Stochastic Petri Net Model Research Articles

Vulnerability Analysis of LTE-R Train-to-Ground Communication Time Synchronization

The time synchronization of LTE-R train-to-ground communication systems plays an important role in ensuring the safety of high-speed railways. In the LTE-R time synchronization process, existing problems, such as the time synchronization message broadcast address and LTE-R all-IP architecture, are vulnerable to attack. In order to analyze the impact of these problems, we propose a new vulnerability analysis method of LTE-R time synchronization based on stochastic Petri nets. Firstly, we construct a stochastic Petri net model of an LTE-R time synchronization process under attack. Secondly, steady-state probability expressions are obtained using the model isomorphism Markov chain. Finally, bychanging the firing rate of several key vulnerable nodes, the relationship curve between the firing rate and the steady-state probability of the clock node is obtained. Simulations show that the vulnerability of LTE-R time synchronization is most affected by the attack on eNodeB of the LTE-R base station. The results can provide a certain theoretical basis for the evolution of high-speed railway GSM-R communication systems to LTE-R.

Reliability Analysis and Modelling of Containment Spray System Based on Petri Net

Reliability modelling for digital instrumentation and control systems in nuclear power plants is one of the new trends. The containment spray system in the digital I&C system of nuclear power plant is selected, and the generalized stochastic Petri net model is used to model the reliability of the containment spray system. A single-cycle simulation of the generalized stochastic Petri net model is carried out under consideration of a variety of dynamic events, and the probability of system start-up failure is obtained. The results show that the generalized stochastic Petri net model can well reflect the impact of various dynamic events on system security. Therefore, the generalized stochastic Petri net model is suitable for reliability modelling of I&C systems in nuclear power plants.

A New Multi-Resolution Approach to EEG Brain Modeling Using Local-Global Graphs and Stochastic Petri-Nets.

Recent modeling of brain activities encompasses the fusion of different modalities. However, fusing brain modalities requires not only the efficient and compatible representation of the signals but also the benefits associated with it. For instance, the combination of the functional characteristics of EEGs with the structural features of functional magnetic resonance imaging contributes to a better interpretation localization of brain activities. In this paper, we consider the EEG signals as parallel 2D string images from which we extract their visual abstract representations of EEG features. This representation can benefit not only the EEG modeling of the signals but also a future fusion with another modality, like fMRI. In particular, the new methodology, called Bar-LG, provides a reduced discretization of the EEG signals into selected minima/maxima in order to be used in a form of tokens for EEG brain activities of interest. A formal context-free language is used to express and represent the extracted tokens for the selected active brain regions. Then, a Generalized Stochastic Petri-Nets (GSPN) model is used for expressing the functional associations and interactions of these EEG signals as 2D image regions. An illustrative EEG example of epileptic seizure is presented to show the Bar-LG methodology's abstract capabilities.

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.

Performance-Cost Trade-Off in Auto-Scaling Mechanisms for Cloud Computing.

Cloud computing has been widely adopted over the years by practitioners and companies with a variety of requirements. With a strong economic appeal, cloud computing makes possible the idea of computing as a utility, in which computing resources can be consumed and paid for with the same convenience as electricity. One of the main characteristics of cloud as a service is elasticity supported by auto-scaling capabilities. The auto-scaling cloud mechanism allows adjusting resources to meet multiple demands dynamically. The elasticity service is best represented in critical web trading and transaction systems that must satisfy a certain service level agreement (SLA), such as maximum response time limits for different types of inbound requests. Nevertheless, existing cloud infrastructures maintained by different cloud enterprises often offer different cloud service costs for equivalent SLAs upon several factors. The factors might be contract types, VM types, auto-scaling configuration parameters, and incoming workload demand. Identifying a combination of parameters that results in SLA compliance directly in the system is often sophisticated, while the manual analysis is prone to errors due to the huge number of possibilities. This paper proposes the modeling of auto-scaling mechanisms in a typical cloud infrastructure using a stochastic Petri net (SPN) and the employment of a well-established adaptive search metaheuristic (GRASP) to discover critical trade-offs between performance and cost in cloud services.The proposed SPN models enable cloud designers to estimate the metrics of cloud services in accordance with each required SLA such as the best configuration, cost, system response time, and throughput.The auto-scaling SPN model was extensively validated with 95% confidence against a real test-bed scenario with 18.000 samples. A case-study of cloud services was used to investigate the viability of this method and to evaluate the adoptability of the proposed auto-scaling model in practice. On the other hand, the proposed optimization algorithm enables the identification of economic system configuration and parameterization to satisfy required SLA and budget constraints. The adoption of the metaheuristic GRASP approach and the modeling of auto-scaling mechanisms in this work can help search for the optimized-quality solution and operational management for cloud services in practice.

Diagnosability of fault patterns with labeled stochastic Petri nets

This paper is about the diagnosability of fault patterns in timed stochastic discrete event systems. For this purpose, the diagnosability problem is formulated with labeled stochastic Petri net models and pure logical fault pattern nets. A particular composition of a labeled stochastic Petri net with a fault pattern net is proposed and is shown to characterize in an explicit way the fault patterns, including the timing and probabilistic aspects of the underlying system. Logical and probabilistic verifiers are derived, and used to establish a set of conditions to check not only the strong diagnosability property but also weaker notions of diagnosability.

SPN-Based Performance Analysis of Multiple Users’ Behaviors for SNS

With the rapid development of various applications of Information Technology, big data are increasingly generated by social network services (SNS) nowadays. The designers and providers of SNS distribute different client applications for PC, Mobile phone, IPTV etc., so that users can obtain related service via mobile or traditional Internet. Good scalability and considerably short time delay are important indices for evaluating social network systems. As a result, investigating and mining the principle of users’ behaviors is an important issue which can guide service providers to establish optimal systems with SNS. On the basis of analyzing the characteristics of social network system, this paper constructed a Stochastic Petri Net (SPN) model for describing the behaviors of three users for SNS. Moreover, the scalability of users’ behaviors of SNS was studied by extending the SPN model of three users to the one of four users. Furthermore, average time delay was chosen as the performance index to evaluate the performance of these two constructed SPN models with Stochastic Petri Net Package (SPNP) 6.0. For different parameters of number of connections, traffic load and buffer size, various trends and numerical results are derived thereby. The methodology of modeling and simulation in this paper can be further used to study the performance of SNS.

Reliability and availability evaluation of subsea high integrity pressure protection system using stochastic Petri net

In this paper, a safety evaluation method of subsea High Integrity Pressure Protection System (HIPPS) based on a generalized stochastic Petri net model is proposed. Different test methods were used to detect different types of failures and to analyze the reliability of HIPPS components under the influence of common cause failures and incomplete repair. The reliability curve of a diagnostic system consisting of a transmitter system and a logic system under the influence of uncertainty over time is analyzed. The safety of HIPPS with diverse test methods were quantitatively analyzed. The results show a significant improvement in the performance of the system after testing and maintenance. Both partial-stroke testing and increased partial-stroke test coverage can be used to increase the HIPPS performance compared to traditional methods. The analysis of the Partial stroke test (PST) strategy can afford a academic basis for the selection of PST frequency and Functional test (FT) interval in practical engineering.

Reliability Modeling and Analysis of Reactor Protection System Based on FPGA

In order to establish a reactor protection system reliability model based on the field programmable gate array (FPGA) to provide effective analysis and verification methods for system safety, this study adopts the fault tree and stochastic Petri net (SPN) models to perform reliability modeling and analysis for the single channel of CANDU reactor shutdown system 1 (SDS1). The analysis by fault tree model provides the minimal cut set. With the top event probability taken as the system fault probability, and in consideration of the fault detection, maintenance and periodic testing, the probability of rejection of the system is obtained by the stochastic Petri net model simulation. The results show that both the fault tree and state space representation are limited to a certain extent, while the stochastic Petri net can reflect the impact of fault detection and periodic tests on the reactor protection system, dynamically present the system reliability, and avoid the problem of state space explosion. Therefore, the stochastic Petri net model established in this study is suitable for the reliability modeling of the reactor protection system.

Modified Stochastic Petri Net-Based Modeling and Optimization of Emergency Rescue Processes during Coal Mine Accidents

The coal mine accidents seriously affect the safety and efficiency of mining for coal mining enterprises. The reliable emergency rescue (ER) processes are explored to minimize the loss of accidents. This paper introduces the stochastic Petri net (SPN) and Markov chain (MC) models based on the system structure flow to analyze the ER processes of coal mine accidents. In addition, a triangle fuzzy strategy is presented to optimize the SPN model. The “9·28” major water inrush accident in Shanxi Fenxi Zhengsheng Coal Company of China is adopted to evaluate the time performance and accident data of the ER process. The MC model-based steady-state probabilities of the system under various states are used to calculate the average delay time of this system. The triangular fuzzy strategy is used to analyze the change value of the total time in the ER system at the unit transition speed when the firing rate of each transition is changed, which finds the most time-consuming key activities in the ER process. The results show that SPN and MC can reflect the dynamic behaviors of ER process, which provides a reference for the rescue operations of other coal mine accidents. The triangular fuzzy strategy can quickly find out the key activities affecting the ER time, which greatly decreases the calculations generated by analyzing the total time of the system changed at the unit transition speed.

Offloading Data through Unmanned Aerial Vehicles: A Dependability Evaluation

Applications in the Internet of Things (IoT) context continuously generate large amounts of data. The data must be processed and monitored to allow rapid decision making. However, the wireless connection that links such devices to remote servers can lead to data loss. Thus, new forms of a connection must be explored to ensure the system’s availability and reliability as a whole. Unmanned aerial vehicles (UAVs) are becoming increasingly empowered in terms of processing power and autonomy. UAVs can be used as a bridge between IoT devices and remote servers, such as edge or cloud computing. UAVs can collect data from mobile devices and process them, if possible. If there is no processing power in the UAV, the data are sent and processed on servers at the edge or in the cloud. Data offloading throughout UAVs is a reality today, but one with many challenges, mainly due to unavailability constraints. This work proposes stochastic Petri net (SPN) models and reliability block diagrams (RBDs) to evaluate a distributed architecture, with UAVs focusing on the system’s availability and reliability. Among the various existing methodologies, stochastic Petri nets (SPN) provide models that represent complex systems with different characteristics. UAVs are used to route data from IoT devices to the edge or the cloud through a base station. The base station receives data from UAVs and retransmits them to the cloud. The data are processed in the cloud, and the responses are returned to the IoT devices. A sensitivity analysis through Design of Experiments (DoE) showed key points of improvement for the base model, which was enhanced. A numerical analysis indicated the components with the most significant impact on availability. For example, the cloud proved to be a very relevant component for the availability of the architecture. The final results could prove the effectiveness of improving the base model. The present work can help system architects develop distributed architectures with more optimized UAVs and low evaluation costs.

Performance and availability evaluation of an smart hospital architecture

Low latency and high availability of resources are essential characteristics to guarantee the quality of services in health systems. Hospital systems must be efficient to prevent loss of human life. Smart hospitals promise a health revolution by capturing and transmitting patient data to doctors in real-time via a wireless sensor network. However, there is a significant difficulty in assessing the performance and availability of such systems in real contexts due to failures not being tolerated and high implementation costs. This paper adopts analytical models to assess the performance and availability of intelligent hospital systems without having to invest in real equipment beforehand. Two Stochastic Petri Net models were proposed to represent intelligent hospital architectures. One model is used to assess performance, and another to assess availability. The models are pretty parametric, making it possible to calibrate the resources, service times, times between failures, and times between repairs. The availability model, for example, allows you to define 48 parameters, allowing you to evaluate a large number of scenarios. The analysis showed that the arrival rate in the performance model is an impacting parameter. It was possible to observe the close relationship between MRT, resource utilization, and discard rate in different scenarios, especially for high arrival rates. Three scenarios were explored considering the second model. The highest availability results were observed in scenario A, composed of server redundancy (local and remote). Such scenario—with redundancy—presented an availability of 99.9199%, that is, 7.01 h/year of inactivity. In addition, this work presents a sensitivity analysis that identifies the most critical components of the architecture. Therefore, this work can help hospital system administrators plan more optimized architectures according to their needs.

Performance evaluation in BRT systems: An analysis to predict the BRT systems planning

Mobility issues may create various inconveniences in urban areas due to traffic light delays, traffic jams and acidents. Alternatives have been created to improve public transportation. One of them is the Bus rapid transit system (BRT), delivering convincing results from a cost-effective perspective; i.e., lower deployment costs and a greater number of passengers. This paper proposes a Stochastic Petri Net (SPN) model for performance evaluation of the BRT system, focusing on the mean system size, mean queue size, mean queue time and the probability that the user will miss the bus (discard probability). Scenarios based on the BRT system were created, improving a set of solutions being with a variation in headways and in the number of vehicles on the route. The results show that, from a management perspective, it is up to the decision maker to define which is the most important metric at a given moment and, thus, to define the start intervals, as well as the number of vehicles to have on the route. Under the perspective in study, the best scenario is presented with headways of 300s and 5 vehicles in the route, operating as the one that leads to lower waiting times for passengers.

SystemC Implementation of Stochastic Petri Nets for Simulation and Parameterization of Biological Networks

Model development and simulation of biological networks is recognized as a key task in Systems Biology. Integrated with in vitro and in vivo experimental data, network simulation allows for the discovery of the dynamics that regulate biological systems. Stochastic Petri Nets (SPNs) have become a widespread and reference formalism to model metabolic networks thanks to their natural expressiveness to represent metabolites, reactions, molecule interactions, and simulation randomness due to system fluctuations and environmental noise. In the literature, starting from the network model and the complete set of system parameters, there exist frameworks that allow for dynamic system simulation. Nevertheless, they do not allow for automatic model parameterization, which is a crucial task to identify, in silico, the network configurations that lead the model to satisfy specific temporal properties. To cover such a gap, this work first presents a framework to implement SPN models into SystemC code. Then, it shows how the framework allows for automatic parameterization of the networks. The user formally defines the network properties to be observed and the framework automatically extrapolates, through Assertion-based Verification (ABV), the parameter configurations that satisfy such properties. We present the results obtained by applying the proposed framework to model the complex metabolic network of the purine metabolism. We show how the automatic extrapolation of the system parameters allowed us to simulate the model under different conditions, which led to the understanding of behavioral differences in the regulation of the entire purine network. We also show the scalability of the approach through the modeling and simulation of four biological networks, each one with different structural characteristics.

Performance safety enforcement in stochastic event graphs against boost and slow attacks

This paper studies a performance safety enforcing problem in stochastic event graphs, a subclass of stochastic Petri net models. We assume that an intruder can attack part of the transitions to increase/decrease their firing rate such that the performance of the system violates a given safety interval. The difficulty in solving this problem is that the capability of the intruder, i.e., the number of transitions that can be simultaneously attacked, is limited. The control aim is to find a protecting policy such that the performance of the protected plant is guaranteed to be in a given safety interval. We show that this problem can be formulated as a two-player game between the intruder and the operator of the plant. By using mixed integer linear programming technique, we develop a heuristic method to compute a protecting policy that is locally optimal.

Deep Understanding of Technical Documents: Part I. Diagrams Structural-functional Modeling

The automatic deep understanding of technical documents is a privilege only to humans so far, since it requires knowledge coming from many different modalities, like text, diagrams, formulas, tables, graphics, pictures, etc. Thus, in response to this very large and complex challenge, this paper investigates the synergistic association of only two modalities, the diagrams as main modality and natural language text as an assistive one in an effort to combine them together for deeper understanding of technical documents. In particular, it presents the formal modelling of a hybrid methodology capable to automatically extract the structural and functional behavior of a system described in a technical document without the use of original code. By system here we mean the block diagram(s) of a system. The methodology presented here is based on a formal language, called Synergy, to efficiently represent and synthesize the structural features of the system, and convert them into a Stochastic Petri-nets (SPN) model as for expressing the functional behavior of the understudy system. The overall methodology will contribute to an automatic deep understanding of technical documents (TD) without the main involvement of human users.

Stochastic Model Driven Performance and Availability Planning for a Mobile Edge Computing System

Mobile Edge Computing (MEC) has emerged as a promising network computing paradigm associated with mobile devices at local areas to diminish network latency under the employment and utilization of cloud/edge computing resources. In that context, MEC solutions are required to dynamically allocate mobile requests as close as possible to their computing resources. Moreover, the computing power and resource capacity of MEC server machines can directly impact the performance and operational availability of mobile apps and services. The systems practitioners must understand the trade off between performance and availability in systems design stages. The analytical models are suited to such an objective. Therefore, this paper proposes Stochastic Petri Net (SPN) models to evaluate both performance and availability of MEC environments. Different to previous work, our proposal includes unique metrics such as discard probability and a sensitivity analysis that guides the evaluation decisions. The models are highly flexible by considering fourteen transitions at the base model and twenty-five transitions at the extended model. The performance model was validated with a real experiment, the result of which indicated equality between experiment and model with p-value equal to 0.684 by t-Test. Regarding availability, the results of the extended model, different from the base model, always remain above 99%, since it presents redundancy in the components that were impacting availability in the base model. A numerical analysis is performed in a comprehensive manner, and the output results of this study can serve as a practical guide in designing MEC computing system architectures by making it possible to evaluate the trade-off between Mean Response Time (MRT) and resource utilization.

An analytical approach for optimization of computer network design considering the integration of the communication and power infrastructures

SummaryNowadays, computer networks are critical to the success of small and large businesses. They connect people, support applications and services, and provide access to the resources that keep the businesses running. Our work proposes analytical models and a methodology for supporting the optimization of the network infrastructure design, considering both technical and business oriented metrics, such as availability, reliability, and total cost. The integration of communication and power infrastructures is supported by this methodology. The dependability (availability/reliability) models were created using the Reliability Block Diagram and Stochastic Petri Net modeling mechanisms following a hierarchical approach. A case study considering the design of a real‐world network infrastructure is presented to illustrate the proposed methodology. The results showed a significant reduction in the design complexity as well as an improvement in the relationship between technical and business aspects.

Model-based pathway enrichment analysis applied to the TGF-beta regulation of autophagy in autism

To differentiate between conditions of health and disease, current pathway enrichment analysis methods detect the differential expression of distinct biological pathways. System-level model-driven approaches, however, are lacking. Here we present a new methodology that uses a dynamic model to suggest a unified subsystem to better differentiate between diseased and healthy conditions. Our methodology includes the following steps: 1) detecting connections between relevant differentially expressed pathways; 2) construction of a unified in silico model, a stochastic Petri net model that links these distinct pathways; 3) model execution to predict subsystem activation; and 4) enrichment analysis of the predicted subsystem. We apply our approach to the TGF-beta regulation of the autophagy system implicated in autism. Our model was constructed manually, based on the literature, to predict, using model simulation, the TGF-beta-to-autophagy active subsystem and downstream gene expression changes associated with TGF-beta, which go beyond the individual findings derived from literature. We evaluated the in silico predicted subsystem and found it to be co-expressed in the normative whole blood human gene expression data. Finally, we show our subsystem’s gene set to be significantly differentially expressed in two independent datasets of blood samples of ASD (autistic spectrum disorders) individuals as opposed to controls. Our study demonstrates that dynamic pathway unification can define a new refined subsystem that can significantly differentiate between disease conditions.

Surveillance System in Smart Cities: A Dependability Evaluation Based on Stochastic Models

Surveillance monitoring systems are highly necessary, aiming to prevent many social problems in smart cities. The internet of things (IoT) nowadays offers a variety of technologies to capture and process massive and heterogeneous data. Due to the fact that (i) advanced analyses of video streams are performed on powerful recording devices; while (ii) surveillance monitoring services require high availability levels in the way that the service must remain connected, for example, to a connection network that offers higher speed than conventional connections; and that (iii) the trust-worthy dependability of a surveillance system depends on various factors, it is not easy to identify which components/devices in a system architecture have the most impact on the dependability for a specific surveillance system in smart cities. In this paper, we developed stochastic Petri net models for a surveillance monitoring system with regard to varying several parameters to obtain the highest dependability. Two main metrics of interest in the dependability of a surveillance system including reliability and availability were analyzed in a comprehensive manner. The analysis results show that the variation in the number of long-term evolution (LTE)-based stations contributes to a number of nines (#9s) increase in availability. The obtained results show that the variation of the mean time to failure (MTTF) of surveillance cameras exposes a high impact on the reliability of the system. The findings of this work have the potential of assisting system architects in planning more optimized systems in this field based on the proposed models.