Availability Evaluation of Overhead Contact Lines Based on a Stochastic Colored Petri Nets Model

Petri nets are an increasingly used modeling framework for the spread of disease across populations or within an individual. For example, the Susceptible-Infectious-Recovered (SIR) compartment model is foundational for population epidemiological modeling and has been implemented in several prior Petri net studies. While the SIR model is typically expressed as Ordinary Differential Equations (ODEs), with continuous time and variables, Petri nets operate as discrete event simulations with deterministic or stochastic timings. We present the first systematic study of the numerical convergence of two distinct Petri net implementations of the SIRS compartment model relative to the standard ODE. In particular, we introduce a novel deterministic implementation of the SIRS model using variable transition weights in the GPenSIM package and stochastic Petri net models using Spike. We show how rescaling and rounding procedures are critical for the numerical convergence of Petri net SIR models relative to the ODEs, and we achieve a relative root mean squared error of less than 1% compared to ODE simulations for biologically relevant parameter ranges. Our findings confirm that both stochastic and deterministic discrete time Petri nets are valid for modeling SIR-type dynamics with appropriate numerical procedures, laying the foundations for larger-scale use of Petri net models.

In this paper, we analyse Stochastic Petri Net (SPN) models of slotted-ring networks. We show that a simple SPN model of a slotted-ring network, which exhibits a product-form solution, yields similar results to a more detailed SPN model that has to be analysed by numerical means. Furthermore, we demonstrate a Mean-Value Analysis (MVA) approach to calculate efficiently the results for the simple model. This MVA approach allows for the movement of groups of tokens (customers) rather than just individual customers, as traditional MVA schemes for queueing network models do. Also, the MVA allows for non-disjoint place invariants, whereas previous MVA schemes addressed disjoint place invariants only. From the MVAs, it can be concluded that slotted-rings have very attractive performance characteristics, even under overload conditions (there is no "thrashing"). Also, we found that the choice of the slot size is a key factor in calibrating slotted-ring systems for optimal performance. Having a fast and reasonably accurate means available to evaluate the performance of slotted-ring systems, such as our proposed MVA, eases this calibration task. The proposed MVA for the product-form SPN models should therefore be regarded as a "quick engineering" tool.

The objectives of this work are to model a manufacturing system using top-down Petri net modeling approaches and mutual exclusion concepts; to construct stochastic Petri nets by considering the random failures of the machines, as well as such resources as robots and automated guided vehicle systems, and by incorporating temporal variables to transitions and places; to derive the performance of the system using stochastic Petri net performance models for different cases; and to compare performance results. Performance analysis problems on both deadlock-free and deadlock-prone systems are addressed and a comparison between them is made. First the stochastic Petri net modeling process is discussed on the basis of top-down and bottom-up ideas. Then, system performance indices, such as throughput for a resource-sharing manufacturing system, are derived by using existing software packages such as SPNP. Finally, conclusions are drawn and future directions are discussed for Petri net evaluation of manufacturing systems. >

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.

We focus on the specification and assessment of stochastic Petri net (SPN) models to evaluate the design of an embedded system for reliability and availability. The system provides dynamic driving regulation (DDR) to improve vehicle derivability (anti-skid, -slip and steering assist). A functional SPN abstraction was developed for each of three subsystems that incorporate mechanics, failure modes/effects and model parameters. The models are solved in terms of the subsystem and overall system reliability and availability. Four sets of models were developed. The first three sets include subsystem representations for the TC (traction control), AB (antilock braking) and ESA (electronic steering assistance) systems. The last set combines these systems into one large model. We summarize the general approach and provide sample Petri net graphs and reliability charts that were used to evaluate the design of the DDR in parts and as a whole.

The Healthcare Critical Infrastructure (HCI) protects all sectors of the society from hazards such as terrorism, infectious disease outbreaks, and natural disasters. HCI plays a significant role in response and recovery across all other sectors in the event of a natural or manmade disaster. However, for its continuity of operations and service delivery HCI is dependent on other interdependent Critical Infrastructures (CI) such as Communications, Electric Supply, Emergency Services, Transportation Systems, and Water Supply System. During a mass casualty due to disasters such as floods, a major challenge that arises for the HCI is to respond to the crisis in a timely manner in an uncertain and variable environment. To address this issue the HCI should be disaster prepared, by fully understanding the complexities and interdependencies that exist in a hospital, emergency department or emergency response event. Modelling and simulation of a disaster scenario with these complexities would help in training and providing an opportunity for all the stakeholders to work together in a coordinated response to a disaster. The paper would present interdependencies related to HCI based on Stochastic Coloured Petri Nets (SCPN) modelling and simulation approach, given a flood scenario as the disaster which would disrupt the infrastructure nodes. The entire model would be integrated with Geographic information based decision support system to visualize the dynamic behaviour of the interdependency of the Healthcare and related CI network in a geographically based environment.

Abstract. The Healthcare Critical Infrastructure (HCI) protects all sectors of the society from hazards such as terrorism, infectious disease outbreaks, and natural disasters. HCI plays a significant role in response and recovery across all other sectors in the event of a natural or manmade disaster. However, for its continuity of operations and service delivery HCI is dependent on other interdependent Critical Infrastructures (CI) such as Communications, Electric Supply, Emergency Services, Transportation Systems, and Water Supply System. During a mass casualty due to disasters such as floods, a major challenge that arises for the HCI is to respond to the crisis in a timely manner in an uncertain and variable environment. To address this issue the HCI should be disaster prepared, by fully understanding the complexities and interdependencies that exist in a hospital, emergency department or emergency response event. Modelling and simulation of a disaster scenario with these complexities would help in training and providing an opportunity for all the stakeholders to work together in a coordinated response to a disaster. The paper would present interdependencies related to HCI based on Stochastic Coloured Petri Nets (SCPN) modelling and simulation approach, given a flood scenario as the disaster which would disrupt the infrastructure nodes. The entire model would be integrated with Geographic information based decision support system to visualize the dynamic behaviour of the interdependency of the Healthcare and related CI network in a geographically based environment.

To increase our understanding of the interactions between the different cellular and intercellular processes, it is imperative to construct accurate biological models. An important class of these models are usually used to predict the time evolution of the corresponding chemical species over a specified period of time. Stochastic and coloured stochastic Petri nets can be adopted to construct graphical models that can be executed to simulate the firing of a set of reactions in a well-mixed chemical system. For the purpose of this specific application, (coloured) stochastic Petri nets employ internally the stochastic simulation algorithm (SSA) to perform the simulation. Although the result of the SSA is accurate in comparison with similar numerical simulation approaches (e.g., the systems of ordinary differential equations), it is empirically considered as a computationally expensive algorithm. In this paper, we propose an efficient parallel simulation algorithm for SSA to improve the execution of (coloured) stochastic Petri nets. We illustrate our proposal by applying it to a well-known model in the biological context: reaction diffusion. Furthermore, we evaluate the performance of the parallel algorithm and compare its runtime behaviour with the sequential one.

With the development of satellite communication networks and the increase of satellite services, security problems have gradually become some of the most concerning issues. Researchers have made great efforts, including conventional safety methods such as secure transmission, anti-jamming, secure access, and especially the new generation of active defense technology represented by MTD. However, few scholars have theoretically studied the influence of active defense technique on the performance of satellite networks. Formal modeling and performance analysis have not been given sufficient attention. In this paper, we focus on the performance evaluation of satellite network moving target defense system. Firstly, two Stochastic Petri Nets (SPN) models are constructed to analyze the performance of satellite network in traditional and active defense states, respectively. Secondly, the steady-state probability of each marking in SPN models is obtained by using the isomorphism relation between SPN and Markov Chains (MC), and further key performance indicators such as average time delay, throughput, and the utilization of bandwidth are reasoned theoretically. Finally, the proposed two SPN models are simulated based on the PIPE platform. In addition, the effect of parameters on the selected performance indexes is analyzed by varying the values of different parameters. The simulation results prove the correctness of the theoretical reasoning and draw the key factors affecting the performance of satellite network, which can provide an important theoretical basis for the design and performance optimization of the satellite network moving target defense system.

Software as a Service (SaaS) has become an important application development and service delivery model. Among different architectures, multi-tenant architecture (MTA) not only has advantage on maintenance, but also increases resource utilization by sharing instances. However, sharing instances brings challenges to the security of the service. As one of the three principal properties of the security, availability receives more and more attentions. Recently, there are extensive efforts on technical methods to implement a secure multi-tenant SaaS, but few works on the modeling and analysis of its availability. In this paper, we firstly present the availability issues of the multi-tenant SaaS. Two important mechanisms to implement the MTA SaaS are then introduced: network isolation and database sharing. After that, a stochastic Petri net (SPN) model is developed to analyze the availability. Specific metrics are proposed to measure the availability both from the aspects of the system and the tenant. To extend the SPN model for large scale analysis, we solve the state space explosion problem of SPN model based on the theory of Markov chain aggregation. Finally, numerical results are provided to demonstrate the effectiveness of the SPN model and the analysis is efficient.

A stochastic Petri net model was developed for simulating the sigma(32) stress circuit in E. coli. Transcription factor sigma(32) is the principal regulator of the response of E. coli to heat shock. Stochastic Petri net (SPN) models are well suited for kinetics characterization of fluxes in biochemical pathways. Notably, there exists a one-to-one mapping of model tokens and places to molecules of particular species. Our model was validated against experiments in which ethanol (inducer of heat shock response) and sigma(32)-targeted antisense (downward regulator) were used to perturb the sigma(32) regulatory pathway. The model was also extended to simulate the effects of recombinant protein production. Results show that the stress response depends heavily on the partitioning of sigma(32) within the cell; that is, sigma(32) becomes immediately available to mediate a stress response because it exists primarily in a sequestered, inactive form, complexed with chaperones DnaK, DnaJ, and GrpE. Recombinant proteins, however, also compete for chaperone proteins, particularly when folded improperly. Our simulations indicate that when the expression of recombinant protein has a low requirement for DnaK, DnaJ, and GrpE, the overall sigma(32) levels may drop, but the level of heat shock proteins will increase. Conversely, when the overexpressed recombinant protein has a strong requirement for the chaperones, a severe response is predicted. Interestingly, both cases were observed experimentally.

In this study, we focus on the specification and assessment of Stochastic Petri net (SPN) models to evaluate the design of an embedded system for reliability and availability. The system provides dynamic driving regulation (DDR) to improve vehicle derivability (anti-skid, -slip and steering assist). A functional SPN abstraction was developed for each of three subsystems that incorporate mechanics, failure modes/effects and model parameters. The models are solved in terms of the subsystem and overall system reliability and availability. Four sets of models were developed. The first three sets include subsystem representations for the TC (Traction Control), AB (Antilock Braking) and ESA (Electronic Steering Assistance) systems. The last set combines these systems into one large model. We summarize the general approach and provide sample Petri net graphs and reliability charts that were used to evaluate the design of the DDR in parts and as a whole.

A model for analyzing a FCS (fault-tolerant clock synchronization) system of the type supported by a statistical self-diagnosis is described. Once a self-diagnosis scheme is integrated into an FCS design, the problem of controlling and measuring the system's self-stability arises. A stochastic Petri net (SPN) model is constructed to derive the self-stability measures of such FCS systems. An example is given to demonstrate the entire modeling and analyzing procedure. The mapping from SPN model to Markov model shown in an example can be automated by using an SPN software package. The results show that the SPN model is an excellent tool for obtaining self-stability measures and that several important system features, such as synchronization and parallelism, can be modeled using the SPN method in a much clearer manner than they can be modeled using other available tools. >

Reliability analysis for dynamical systems is often based on timed stochastic Petri net (PN) models. A priori knowledge about failure processes is difficult to obtain and, as a consequence, the model structure and parameters are mainly unknown. In that case, synthesis and identification methods based on analysis of collected event sequences are of great interest. The contribution of this paper concerns the identification of timed stochastic PN models. Stochastic and deterministic stochastic PNs with deterministic and exponentially distributed transition durations are considered. A systematic identification method is proposed according to event sequences that are recorded by supervision systems. This method is based on the idea that the dynamic behaviour of considered PN can be mapped into a Markov model with state space isomorphic to the reachability graph of the untimed PN model.

One of the major arguments about hierarchical control structure is that most of the processing tasks are concentrated in the central controller. Recently, modified hierarchical control frameworks have addressed many attentions. Due to the autonomous capabilities added to the local controllers, certain functions originally carried out by the central controller are performed by local controllers. However, in the development of such control framework, the information flow and the required computation resources for various functions might be a valuable reference for system designers. Therefore, in this research, a coloured stochastic Petri nets (CSPN) model was developed to describe the information flow in a modified hierarchical structure. The developed model was simulated by using a commercial package ALPHA/Sim. The experimental results have shown the required computation resources for the main functions in the shop floor controller. In addition, the data also indirectly confirm the loose master/slave relation that exists between the central and cell controllers.