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In this study, we analyzed the evolution of online public opinion on emergencies using a new Stochastic Petri Net modeling approach. First, an intuitive description of the emergency online public opinion development process was conceptualized from the life cycle evolution law perspective. Then, based on Petri net theory, a Stochastic Petri Net isomorphic Markov chain model was constructed to simulate the evolution of online public opinion on emergencies. Finally, four real-life cases were selected to validate and analyze the model, demonstrating that the evolutionary leaps, complexity, critical nodes, evolutionary rate, and execution time differ across different online public opinions on emergencies. The study results indicate that this modeling approach has certain advantages in examining the evolution based on multi-factor coupling and quantifying the evolution law in online public opinion on emergencies. [ABSTRACT FROM AUTHOR]

In recent years, RNA research has grown due to the discovery of its important role in biological systems. RNA molecules are involved in protein synthesis and play a critical role in gene expression. Many of these molecules are produced through the enzymatic digestion or spontaneous degradation of larger molecules, and are consequently essential for cellular processes. The mechanisms of RNA degradation appear to be one of the most important factors influencing RNA activity. In this study, a stochastic Petri net-based model of spontaneous (non-enzymatic) RNA degradation was built and analysed. The model was analysed using t-invariants, MCT sets, and simulation-based analyses. The systems approach enabled a thorough analysis of the phenomenon, resulting in significant biological insights.

In this study, we analyzed the evolution of online public opinion on emergencies using a new Stochastic Petri Net modeling approach. First, an intuitive description of the emergency online public opinion development process was conceptualized from the life cycle evolution law perspective. Then, based on Petri net theory, a Stochastic Petri Net isomorphic Markov chain model was constructed to simulate the evolution of online public opinion on emergencies. Finally, four real-life cases were selected to validate and analyze the model, demonstrating that the evolutionary leaps, complexity, critical nodes, evolutionary rate, and execution time differ across different online public opinions on emergencies. The study results indicate that this modeling approach has certain advantages in examining the evolution based on multi-factor coupling and quantifying the evolution law in online public opinion on emergencies.

Abstract Introduction Syphilis 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. Methods The 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. Results According 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. Conclusions The 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.

Cloud computing provides an abstraction of the physical tiers, allowing a sense of infinite resources. However, the physical resources are not unlimited and need to be used more assertively. The challenge of cloud computing is to improve the use of resources without jeopardizing the availability of environments. Stochastic models can efficiently evaluate cloud computing systems, which is needed for proper capacity planning. This paper proposes an availability evaluation from a system hosted on a private cloud. To achieve this goal, we created hierarchical models to represent the studied environment. Sensitivity analysis is performed to identify the most influential parameters and components that must be compatible with improving system availability. A case study supports the demonstration of the accuracy and utility of our methodology. We propose structural changes in the environment using different redundancies in the components to obtain satisfactory results. Finally, we analyze scenarios regarding DC's redundancy. [ABSTRACT FROM AUTHOR]

Introduction: Syphilis 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. Methods: The 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. Results: According 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. Conclusions: The 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. [ABSTRACT FROM AUTHOR]

Modeling of reliability of the complex systems (machines, large networks, human body) is an important area of recent research. There are two main approaches applied: i) fault trees, ii) Petri nets. For the probabilistic study of a system is vital to know its minimal cut/minimal path sets. Both for fault trees and Petri Nets it is an NP-hard problem. Liu and Chiou (1997) described the equivalence of both representations for a given system. Furthermore, they found a top-down matrix algorithm to find critical cuts and minimal paths of the Petri net of the system. They claim without proof that their algorithm is more efficient than the ones for fault trees. We present both representations of a system. The algorithm is illustrated on a simple example of a three-masted vessel and a more complex “three-motor” system by Vesely et al. (1981).

With the prevalence of Internet of Things (IoT), edge computing has emerged as a novel computing model for optimizing traditional cloud computing systems by moving part of the computational tasks to the edge of the network for better performance and security. With the technique of services computing, edge computing systems can accommodate the application requirements with more agility and flexibility. In large-scale edge computing systems, service composition as one of the most important problems in services computing suffers from several new challenges, i.e., complex layered architecture, failures and recoveries always in the lifecycle, and search space explosion. In this paper, we make an attempt at addressing these challenges by designing a simulation-based optimization approach for reliability-aware service composition. Composite stochastic Petri net models are proposed for formulating the dynamics of multi-layered edge computing systems, and their corresponding quantitative analysis is conducted. To solve the state explosion problem in large-scale systems or complex service processes, time scale decomposition technique is applied to improving the efficiency of model solving. Additionally, simulation schemes are designed for performance evaluation and optimization, and ordinal optimization technique is introduced to significantly reduce the size of the search space. Finally, we conduct experiments based on real-life data, and the empirical results validate the efficacy of the approach.

Efficient business process is important to the operations of supply chain finance (SCF). Many deficiencies exist in the processes of SCF such as complicated workflows and high time-consuming steps. However, few studies have paid attention to evaluate and improve the performance of SCF processes. We empirically model and investigate the processes of supply chain finance by constructing a Stochastic Petri Net based on the field survey of a focal firm. Two critical indices, place busy rate and transition utilization rate, are evaluated. The results demonstrate that some places (transitions) of the Petri Net have high busy rates (utilization rates). By integrating the Petri Net and dependency graph, several key places and transitions in the Petri Net of SCF processes are identified for further optimization. To improve the performance of SCF processes, we propose three optional adjusting schemes on the basis of information sharing perspective (for the first half of the Petri Net) and risk sharing perspective (for the second half of the Petri Net). The proposed optimization strategies have further been proven to reduce the place busy rates, shorten the process, and improve the process efficiency of the supply chain finance.

In this paper, we develop a methodology to capture and analyze the interplay of attack-defense strategies for intrusion detection in an autonomous distributed Internet of Things (IoT) system. In our formulation, every node must participate in lightweight intrusion detection of a neighbor target node. Consequently, every good node would play a set of defense strategies to faithfully defend the system while every bad node would play a set of attack strategies for achieving their own goals. We develop an analytical model based on Stochastic Petri Net (SPN) modeling techniques. Our methodology allows the optimal defense strategies to be played by good nodes to maximize the system lifetime when given a set of parameter values characterizing the distributed IoT system operational environment. We conduct a detailed performance evaluation based on an experiment dataset deriving from a reference autonomous distributed IoT system comprising 128 sensor-carrying mobile nodes and show how IDS defense mechanisms can counter malicious attack mechanisms under the ADIoTS system while considering multiple failure conditions.

Cyber–physical system (CPS) is a complex system that contains multiple components working cooperatively. According to its characteristics, we propose an object-oriented generalized stochastic Petri net (OGSPN), in which the CPS is abstracted into several types of objects and its logical structure and working process is visually described. Moreover, we model and measure the time consumed by each activity in CPS for quantitative analysis. To simplify the process of performance analysis on this model, in this article we propose a compression algorithm to convert OGSPN into a generalized stochastic Petri net (GSPN). Considering the uncertainty in CPS, we use a fuzzy mathematics based method to process the compressed model of GSPN for improving the accuracy of the performance analysis. We apply our method to a real-world thick metal plate production line in a manufacturing company, and the availability of our method is verified by extensive experiments. [ABSTRACT FROM AUTHOR]

As a common geological disaster in the Loess Plateau, loess collapse has a huge impact on local industry, agriculture, transportation and water conservancy projects. Loess collapse is due to instability caused by the influence of weather, topography, soil type, human engineering activities and other factors that cause environmental destruction. To reveal the relationship between the collapse of loess and its influencing factors, a calculation model for the probability of loess collapse was proposed in this study. In this study, the causes of loess collapse were analyzed by establishing a multivariate aggregate structure. Stochastic Petri net and its isomorphic Markov chain were applied to examine the collapse process and the accuracy of the model was verified through experiments. Results demonstrate that road network density and soil stability have large utilization rate and great influence on the entire system. The daily temperature difference and daily rainfall below 10 °C and 30 mm strongly influence the probability of collapse warning. The change of road network density affects the probability of early warning, but the effect decreases with the increase of density. By examining the early warning mechanism of loess collapse, this study provides a reference value for the prevention and control of other types of loess collapse disasters. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Cloud computing is attractive to business owners and allows enterprises to start from the small and increase resources only when there is a rise in service demand, but cloud may become expensive. Fog computing has many advantages, and it is suited for the applications whereby real time is very important, but fog resources may also be highly limited. The cloud and fog computing may perform tasks together to attend different types of applications and mitigate their limitations. However, taking into account variables such as latency, workload and computational capacity, it becomes complex to define under what circumstances it is more advantageous to use the cloud layer or the fog. This paper proposes a stochastic Petri net to model such a scenario by considering cloud and fog. The model permits to configure 12 parameters including, for example, the number of available resources, workload and mean requests arrival time. We present a case study using a classical big data algorithm to validate the model. The case study is a practical guide to infrastructure administrators to adjust their architectures by finding the trade-off between cost and performance. [ABSTRACT FROM AUTHOR]

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.

The spread of the Coronavirus (COVID-19) pandemic across countries all over the world urges governments to revolutionize the traditional medical hospitals/centers to provide sustainable and trustworthy medical services to patients under the pressure of the huge overload on the computing systems of wireless sensor networks (WSNs) for medical monitoring as well as treatment services of medical professionals. Uncertain malfunctions in any part of the medical computing infrastructure, from its power system in a remote area to the local computing systems at a smart hospital, can cause critical failures in medical monitoring services, which could lead to a fatal loss of human life in the worst case. Therefore, early design in the medical computing infrastructure’s power and computing systems needs to carefully consider the dependability characteristics, including the reliability and availability of the WSNs in smart hospitals under an uncertain outage of any part of the energy resources or failures of computing servers, especially due to software aging. In that regard, we propose reliability and availability models adopting stochastic Petri net (SPN) to quantify the impact of energy resources and server rejuvenation on the dependability of medical sensor networks. Three different availability models (A, B, and C) are developed in accordance with various operational configurations of a smart hospital’s computing infrastructure to assimilate the impact of energy resource redundancy and server rejuvenation techniques for high availability. Moreover, a comprehensive sensitivity analysis is performed to investigate the components that impose the greatest impact on the system availability. The analysis results indicate different impacts of the considered configurations on the WSN’s operational availability in smart hospitals, particularly 99.40%, 99.53%, and 99.64% for the configurations A, B, and C, respectively. This result highlights the difference of 21 h of downtime per year when comparing the worst with the best case. This study can help leverage the early design of smart hospitals considering its wireless medical sensor networks’ dependability in quality of service to cope with overloading medical services in world-wide virus pandemics.

Modeling of reliability of the complex systems (machines, large networks, human body) is an important area of recent research. There are two main approaches applied: i) fault trees, ii) Petri nets. For the probabilistic study of a system is vital to know its minimal cut/minimal path sets. Both for fault trees and Petri Nets it is an NP-hard problem. Liu and Chiou (1997) described the equivalence of both representations for a given system. Furthermore, they found a top-down matrix algorithm to find critical cuts and minimal paths of the Petri net of the system. They claim without proof that their algorithm is more efficient than the ones for fault trees. We present both representations of a system. The algorithm is illustrated on a simple example of a three-masted vessel and a more complex “three-motor” system by Vesely et al. (1981). [ABSTRACT FROM AUTHOR]

The characteristics of cloud computing, such as large-scale, dynamics, heterogeneity and diversity, present a range of challenges for the study on modeling and performance evaluation on cloud data centers. Performance evaluation not only finds out an appropriate trade-off between cost-benefit and quality of service (QoS) based on service level agreement (SLA), but also investigates the in uence of virtualization technology. In this paper, we propose an Energy-Aware Optimization (EAO) algorithm with considering energy consumption, resource diversity and virtual machine migration. In addition, we construct a stochastic model for Energy- Aware Migration-Enabled Cloud (EAMEC) data centers by introducing Dynamic Scalable Stochastic Petri Net (DSSPN). Several performance parameters are defined to evaluate task backlogs, throughput, reject rate, utilization, and energy consumption under different runtime and machines. Finally, we use a tool called SPNP to simulate analytical solutions of these parameters. The analysis results show that DSSPN is applicable to model and evaluate complex cloud systems, and can help to optimize the performance of EAMEC data centers. [ABSTRACT FROM AUTHOR]

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.

Software performance engineering is a mature field that offers methods to assess system performance. Process mining is a promising research field applied to gain insight on system processes. The interplay of these two fields opens promising applications in the industry. In this work, we report our experience applying a methodology, based on process mining techniques, for the performance assessment of a commercial data-intensive software application. The methodology has successfully assessed the scalability of future versions of this system. Moreover, it has identified bottlenecks components and replication needs for fulfilling business rules. The system, an integrated port operations management system, has been developed by PRODEVELOP, a medium-sized software enterprise with high expertise in geospatial technologies. The performance assessment has been carried out by a team composed by practitioners and researchers. Finally, the paper offers a deep discussion on the lessons learned during the experience, that will be useful for practitioners to adopt the methodology and for researcher to find new routes. [ABSTRACT FROM AUTHOR]

Aiming at the defect that the security attribute of RSCN couldn't be described with measurement,a survivabil-ity model for RSCN was proposed based on the stochastic Petri net.Firstly,a non-Markovian stochastic Petri net for RSCN was proposed,and then the state schematics was educed based on the FCFS fault repair policy subsequently.Fina-ly,the survivability model was concluded based on the probability equation of system state by importing supplementary variable.The model was analyzed and validated for validity through emu ational experiments.The emulational results show that the comparability between the computed-results of model and emulational results is good,and the model can be used to discribe the survivability for RSCN.

Alzheimer's Disease (AD) is the most common neuro-degenerative disorder in the elderly that leads to dementia. The hallmark of AD is senile lesions made by abnormal aggregation of amyloid beta in extracellular space of brain. One of the challenges in AD treatment is to better understand the mechanism of action of key proteins and their related pathways involved in neuronal cell death in order to identify adequate therapeutic targets. This study focuses on the phenomenon of aggregation of amyloid beta into plaques by considering the signal transduction pathways of Calpain-Calpastatin (CAST) regulation system and Amyloid Precursor Protein (APP) processing pathways along with Ca2+ channels. These pathways are modeled and analyzed individually as well as collectively through Stochastic Petri Nets for comprehensive analysis and thorough understating of AD. The model predicts that the deregulation of Calpain activity, disruption of Calcium homeostasis, inhibition of CAST and elevation of abnormal APP processing are key cytotoxic events resulting in an early AD onset and progression. Interestingly, the model also reveals that plaques accumulation start early (at the age of 40) in life but symptoms appear late. These results suggest that the process of neuro-degeneration can be slowed down or paused by slowing down the degradation rate of Calpain-CAST Complex. In the light of this study, the suggestive therapeutic strategy might be the prevention of the degradation of Calpain-CAST complexes and the inhibition of Calpain for the treatment of neurodegenerative diseases such as AD.

To evaluate and predict component-based software security, a two-dimensional model of software security is proposed by Stochastic Petri Net in this paper. In this approach, the software security is modeled by graphical presentation ability of Petri nets, and the quantitative prediction is provided by the evaluation capability of Stochastic Petri Net and the computing power of Markov chain. Each vulnerable component is modeled by Stochastic Petri net and two parameters, Successfully Attack Probability (SAP) and Vulnerability Volume of each component to another component. The second parameter, as a second dimension of security evaluation, is a metric that is added to modeling to improve the accuracy of the result of system security prediction. An isomorphic Markov chain is obtained from a corresponding SPN model. The security prediction is calculated based on the probability distribution of the MC in the steady state. To identify and trace back to the critical points of system security, a sensitive analysis method is applied by derivation of the security prediction equation. It provides the possibility to investigate and compare different solutions with the target system in the designing phase.

Alzheimer's Disease (AD) is the most common neuro-degenerative disorder in the elderly that leads to dementia. The hallmark of AD is senile lesions made by abnormal aggregation of amyloid beta in extracellular space of brain. One of the challenges in AD treatment is to better understand the mechanism of action of key proteins and their related pathways involved in neuronal cell death in order to identify adequate therapeutic targets. This study focuses on the phenomenon of aggregation of amyloid beta into plaques by considering the signal transduction pathways of Calpain-Calpastatin (CAST) regulation system and Amyloid Precursor Protein (APP) processing pathways along with Ca2+ channels. These pathways are modeled and analyzed individually as well as collectively through Stochastic Petri Nets for comprehensive analysis and thorough understating of AD. Themodel predicts that the deregulation of Calpain activity, disruption of Calcium homeostasis, inhibition of CAST and elevation of abnormal APP processing are key cytotoxic events resulting in an early AD onset and progression. Interestingly, the model also reveals that plaques accumulation start early (at the age of 40) in life but symptoms appear late. These results suggest that the process of neuro-degeneration can be slowed down or paused by slowing down the degradation rate of Calpain-CAST Complex. In the light of this study, the suggestive therapeutic strategy might be the prevention of the degradation of Calpain-CAST complexes and the inhibition of Calpain for the treatment of neurodegenerative diseases such as AD. [ABSTRACT FROM AUTHOR]

Purpose: Using mathematical models for cancer treatment had excellent outcomes in recent years. Modeling of the tumor-immune interactions is possible by several mathematical models. Stochastic models such as Stochastic Petri Net (SPN) consider the random effects and uncertainty in the biological environments. Therefore, they are a good choice for simulation of biological systems, specially the complex dynamical network of tumor-immune interactions. Methods: In this paper we have modeled the interactions of the B16-F10 tumor cells, Cytotoxic T cells (CTL) and Myeloid Derived Suppressor cell (MDSC) by SPN. By systematic search on immunology resources, we identified the behaviors, characteristics, and effective interactions between these cells. We used SPN to construct the dynamics of these cells, therefore a dynamical network of tumor-immune interactions (DNTII) has been made. By considering these cells as places and all interactions as transitions of SPN, we can simulate this complex biological network. The model has control parameters that their regulation causes DNTII to mimic different behaviors of tumor-immune system. Results: The model can properly simulate dynamical complex network of tumor-immune interactions compared to biological reality. This model is capable to represent different behavior of tumor-immune system such as tumor escape from immune response, overcoming the immune system on the tumor cells and equilibrium of the tumor and immune system. Conclusion: By using this model, we can test different immunology hypothesis in a simulation environment without spending any time and cost.