Stochastic Petri Net Approach Research Articles

Dynamic risk investigation of urban natural gas pipeline accidents using Stochastic Petri net approach

The safety of urban gas pipelines is challenged by a series of adverse factors, and the unexpected accidents may pose a catastrophic threat to humans, the environment and assets. The existing studies mainly focused on causation investigation of natural gas pipeline accident, the dynamic evolution process of urban natural gas pipeline accident is still challenging task for accident prevention. To find out the unfavorable factors that cause accidents, this study presents a dynamic risk modeling of urban natural gas pipeline accidents using Stochastic Petri net (SPN). An SPN model of an accident evolution process is constructed based on the discrete events in an accident flowchart, and the critical places and transitions are evaluated through this model. Considering the slow development of the early events leading to accidents, the delay time of the transitions at this stage cannot be determined, Bayesian theory is used to dynamically update SPN model. Critical accident nodes and their occurrence probabilities are estimated, which are used to support the efficient risk management strategies. The gas explosion accident in Shiyan, Hubei, as a representative case is investigated, and the results show that pipeline corrosion, ignition sources, inefficient information feedback and unreasonable solutions are critical accident causations. The probabilities of critical accident nodes increase over time, which means that these factors need to be managed efficiently to prevent the accidents. The application shows that the model can be used as a tool for gas companies and governments to investigate urban gas pipeline accidents.

Stochastic Petri net model describing the relationship between reported maternal and congenital syphilis cases in Brazil

IntroductionSyphilis is a sexually transmitted disease (STD) caused by Treponema pallidum subspecies pallidum. In 2016, it was declared an epidemic in Brazil due to its high morbidity and mortality rates, mainly in cases of maternal syphilis (MS) and congenital syphilis (CS) with unfavorable outcomes. This paper aimed to mathematically describe the relationship between MS and CS cases reported in Brazil over the interval from 2010 to 2020, considering the likelihood of diagnosis and effective and timely maternal treatment during prenatal care, thus supporting the decision-making and coordination of syphilis response efforts.MethodsThe model used in this paper was based on stochastic Petri net (SPN) theory. Three different regressions, including linear, polynomial, and logistic regression, were used to obtain the weights of an SPN model. To validate the model, we ran 100 independent simulations for each probability of an untreated MS case leading to CS case (PUMLC) and performed a statistical t-test to reinforce the results reported herein.ResultsAccording to our analysis, the model for predicting congenital syphilis cases consistently achieved an average accuracy of 93% or more for all tested probabilities of an untreated MS case leading to CS case.ConclusionsThe SPN approach proved to be suitable for explaining the Notifiable Diseases Information System (SINAN) dataset using the range of 75–95% for the probability of an untreated MS case leading to a CS case (PUMLC). In addition, the model’s predictive power can help plan actions to fight against the disease.

General Stochastic Petri Net approach for the estimation of power system restoration duration

Blackouts rarely occur in power systems; nevertheless, in case of occurrence, its impact on the economy, industry, and social life can be noticeable. To minimize the negative financial and social impacts of blackouts, power systems should be restored in the shortest possible time. Therefore, system operators should access a formulated method to estimate the restoration duration. In this paper, a method based on the Petri Net is used to calculate the restoration duration. Therefore, a restoration plan is resolved into its constituent steps, and for each step, a stochastic duration is considered. Applying the Petri Net model of the restoration plan and the duration of each restoration step, the total restoration time can be calculated. The proposed method is applied in two system tests, and the results show consistency with those of the critical path method.

Modelling and analysis of two production solutions for precast concrete elements: a petri-nets approach

The adoption of precast concrete construction has been increasingly emphasised globally, due to its advancements in productivity, waste management, cost control, quality and safety. Meanwhile, the production solutions differ greatly in the off-site plants in terms of traditional stationary production and modern circulation production with different levels of automation. Practical cases show that improper selection or upgrade of production solution could lead to resource slack or even business failure, and there is limited knowledge to quantitively support the decision making. Furthermore, existing works seldom dig deep into the fundamental setup of the production plant, and reckon without the stochasticity and variability of production operation. Therefore, this paper aims to develop an analytical model to facilitate the understanding of the production solutions of precast concrete elements, which should further support the decision making in factory planning or upgrade towards increased level of automation. Stochastic Petri-nets approach has been applied, with stochastic features embraced, to graphically modelled stationary and circulation solutions. Simulation and comparative performance analysis was conducted with a numerical case study. Results demonstrate that stationary solution can achieve even higher outputs during production period provided that enough resources are given, whilst circulation solution has a more flexible and stable production.

A Generalized Stochastic Petri Net Approach for Modeling Activities of Human Operators in Intermodal Container Terminals

This paper proposes a Petri net (PN) representation of the activities performed by the key human operators for unloading/loading containers in an intermodal maritime container terminal (CT) with a low level of automation. These processes are the core of the export, import, and transshipment cycles executed in the terminal. The aim of this paper is to consider both the human component and the material handling resources, e.g., cranes and transporters, by defining an accurate model, which describes how to coordinate humans and use the system resources necessary for serving mother or feeder ships. The developed generalized stochastic PN-based model is of limited complexity and represents a complete, unambiguous, and readable model of the target process before coding it in the target simulation tool. The modular integrated model is tested and validated by the simulation of typical and perturbed scenarios of the Taranto CT, a real terminal that is taken as a case study for its complexity and similarity to CTs with multiple transport modes.

Colored Stochastic Petri Nets for Modeling Complex Biological Systems

The stochastic modeling of biological systems is gaining more and more attention when stochastic fluctuations need to be described. On the other hand, the biological systems under investigation become much more complex than before. Traditional modeling methods like stochastic Petri nets do not easily scale and thus become difficult to tackle this situation. This paper aims to present a colored stochastic Petri net approach for systems biology to modeling complex biological systems. Specifically, this paper describes a type of biochemically-interpreted colored stochastic Petri nets and their extensions and analysis techniques for systems biology and illustrates their applications using Ca 2+ release sites that consist of a set of coupled Ca 2+ channels.

A Stochastic Petri Net Approach for Inventory Rationing in Multi-Echelon Supply Chains

Manufacturing supply chains are considered as discrete event dynamical systems (DEDS) where coordination of material and information flows is essential to satisfy customer orders and to improve the bottomline of the constituent organizations. A critical problem that is often faced by distribution centres that hold finished good inventory is that of inventory rationing. Inventory rationing is a useful strategy to tackle the problem of conflicting objectives i.e., minimizing inventory costs (holding and backorder) on the one hand and achieving the desired customer service levels (CSLs) on the other. The focus of this paper is to formulate Generalized Stochastic Petri net models to address the inventory rationing problem in the context of multi-echelon make-to-stock distribution chains, where the goods flow through multiple echelons, typically from product manufacturers all the way up-to the retail outlets. The statistical inventory control (SIC) policies modeled by the GSPN are (R, s, S) and a variant that we propose, (R?, s, S). We compare the performance of the model under two rationing settings. The first setting considers a case without cooperation, where the individual local stockpoints maximize their own performance. The second setting considers a case with cooperation, where the local stockpoints cooperate with each other to maximize the overall system performance. We provide a methodology to approximately determine the optimal rational fractions with different weights assigned to expected backorder and holding cost components (b/h). We present some interesting results obtained after rigorous numerical experimentation on the model.

Circulant preconditioners for stochastic automata networks

Stochastic Automata Networks (SANs) are widely used in modeling communication systems, manufacturing systems and computer systems. The SAN approach gives a more compact and efficient representation of the network when compared to the stochastic Petri nets approach. To find the steady state distribution of SANs, it requires solutions of linear systems involving the generator matrices of the SANs. Very often, direct methods such as the LU decomposition are inefficient because of the huge size of the generator matrices. An efficient algorithm should make use of the structure of the matrices. Iterative methods such as the conjugate gradient methods are possible choices. However, their convergence rates are slow in general and preconditioning is required. We note that the MILU and MINV based preconditioners are not appropriate because of their expensive construction cost. In this paper, we consider preconditioners obtained by circulant approximations of SANs. They have low construction cost and can be inverted efficiently. We prove that if only one of the automata is large in size compared to the others, then the preconditioned system of the normal equations will converge very fast. Numerical results for three different SANs solved by CGS are given to illustrate the fast convergence of our method.

APPLICATION OF EXTENDED STOCHASTIC PETRI NETS TO SIMULATION AND MODELLING OF CONSTRUCTION SYSTEMS

An extended stochastic Petri net approach to modelling and simulation of construction systems is developed. The basics of Petri nets, a technique previously used for modelling computer systems and automated manufacturing, are described. Extended stochastic Petri net features useful in construction systems modelling are detailed along with structures that can represent characteristics commonly present in construction systems. Two illustrative examples are presented and the advantages and disadvantages of extended stochastic Petri nets as a tool for construction system modelling are discussed.

A combined queueing network and stochastic Petri-net approach for evaluating the performability of fault-tolerant computer systems

In this paper the performability analysis of fault-tolerant computer systems using a hierarchical decomposition technique is presented. A special class of queueing network (QN) models, the so-called BCMP [4], and generalized stochastic Petri nets (GSPN) [1] which are often used to separately model performance and reliability respectively, have been combined in order to preserve the best modelling features of both. A conceptual model is decomposed into GSPN and BCMP submodels, which are solved in isolation. Then, the remaining GSPN portion of the model is aggregated with flow-equivalents of BCMP models, in order to compute performability measures. The substitutes of BCMP models are presented by means of simple GSPN constructs, thereby preserving the 1st and 2nd moments of the throughput. A simple example of a data communication system where failed transmissions are corrected, is presented.