Generalized Stochastic Petri Net Model Research Articles

Integrating security in hazard analysis using STPA-Sec and GSPN: A case study of automatic emergency braking system

Hazard analysis is a vital step in developing intelligent connected vehicles, aiming to eliminate or control hazards in the initial stages of system development and to provide theoretical support for the system’s safety design. However, conventional hazard analysis methods, such as Fault Tree Analysis and Failure Mode and Effects Analysis, suffer from two shortcomings: they do not account for the impact of cybersecurity factors on system safety and do not provide sufficient quantification of hazard scenarios. To this end, we propose a quantifiable hazard analysis method with security consideration, which integrates System Theoretic Process Analysis for Security (STPA-Sec) and Generalized Stochastic Petri Net (GSPN), supporting the extraction, modeling, and quantification of hazards. Specifically, we employ STPA-Sec for qualitative analysis to identify causal scenarios, safety requirements, security requirements, and the corresponding mitigations. Then, based on the identified causal scenarios, a GSPN model is established to quantify system-level hazards. A case study on a real open-source test vehicle demonstrates that the proposed method not only offers a comprehensive analysis of hazards but also provides a quantitative assessment. Comparative assessments suggest that the proposed method exhibits an advantage in terms of analysis processes (integrating security) and results (quantification).

Petri net analysis of a queueing inventory system with orbital search by the server

Abstract In this article, a queueing inventory system with finite sources of demands, retrial demands, service time, lead time, ( s , S ) \left(s,S) replenishment policy, and demands search from the orbit was studied. When the lead time is exponentially distributed (resp. lead time is generally distributed), generalized stochastic Petri net (GSPN) (resp. Markov regenerative stochastic Petri net [MRSPN]) is proposed for this inventory system. The quantitative analysis of this stochastic Petri net model was obtained by continuous time Markov chain for the GSPN model (resp. the supplementary variable method for the MRSPN model). The probability distributions are obtained, witch allowed us to compute performance measures and the expected cost rate of the studied system.

A formal GSPN model of a virtual doctor dialogue system

This paper presents a formal generalized stochastic Petri net (GSPN)–based modeling of a virtual doctor (VDr) dialogue system. The interaction model between the VDr dialogue system and the human patient is a modified version of the Wickens model. The purpose of this model is to provide a better understanding of the interaction between the VDr dialogue system and the patient, as well as the integration of other components in the system, such as the patient’s medical history and emotions. Initially, the formal definition of the GSPN model of the VDr dialogue system is presented by incorporating the token color concept, which is a feature of Color GSPNs. Then, the GSPN formal modeling is described. Note that, the GSPN model presented here is at the simulation level and not a product. Furthermore, some examples are provided with the intention of facilitating the understanding of the token color utilization and the different GSPN markings.

Modeling and Analyzing Transmission of Infectious Diseases Using Generalized Stochastic Petri Nets

Some infectious diseases such as COVID-19 have the characteristics of long incubation period, high infectivity during the incubation period, and carriers with mild or no symptoms which are more likely to cause negligence. Global researchers are working to find out more about the transmission of infectious diseases. Modeling plays a crucial role in understanding the transmission of the new virus and helps show the evolution of the epidemic in stages. In this paper, we propose a new general transmission model of infectious diseases based on the generalized stochastic Petri net (GSPN). First, we qualitatively analyze the transmission mode of each stage of infectious diseases such as COVID-19 and explain the factors that affect the spread of the epidemic. Second, the GSPN model is built to simulate the evolution of the epidemic. Based on this model’s isomorphic Markov chain, the equilibrium state of the system and its changing laws under different influencing factors are analyzed. Our paper demonstrates that the proposed GSPN model is a compelling tool for representing and analyzing the transmission of infectious diseases from system-level understanding, and thus contributes to providing decision support for effective surveillance and response to epidemic development.

Risk assessment of FPSO topside based on generalized Stochastic Petri Net

This paper presents a Generalized Stochastic Petri Net (GSPN) approach to assess risk of FPSO topsides, considering the weather window and imperfect maintenance effect. The FPSO topside is considered as a multi-component system consisting of several assemblies. A GSPN model is developed according to system identification and the correlation between different components. The reliability, availability, and maintenance information of the system are derived using the model, based on failures collected from existing literature and database. An operation and maintenance cost model is established, and an optimized maintenance strategy is finally determined based on the GSPN outcomes. The results indicate that the proposed approach is an effective tool to evaluate the system risk and save the maintenance expenditure of FPSO topsides.

Task Allocation Approach for Minimizing Make-Span in Wireless Sensor Actor Networks

Wireless Sensor Actor Networks (WSANs) have contributed to the development of pervasive computing wherein time consideration to perform the tasks of pervasive applications is necessary. Hence, time constraint is one of the major challenges of WSANs. In this paper, we propose an analytical approach based on queuing theory to minimize the total time taken for completion of tasks, i.e., make-span, in WSANs with hybrid architecture. The best allocation rates of tasks to actor nodes are figured out through solving inequities and qualities resulting from a steady state analysis of the proposed model. Applying the calculated tasks arrival rates at each of the actors, the make-span could be minimized. To assess the accuracy of the tasks assignment rates to each of the actors attained from the suggested analytical approach and to provide a graphical representation of the WSAN a formal model in terms of the generalized stochastic Petri net (GSPN) is presented. The proposed GSPN model is analyzed, tasks distribution weights to the actors are determined, and then tasks allocation rates can be computed. Comparing the results achieved from the analytical approach and the GSPN model demonstrates that allocation rates and hence, the make-span figured out from proposed approach and the formal model are the same. Experimental results in typical scenarios show shorter make-span and longer network lifetime compared to when one of the two popular traditional task allocation algorithms, namely, opportunistic load balancing (OLB), and stochastic allocation (SA) algorithms, is used.

Reliability analysis for complex systems based on generalized stochastic petri nets and EDA approach considering common cause failure

PurposeThis paper aims to deal with the problems of failure dependence and common cause failure (CCF) that arise in reliability analysis of complex systems.Design/methodology/approachFirstly, a dynamic fault tree (DFT) is used to capture the dynamic failure behaviours and converted into an equivalent generalized stochastic petri net (GSPN) for quantitative analysis. Secondly, an efficient decomposition and aggregation (EDA) theory is combined with GSPN to deal with the CCF problem, which exists in redundant systems. Finally, Birnbaum importance measure (BIM) is calculated based on the EDA approach and GSPN model, and it is used to take decisions for system improvement and fault diagnosis.FindingsIn this paper, a new reliability evaluation method for dynamic systems subject to CCF is presented based on the DFT analysis and the GSPN model. The GSPN model is easy to capture dynamic failure behaviours of complex systems, and the movement of tokens in the GSPN model represent the changes in the state of the systems. The proposed method takes advantage of the GSPN model and incorporates the EDA method into the GSPN, which simplifies the reliability analysis process. Meanwhile, simulation results under different conditions show that CCF has made a considerable impact on reliability analysis for complex systems, which indicates that the CCF should not be ignored in reliability analysis.Originality/valueThe proposed method combines the EDA theory with the GSPN model to improve the efficiency of the reliability analysis.

Security Analysis for CBTC Systems under Attack–Defense Confrontation

Communication-based train controls (CBTC) systems play a major role in urban rail transportation. As CBTC systems are no longer isolated from the outside world but use other networks to increase efficiency and improve productivity, they are exposed to huge cyber threats. This paper proposes a generalized stochastic Petri net (GSPN) model to capture dynamic interaction between the attacker and the defender to evaluate the security of CBTC systems. Depending on the characteristics of the system and attack–defense methods, we divided our model into two phases: penetration and disruption. In each phase, we provided effective means of attack and corresponding defensive measures, and the system state was determined correspondingly. Additionally, a semiphysical simulation platform and game model were proposed to assist the GSPN model parameterization. With the steady-state probability of the system output from the model, we propose several indicators for assessing system security. Finally, we compared the security of the system with single defensive measures and multiple defensive measures. Our evaluations indicated the significance of the defensive measures and the seriousness of the system security situation.

An approach to modelling and analysing reliability of Breeze/ADL-based software architecture

Breeze/architecture description language (ADL), is an eXtensible markup language (XML) based architecture description language which is used to model software systems at the architecture level. Though Breeze/ADL provides an appropriate basis for architecture modelling, it can neither analyse nor evaluate the architecture reliability. In this paper, we propose a Breeze/ADL based strategy which, by combining generalized stochastic Petri net (GSPN) and tools for reliability analysis, supports architecture reliability modelling and evaluation. This work expands the idea in three directions: Firstly, we give a Breeze/ADL reliability model in which we add error attributes to Breeze/ADL error model for capturing architecture error information, and at the same time perform the system error state transition through the Breeze/ADL production. Secondly, we present how to map a Breeze/ADL reliability model to a GSPN model, which in turn can be used for reliability analysis. The other task is to develop a Breeze/ADL reliability analysis modelling tool---EXGSPN (Breeze/ADL reliability analysis modelling tool), and combine it with platform independent petri net editor 2 (PIPE2) to carry out a reliability assessment.

Optimizing reliability, maintainability and testability parameters of equipment based on GSPN

Reliability, maintainability and testability (RMT) are important properties of equipment, since they have important influence on operational availability and life cycle costs (LCC). Therefore, weighting and optimizing the three properties are of great significance. A new approach for optimization of RMT parameters is proposed. First of all, the model for the equipment operation process is established based on the generalized stochastic Petri nets (GSPN) theory. Then, by solving the GSPN model, the quantitative relationship between operational availability and RMT parameters is obtained. Afterwards, taking history data of similar equipment and operation process into consideration, a cost model of design, manufacture and maintenance is developed. Based on operational availability, the cost model and parameters ranges, an optimization model of RMT parameters is built. Finally, the effectiveness and practicability of this approach are validated through an example.

Urban Transport GSPN Model of Cyber-Physical Systems

Urban transport is an important part of urban activities, and it is not just a public works technical problems or traffic problems, but also is a comprehensive social problems. There are some traffic congestion problems exist in the current urban traffic network. By using the theory of generalized stochastic Petri to the study of Cyber-physical Systems (CPS), this paper established an urban transport GSPN (Generalized Stochastic Petri Net) model, which chosen bus priority strategies to improve the utilization of road.

Stochastic modeling for delay analysis of a VoIP network

VoIP (“Voice Over Internet Protocol”) is the transmission of voice communication through the Internet via IP-based telephony networks. VoIP has become very popular over recent years due to the cost advantages for consumers and businesses compared to the traditional telephony networks. Since it is deployed on packet-based networks, one of the major Quality of Service (QoS) concerns of VoIP technology is the average end-to-end connection delay. The objective of this paper is to present a queuing model for obtaining the end-to-end delay of a VoIP connection. The paper first describes all the partial delay components, and their mathematical formulations. Subsequently, based on all the partial delay components, a queuing model for the end-to-end delay of a VoIP connection is presented. The proposed queueing model is analyzed using a generalized stochastic Petri net (GSPN) model. From the GSPN model, we obtain numerical results for the end-to-end delay, which are presented graphically. The results are in accordance with the expected behavior of delay in a VoIP network.

An assembly strategy scheduling method for human and robot coordinated cell manufacturing

PurposeThe purpose of this paper is to propose a model of assembly strategy generation and selection for human and robot coordinated (HRC) cell assembly. High‐Mix, Low‐Volume production in small production manufacturing industry, tends to employ more flexible assembly cells. The authors propose innovative human and robot coordinated assembly cells to solve the problem of persistent growing cost for human resources and occasional changes in programs and configurations for robots. The first issue is to find out an optimal way to allocate the assembly subtasks to both humans and robots.Design/methodology/approachA dual Generalized Stochastic Petri Net (GSPN) model is theoretically studied and then off line built based on a practical assembly task for human and robot coordination. Based on GSPN, Monte Carlo method is carried out to study the time cost and payment cost or possible strategies, and Multiple‐Objective Optimization (MOOP) method related Cost‐effectiveness analysis is adopted to select the optimal ones.FindingsIt is discovered that human and robot coordinated assembly can reduce the assembly time and meanwhile reduce the assembly cost. The authors demonstrate the effectiveness of this approach by comparing the simulation and experimental results.Originality/valueThe novelty with this work is that the human and robot coordinated flexible assembly cell, as the authors proved, is the main stream in small production in future due to the higher human source pressure from society and cost pressure upon the company. Based on this innovative work, the authors proposed a dual GSPN model to model the assembly task allocation process for human and robot, the model of which is also effective in modeling the possible robot and human behaviors.

Dynamic Bandwidth Allocation for Multiple Traffic Classes in IEEE 802.16e WiMax Networks: A Petrinet Approach

Problem statement: WiMAX supports multiple types of traffic such as data, voice and video. Each flow requires a certain minimum bandwidth to achieve its QoS. Bandwidth allocation to traffic classes should be in such a way that fairness criteria is met with. Hence, we propose a dynamic bandwidth allocation mechanism to achieve fair and efficient allocation. Approach: We present a Generalized Stochastic Petri Net (GSPN) approach to model bandwidth allocation in Broadband Wireless Access (BWA) networks with multiple traffic classes. A dynamic weight assignment mechanism is proposed to enable fair bandwidth allocation among the competing traffic classes. Performance of the weight assignment mechanism is analytically evaluated using the GSPN model developed. Results: Results show performance improvement in terms of mean delay and normalized throughput of traffic classes compared to existing mechanisms. Simulation is carried out for different traffic rates. Analytical results are validated using simulations. Conclusion: Performance of the proposed system is evaluated in terms of mean delay and normalized system throughput. The model developed is generic and can be extended to any wireless network with multiple traffic classes.

An algorithmic approach for analysis of finite-source retrial systems with unreliable servers

This paper aims at presenting an approach for analyzing finite-source retrial systems with servers subject to breakdowns and repairs, using Generalized Stochastic Petri Nets (GSPNs). This high-level formalism allows a simple representation of such systems with different breakdown disciplines. From the GSPN model, a Continuous Time Markov Chain (CTMC) can be automatically derived. However, for multiserver retrial systems with unreliable servers, the models may have a huge state space. Using the GSPN model as a support, we propose an algorithm for directly computing the infinitesimal generator of the CTMC without generating the reachability graph. In addition, we develop the formulas of the main stationary performance and reliability indices, as a function of the number of servers, the size of the customer source and the stationary probabilities. Through numerical examples, we discuss the effect of the system parameters and the breakdown disciplines on performance.

Task dispatching approach to reduce the number of waiting tasks in grid environments

In this paper, a mathematical solution for reducing the mean number of the tasks waiting to be processed in a grid environment is proposed. The approach uses queuing theory and models the grid environment in the form of an open queuing network (QN). Applying the steady state analysis to the proposed QN and minimizing the mean number of waiting tasks within the grid environment, an equality and inequality system is obtained. Solving the equality and inequality system, subtasks arrival rates at each of the resources within the grid environment can be estimated. Applying the obtained subtasks arrival rates at each of the grid resources, the mean number of the waiting tasks in the grid environment could be minimized. To evaluate the results obtained from the proposed QN and provide a graphical representation of the grid environment a formal description of the environment in terms of generalized stochastic Petri nets (GSPNs) is presented. Steady state analyzing of the GSPN model and finding the subtask dispatching weights at each of the grid resources, subtask arrival rates can be estimated. Comparing the results obtained from two proposed approaches shows that the subtasks arrival rates achieved from QNs and GSPNs are the same.

Error recovery framework for integrated navigation system based on generalized stochastic petri nets

A mobile robot usually works in dynamic environments with many uncertainties caused by either humans or various obstacles. Such uncertainties may cause unexpected error situations that often lead to navigation failure. Therefore, the robot should be able to recover from these unexpected error situations. This paper proposes an error recovery framework based on generalized stochastic Petri nets (GSPN). The approach can provide several advantages. The proposed framework can model various error situations occurring in real environments, thereby enabling a robot to recover from error situations autonomously. The modeling, analysis, and performance evaluation can be also carried out using the GSPN model. Experimental results show that the proposed error recovery framework is useful for dependable navigation of a mobile robot operating autonomously.

The Quantitative Assessment of Domino Effects Based on Stochastic Petri Nets

The quantitative analysis of “domino” effects is one of the main aspects of hazard assessment in chemical industrial park. This paper demonstrates the application of heterogeneous stochastic Petri net modeling techniques to the quantitative assessment of the probabilities of domino effects of major accidents in chemical industrial park. First, five events are included in the domino effect models of major accidents: pool fire, explosion, boiling liquid expanding vapour explosion (BLEVE) giving rise to a fragment, jet fire and delayed explosion of a vapour cloud. Then, the domino effect models are converted into Generalized Stochastic Petri net (GSPN) in which the probability of the domino effect is calculated automatically. The Stochastic Petri nets’ models, which are state-space based ones, increase the modeling flexibility but create the state-space explosion problems. Finally, in order to alleviate the state-space explosion problems of GSPN models, this paper employs Stochastic Wellformed Net (SWN), a particular class of High-Level (colored) SPN. To conduct a case study on a chemical industrial park, the probability of domino effects of major accidents is calculated by using the GSPN model and SWN model in this paper.

QoS assessment via stochastic analysis

Using a stochastic modeling approach based on the Unified Modeling Language and enriched with annotations that conform to the UML profile for schedulability performance, and time, the authors propose a method for assessing quality of service (QoS) in fault-tolerant (FT) distributed systems. From the UML system specification, they produce a generalized stochastic Petri net (GSPN) performance model for assessing an FT application's QoS via stochastic analysis. The ArgoSPE tool provides support for the proposed technique, helping to automatically produce the GSPN model

Performance evaluation on a double-layered satellite network

How to evaluate the performance of satellite networks is a prerequisite to the construction of satellite networks, and is also one of challenges in the researches on satellite networks. In this paper, generalized stochastic Petri net (GSPN) models are presented to carry out the performance analysis of a double-layered satellite network. Firstly, the GSPN model of a double-layered satellite network is simplified by proper analysis. Then, two sets of experiments are conducted to analyse the performance of the satellite networks, and show that the double-layered satellite network outperforms single-layered ones on the heavy traffic load. Finally, the feasibility and effectiveness of the proposed approach is verified by simulation experiments. Copyright © 2005 John Wiley & Sons, Ltd.