Modelling construction material logistics system with stochastic Petri nets

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.

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.

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.

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.

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.

Stochastic Petri nets: Properties, applications and tools

Stochastic Petri nets (SPNs) and generalized stochastic Petri nets (GSPNs) are compared in order to investigate the role of immediate transitions. The comparison is based on the ability of the two formalisms to define models that can be 'scalable' with respect to the initial marking. An intermediate model between (G)SPN structures and (G)SPN systems called 'family' is introduced as a reference for the comparison. It is shown that GSPN families exist that do not have SPN counter- parts. An algorithm is given to reduce GSPN to SPN families in the cases in which this is possible. The application of this structural reduction algorithm allows a more efficient generation of the state space of GSPN systems. >

Supply chains are becoming more global, complex and increasingly vulnerable. Specifically, the latest evolution of the modern supply chains creates crucial cyber-risks and cyber-security challenges. Nowadays, supply chain risk managers need methods and tools for control, analysis, risk mitigation and managing of their cyber vulnerabilities. In this context, cyber-risk modeling and analysis in supply chain has become one of the major research subjects. The first part of this chapter provides a survey of the field and investigates the use of Petri Nets as a tool for modeling and performance analysis of supply chains, as well as their great potential for supply chain risk analysis. The second part of this work is dedicated to our contributions for modeling and performance evaluation of supply chain networks by using discrete event dynamic approaches. Based on the modeling and performance analysis power of Batch Deterministic and Stochastic Petri nets (BDSPN) for supply chain and logistic systems, two original risk-modeling approaches are introduced for this emerging research topic.

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.

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

Modeling real system is one of the difficult and important parts as teaching the knowledge of computer system performance evaluation. This paper takes the modeling of video-on-demand (VOD) system for example, and uses the stochastic Petri nets (SPN) introduced in Prof. Lin Chuang's book [6] to discuss the application of SPN theory in detail. Through the experiment results, we also analyze some performance metrics with various arrival rates. To teach and apply the knowledge of SPN, the SPN theory will be intuitive and easily understood if it can be applied to the modeling process of an easy instance.

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.

This paper is dedicated to modeling and performances analysis of inventory systems using BDSPN, a stochastic Petri net model capable of describing essential characteristics of logistical systems (batch behaviors, randomness, operational policies, synchronization of various flows). In this paper, an analytic method based on the Markov regenerative theory introduced by Choi for a particular class of stochastic Petri nets is presented and applied to our model. An inventory system with (batch) stochastic demand; constant replenishment lead time and continuous review (s, S) policy is modeled and its performances are evaluated using the analytic method