Implementation of Importance Splitting Techniques in Stochastic Petri Net Package

The stochastic Petri net package (SPNP) is a versatile modeling tool for the solution of generalized stochastic Petri nets (GSPN). The GSPN models are described in the input language for SPNP called C-based SPN language (CSPL). The CSPL is an extension of the C programming language with additional constructs that facilitate easy description of GSPN models. The GSPN models specified to SPNP are actually “GSPN reward models” that are based on the “Markov reward models” paradigm. This provides a powerful modeling environment for dependability analysis, performance analysis, and performability modeling. A number of important Petri net constructs like marking dependency, variable cardinality arc, and enabling functions facilitate the construction of models for complex systems.

We compare discrete-state stochastic Petri nets (SPNs) and fluid stochastic Petri nets (FSPNs) with a mixed discrete-continuous state space in their application to openloop video broadcasting systems. For both classes, we present models of the Video-on-Demand client-server system, which generally capture all relevant system aspects in a concise and graphical way. Differences in model design as well as solution techniques for various variants of these models are discussed. By simulation, we obtain measures related to blocked video playout, which allow us to evaluate customer satisfaction against bandwidth requirements. While the FSPN model has advantages in model specification and evaluation efficiency, all presented models excel in their flexibility – both in defining various performance measures and in their extensibility to include, for instance, full VCR functionality and arbitrary user behavior.

Automated construction of GSPN models for flexible manufacturing systems

Stochastic Petri Net-based performance evaluation of hybrid traffic for social networks system

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.

Stochastic Petri Nets (SPNs) are used in engineering and systems analysis to model communication systems, computer systems and software, flexible manufacturing systems, and other applications. The objective of this thesis is to improve the solution techniques for SPN, in particular, to solve or alleviate the state space explosion problem--the bottleneck of SPN analysis. Several solution techniques have been examined, ranging from separable SPN with product form solution, Norton's aggregation, a new approximate convolution algorithm for solving large, colored SPNs, to the core of this thesis--the iterative SPN decomposition technique. This technique uses the concept of divide and conquer. It iteratively solves several size-reduced auxiliary SPN models for performance measures of the original SPN. The structure of the auxiliary SPNs is obtained by aggregating some subnets in the original SPN according to some formal PN reduction rules while preserving the external black-box equivalence of the subnets such that the structural and behavioral properties of the unaggregated part are not affected. The rate parameters of the auxiliary models are obtained iteratively. This approximate technique has good accuracy and large computation reduction, and has been applied to a large application example with success. The major contribution of this thesis is the proposed iterative decomposition technique, which is applicable to general classes of SPNs, and to large models. For the technique, this thesis defines the black-box equivalence criterion for aggregating subnets in PN so that the desired structural and behavioral properties can be preserved, and several formal reduction rules that are shown to preserve the black-box equivalence. The iterative parameter tuning process can be regarded as a generalization of Jacobson and Lazowska's surrogate delay method to SPN domain by allowing multi-arc connections between subnets, several subnets aggregated separately in one auxiliary model, several auxiliary models to control the degree of the structural reduction, and local marking dependent or constant rate for an aggregated transition with degrees of accuracies and complexities.

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.

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.

Since the publication of the initial American College of Cardiology (ACC)/American Heart Association (AHA) Methodology for the Selection and Creation of Performance Measures,1 there has been an explosion in the development and application of performance measures. Although initially envisioned as a means for physician-led quality-improvement efforts, performance measures have been primarily used as tools for accountability and performance-based reimbursement instead. Given the centrality of and experience with performance measures for quantifying healthcare quality, the American College of Cardiology Foundation (ACCF)/AHA Task Force on Performance Measures sought to update its methodology so that ongoing efforts to measure performance could benefit from emerging insights. The original methodology, proposed in 2005,1 remains the foundation for developing process performance measures. The principal recommendations of the 2005 report are summarized in Table 1. The 2010 report does not address detailed issues of analysis,3 pay for performance,4 or nonfinancial rewards for better performance5 because these topics have been addressed in other statements. The focus of the 2010 report is to provide a state-of-the-art perspective on the construction, collection, and emerging directions of performance measurement as a means to improve healthcare quality. View this table: Table 1. ACCF/AHA Attributes of Performance Measures Figure 1. An overview of the steps in providing care by domain. Reprinted from Spertus et al.1 Performance measures that articulate discrete processes of care, as opposed to structural aspects of care or outcomes, are distinctly different from both clinical practice guidelines and appropriate use criteria because they represent a subset of the clinical guidelines for which the evidence is sufficiently strong: typically where the highest-quality evidence of benefit unequivocally exceeds risk (Class I recommendation, Level of Evidence: A),8 failure to provide the therapy to an eligible patient meaningfully reduces the likelihood that the patient will experience the best possible outcome. In this report, …

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 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 extensions for the development of MIMO net models of automated manufacturing systems

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.

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.

There is a need to quantify system properties methodically. Dependability and security models have evolved nearly independently. Therefore, it is crucial to develop a classification of dependability and security models which can meet the requirement of professionals in both fault-tolerant computing and security community. In this paper, we present a new classification of dependability and security models. First we present the classification of threats and mitigations in systems and networks. And then we present several individual model types such as availability, confidentiality, integrity, performance, reliability, survivability, safety and maintainability. Finally we show that each model type can be combined and represented by one of the model representation techniques: combinatorial (such as reliability block diagrams (RBD), reliability graphs, fault trees, attack trees), state-space (continuous time Markov chains, stochastic Petri nets, fluid stochastic Petri nets, etc) and hierarchical (e.g., fault trees in the upper level and Markov chains in the lower level). We show case studies for each individual model types as well as composite model types.