Probabilistic Model Checking Technique Research Articles

A Compositional Semantics of Boolean-Logic Driven Markov Processes

Boolean-logic driven Markov processes (BDMPs) is a prominent dynamic extension of static fault trees to model repairable and complex dynamic systems. While BDMPs are intensively used in an industrial context for dependability analysis of energy systems, its formal semantics has not been systematically treated. To date, BDMPs are defined as a library of the domain-specific dependability-modelling language Figaro, a library that is neither open source nor publicly available. A rigorous semantic underpinning of BDMPs is indispensable for (1) developing BDMP analysis tools and (2) comparing its expressive power to other related reliability modelling languages. This paper presents a formal semantics to BDMPs using Markov automata (MA), an extension of continuous-time Markov chains (CTMCs) with action transitions that can be used to compose complex MA from smaller MA. This enables us to provide a compositional semantics. That is, we express the semantics of each individual BDMP element as an MA and obtain the MA for the entire BDMP by combining the MA of its elements. This makes the semantics comprehensible, for those who are familiar with automata theory, and easily extensible with new BDMP elements, e.g., to model security aspects. After the entire BDMP is considered, the actions in its MA that were used to “glue” the MA of BDMP elements, are ignored. This results in a CTMC that is amenable to exact numerical analysis by, e.g., efficient probabilistic model-checking techniques. We report on a prototypical implementation of our semantics and empirically show that our semantics yields dependability metrics that correspond to the interpretation by the Figaro knowledge base of BDMPs.

Enhancing Probabilistic Model Checking with Ontologies

Probabilistic model checking (PMC) is a well-established method for the quantitative analysis of state based operational models such as Markov decision processes. Description logics (DLs) provide a well-suited formalism to describe and reason about knowledge and are used as basis for the web ontology language (OWL). We investigate how such knowledge described by DLs can be integrated into the PMC process, introducing ontology-mediated PMC. Specifically, we propose ontologized programs as a formalism that links ontologies to behaviors specified by probabilistic guarded commands, the de-facto standard input formalism for PMC tools such as Prism. Through DL reasoning, inconsistent states in the modeled system can be detected. We present three ways to resolve these inconsistencies, leading to different Markov decision process semantics. We analyze the computational complexity of checking whether an ontologized program is consistent under these semantics. Further, we present and implement a technique for the quantitative analysis of ontologized programs relying on standard DL reasoning and PMC tools. This way, we enable the application of PMC techniques to analyze knowledge-intensive systems.We evaluate our approach and implementation on amulti-server systemcase study,where different DL ontologies are used to provide specifications of different server platforms and situations the system is executed in.

Fault tree analysis method based on probabilistic model checking and discrete time Markov Chain

ABSTRACTIn order to fully consider the dynamic characteristics of event failure in fault tree analysis, the probabilistic model checking and discrete-time Markov chain are applied to the fault tree analysis. The formal probability of gate events in a fault tree is studied and the fault tree is established based on the probabilistic model checking technique. The logic gates in a fault tree are converted into discrete-time Markov chain that can be encoded into the probabilistic model checker. The discrete-time Markov chain is used to simulate the known behavior probability distribution of the system in the known situational environment, and the Markov decision process is used to simulate the non-deterministic behavior of the system under the unknown environment, and to carry out the quantitative analysis of the system. The fault tree analysis of the spindle system of a certain CNC machine tool is taken as an example to illustrate the proposed method.

An Integrated Modeling, Simulation and Analysis Framework for Engineering Complex Systems

The discipline of component-based modeling and simulation offers promising gains in reducing cost, time, and the complexity of model development through the (re)use of modular components. Model-driven development suggests 1) the realization of a complex system using a conceptual model; 2) its automatic transformation into an executable form using transformation rules, and; 3) its automatic verification using a formal analysis technique for an accurate assessment of its correctness. Both approaches have numerous complementary benefits in rapid prototyping of complex systems using model reuse. In this paper, we propose a framework grounded in a combination of component-based and model-driven approaches to promote rapid prototyping of complex systems through the effective reuse of the simulation models. Our proposed process allows developers to 1) build or select existing components and compose them to formulate the conceptual models of complex systems; 2) automatically transform the conceptual models for the rapid implementation and simulation, and; 3) automatically verify them as per the requirement specifications. We propose the use of the extended finite-state machine (EFSM) as conceptual modeling formalism, anylogic simulation platform for the implementation, and probabilistic model checking technique using communicating sequential process (CSP) formalism for the verification. Finally, we present a case study of a real-time adaptive cruise control system to demonstrate the functionality of our framework. Our proposed component-based model-driven approach facilitates rapid prototyping and effective meaningful reuse of complex system models, which further accelerates the modeling, simulation, and analysis process of real-time systems and aids in complex engineering designs and implementations.

Performance analysis of Israeli‐Jalfon's algorithm using probabilistic model checking

SummaryIsraeli‐Jalfon's self‐stabilization algorithm provides a solution to the problem of fault tolerance in distributed systems. To quantitatively evaluate the algorithm and discover the factors contributing to its performance, we used a probabilistic model checking technique to study the algorithm across different configurations. The mainstream probabilistic model checker PRISM assisted with our final assessment. We focus here on three aspects of the algorithm's performance: convergence, time complexity, and maximum execution time. Our experimental results show that time complexity is O (N^2) when N is less than 23, and we examine the factors contributing to this performance. These prove to be: the number of tokens, the number of processes, the probability of token transmission, and how tokens are spaced. Performance degrades as the number of tokens grows. For a certain number of processes, better performance can be obtained when the probability of token transmission is 0.5. Three tokens spaced evenly, meanwhile, yields the worst performance. The main contribution of this paper is its exhaustive quantitative performance analysis of Israeli‐Jalfon's algorithm and the presentation of accurate rather than approximate numerical results. Moreover, our assessment was undertaken in a reducible fashion, with stable states being set against a proper subset of the set of possible configurations rather than allowing two sets to coincide.

Statistical analysis and probabilistic verification of stress-induced signalling pathways

Recent studies reveal that dysregulation of Endoplasmic Reticulum ER stress signalling pathways is implicated in the pathogenesis of several diseases. ER is a major hub for protein synthesis, modification and sorting, and it also regulates several signalling pathways in the cell cycle progression. Disturbance of endoplasmic reticulum could induce an unfolded protein response, which is a self-protective mechanism. Graphical lasso method was first used to infer the undirected sub-networks of ER stress signalling from microarray data. Then, we construct a stochastic model to describe the crosstalk of three major signalling pathways induced by ER stress, and apply a probabilistic model checking technique to formally analyse the temporal logic properties of the model, which is written in the PRISM language. This verification technique can both qualitatively and quantitatively verify the signalling pathway model using the sequential probability ratio test and confidence interval estimation method, respectively.

Locks: Picking key methods for a scalable quantitative analysis

Functional correctness of low-level operating-system (OS) code is an indispensable requirement. However, many applications rely also on quantitative aspects such as speed, energy efficiency, resilience with regards to errors and other cost factors. We report on our experiences of applying probabilistic model-checking techniques for analysing the quantitative long-run behaviour of low-level OS-code. Our approach, illustrated in a case study analysing a simple test-and-test-and-set (TTS) spinlock protocol, combines measure-based simulation with probabilistic model-checking to obtain high-level models of the performance of realistic systems and to tune the models to predict future system behaviour. We report how we obtained a nearly perfect match of analytic results and measurements and how we tackled the state-explosion problem to obtain model-checking results for a large number of processes where measurements are no longer feasible. These results gave us valuable insights in the delicate interplay between lock load, average spinning times and other performance measures.

Predictive Web Service Monitoring using Probabilistic Model Checking

Web service is vulnerable to stochastic failures due to the changeful Internet environment, which will seriously impact the reliability of business-critical applications. Web service must adapt to these changes. This paper studies the monitoring issue of Web service and proposes a predictive service monitoring approach to support service-oriented software dynamic evolutions. It aims to ensure that Web service is high-quality at runtime. Considering functional and non-functional requirements, we employ probabilistic model checking technique to quantitatively verify the interactive behaviour of Web service. However, limited by time and memory, frequently performing probabilistic model checking is not a high-efficiency solution to monitor Web service. Thus, forecasting the reliability becomes an important way to enhance the performance of Web service monitoring, by which we can put forward dynamic reconfigurations before the exception occurs. For this purpose, according to the historical probability values of Web service reliability recorded in monitoring phase, we adopt the mathematical statistics, unary linear regression analysis method, to predict the probability value of reliability based on invocation duration time. Finally, a case study is discussed and experiment results demonstrate the applicability and effectiveness of our approach.

QoS Analysis of Real-Time Distributed Systems Based on Hybrid Analysis of Probabilistic Model Checking Technique and Simulation

For the Internet, system developers often have to estimate the QoS by simulation techniques or mathematical analysis. Probabilistic model checking can evaluate performance, dependability and stability of information processing systems with random behaviors. We apply a hybrid analysis approach onto real-time distributed systems. In the hybrid analysis approach, we perform stepwise analysis using probabilistic models of target systems in different abstract levels. First, we create a probabilistic model with detailed behavior of the system (called detailed model), and apply simulation on the detailed model. Next, based on the simulation results, we create a probabilistic model in an abstract level (called simplified model). Then, we verify qualitative properties using the probabilistic model checking techniques. This prevents from state-explosion. We evaluate the validity of our approach by comparing to simulation results of NS-2 using a case study of a video data streaming system. The experiments show that the result of the proposed approach is very close to that of NS-2 simulation. The result encourages the approach is useful for the performance analysis on various domain.