analysing biological systems in this way is becoming increasing common. As data about the internal components of biological systems is becoming more readily available, biologists are increasingly asking questions about how systems function. In addition to conducting laboratory experiments, they are supported in this exploration by in silico experimentation based on models. The view taken of the biological processes focusses on the stimuli and responses, a view akin to that taken of engineered systems in systems engineering. Thus this new endeavour in biology is known as Systems Biology . Performance analysts have a long tradition of modelling systems in order to understand and predict their function. Their focus is particularly on the dynamic aspects of the system, the use of, and contention for, resources, and the impact of uncertainty or randomness. These issues are important in the biological setting also, and so it is perhaps inevitable that we see some people and techniques from performance modelling being applied in systems biology. In particular some of the high-level modelling formalisms which have supported Markovian performance modelling in the last few decades (stochastic Petri nets, stochastic process algebras, etc.) are being applied in the biological domain. Furthermore analysis techniques, such as Markovian analysis, Monte Carlo simulation and probabilistic model checking have also been adoped. In this volume we have sought to give a snapshot of a variety of work which is going on at this interface between systems biology and more traditional quantitative analysis techniques. It is by no means an exhaustive account of this exciting area, but rather a taster which will hopefully whet your appetite to find out more. To open the volume, the editors provide a survey paper describing the motivations and goals of the systems biology endeavour, summarising the existing modelling techniques and outlining some instances of cross-over between performance modelling and systems biology. This includes an account of the use of ordinary differential equations (ODE) and stochastic simulation to analyse biological systems, and the adoption of high-level modelling formalisms such as Petri nets and process algebras to drive these ODE models and simulations. In their paper Kwiatkowska, Norman and Parker show the application of logic and probabilistic model checking to the analysis of biological signalling pathways. They use the PRISM probabilistic model-checker to check formulae of the CSL logic against CTMC-based models of the MAPK cascade, a sequence of biochemical reactions which sends a message within a cell. The paper provides an introduction to the CSL logic as well as the reactive modules language implemented by the PRISM model checker. Performance measures of interest are described using reward structures and the analysis achieved by PRISM is able to show how the percentage of activated MAPK, a key component of the pathway, and the number of MAPK-MAPKK reactions, vary as a function of time, for different values of the initial number of MAPKs. The paper by Jeschke, Ewald, Park, Fujimoto and Uhrmacher addresses the drive for increased physical accuracy in simulation models which represent the spatial aspects of cell biology. Standard approaches to stochastic simulation of cellular systems assume that the cell is a homogeneous soup of biochemical components. The truth is far removed from this, as the cell has a lot of internal structure which can have a profound effect on the dynamics of reactions. Setting aside the assumption that the reacting chemical species are well-stirred, spatial approaches divide the volume into sub-volumes and apply a structured method which identifies the next reaction to occur in each subvolume. The cost of such an increase in accuracy in the simulation model is a much increased running time so the authors use a parallel and distributed approach to improve performance. To close this special issue we have a paper by DemattB, Priami and Romanel which uses the BlenX language and the Beta Workbench software to analyse the MAPK pathway considered also by Kwiatkowska, Norman and Parker. The BlenX language, and the Beta-binders process calculus which was its inspiration, are examples of a new generation of languages which have been designed specifically for the biological domain, as an alternative to using existing languages designed for modelling computer systems. The paper shows how a well-designed platform for modelling and simulation can lift the user's experience and make their use of process calculi more valuable, delivering insights which would not have been seen otherwise.

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.

This paper proposes fuzzy Colored Petri Nets with stochastic time delay (FCPN-std) as one of methodologies of incorporating qualitative uncertainties and stochastic information in a manufacturing system. As a combined model with fuzzy colored Petri Nets (FCPNs) and stochastic Petri Nets (SPNs), it captures and models statistical and qualitative uncertainties in manufacturing processes. A parametric modular design methodology is proposed for effective design of complex processes. A mold producing process in digital camera making industry is modeled as an example application. The model incorporating uncertain and stochastic information is represented using extended Petri Net Markup Language (xPNML) architecture. xPNML formatted fuzzy colored Petri Net with stochastic time delay is shown as an effective design methodology and representation tool for describing manufacturing processes and capturing uncertainties.

This paper presents a mathematical framework for modeling prognostics at a system level, by combining the prognostics principles with the Plausible Petri nets (PPNs) formalism, first developed in M. Chiachío et al. [Proceedings of the Future Technologies Conference, San Francisco, (2016), pp. 165-172]. The main feature of the resulting framework resides in its efficiency to jointly consider the dynamics of discrete events, like maintenance actions, together with multiple sources of uncertain information about the system state like the probability distribution of end-of-life, information from sensors, and information coming from expert knowledge. In addition, the proposed methodology allows us to rigorously model the flow of information through logic operations, thus making it useful for nonlinear control, Bayesian updating, and decision making. A degradation process of an engineering sub-system is analyzed as an example of application using condition-based monitoring from sensors, predicted states from prognostics algorithms, along with information coming from expert knowledge. The numerical results reveal how theinformation from sensors and prognostics algorithms can be processed, transferred, stored, and integrated with discreteevent maintenance activities for nonlinear control operations at system level.

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.

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.

A new approach to Vulnerability, Uncertainty and Probability (VUP) quantification procedure using Stochastic Petri Nets within a network of interacting satellites is presented. A Stochastic Petri Net based model is developed to quantify VUP in a network of interacting satellites. Three indicators are proposed to determine the VUP definitions in interacting network of satellites. The proposed VUP quantification scheme addresses a methodology which employs a Stochastic Petri Net for quantitative analysis of the behavior of the network. With the random variables associated with the Petri Net transitions, the dynamic behavior of the cooperating satellites in a SPN model can be mapped onto a time-continuous Markov chain with discrete state space. After generating a Markov Stochastic Petri Net model, the probability of a given condition in the network at a specified time can be computed and quantified as well as the vulnerability and uncertainty of the system using the identified indicators.