Construction and Verification of Performance and Reliability Models

Over the last two decades formal methods have been extended towards performance and reliability evaluation. This paper tries to provide a rather intuitive explanation of the basic concepts and features in this area. Instead of striving for mathematical rigour, the intention is to give an illustrative introduction to the basics of stochastic models, to stochastic modelling using process algebra, and to model checking as a technique to analyse stochastic models

Reliability model for component-based systems in cosmic (a case study)

Software component technology has a substantial impact on modern IT evolution. The benefits of this technology, such as reusability, complexity management, time and effort reduction, and increased productivity, have been key drivers of its adoption by industry. One of the main issues in building component-based systems is the reliability of the composed functionality of the assembled components. This paper proposes a reliability assessment model based on the architectural configuration of a component-based system and the reliability of the individual components, which is usage- or testing-independent. The goal of this research is to improve the reliability assessment process for large software component-based systems over time, and to compare alternative component-based system design solutions prior to implementation. The novelty of the proposed reliability assessment model lies in the evaluation of the component reliability from its behavior specifications, and of the system reliability from its topology; the reliability assessment is performed in the context of the implementation-independent ISO/IEC 19761:2003 International Standard on the COSMIC method chosen to provide the component\u27s behavior specifications. In essence, each component of the system is modeled by a discrete time Markov chain behavior based on its behavior specifications with extended-state machines. Then, a probabilistic analysis by means of Markov chains is performed to analyze any uncertainty in the component\u27s behavior. Our hypothesis states that the less uncertainty there is in the component\u27s behavior, the greater the reliability of the component. The system reliability assessment is derived from a typical component-based system architecture with composite reliability structures, which may include the composition of the serial reliability structures, the parallel reliability structures and the p-out-of-n reliability structures. The approach of assessing component-based system reliability in the COSMIC context is illustrated with the railroad crossing case study. © 2008 World Scientific Publishing Company

Using imprecise continuous time Markov chains for assessing the reliability of power networks with common cause failure and non-immediate repair.

We explore how imprecise continuous time Markov chains can improve traditional reliability models based on precise continuous time Markov chains. Specifically, we analyse the reliability of power networks under very weak statistical assumptions, explicitly accounting for non-stationary failure and repair rates and the limited accuracy by which common cause failure rates can be estimated. Bounds on typical quantities of interest are derived, namely the expected time spent in system failure state, as well as the expected number of transitions to that state. A worked numerical example demonstrates the theoretical techniques described. Interestingly, the number of iterations required for convergence is observed to be much lower than current theoretical bounds

Quantitative Verification: Formal Guarantees for Timeliness, Reliability and Performance

Computerised systems appear in almost all aspects of our daily lives, often in safety-critical scenarios such as embedded control systems in cars and aircraft or medical devices such as pacemakers and sensors. We are thus increasingly reliant on these systems working correctly, despite often operating in unpredictable or unreliable environments. Designers of such devices need ways to guarantee that they will operate in a reliable and efficient manner. Quantitative verification is a technique for analysing quantitative aspects of a system's design, such as timeliness, reliability or performance. It applies formal methods, based on a rigorous analysis of a mathematical model of the system, to automatically prove certain precisely specified properties, e.g. ``the airbag will always deploy within 20 milliseconds after a crash'' or ``the probability of both sensors failing simultaneously is less than 0.001''. The ability to formally guarantee quantitative properties of this kind is beneficial across a wide range of application domains. For example, in safety-critical systems, it may be essential to establish credible bounds on the probability with which certain failures or combinations of failures can occur. In embedded control systems, it is often important to comply with strict constraints on timing or resources. More generally, being able to derive guarantees on precisely specified levels of performance or efficiency is a valuable tool in the design of, for example, wireless networking protocols, robotic systems or power management algorithms, to name but a few. This report gives a short introduction to quantitative verification, focusing in particular on a widely used technique called model checking, and its generalisation to the analysis of quantitative aspects of a system such as timing, probabilistic behaviour or resource usage. The intended audience is industrial designers and developers of systems such as those highlighted above who could benefit from the application of quantitative verification,but lack expertise in formal verification or modelling

A model checker for performance and dependability properties

Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [8] and the continuous time setting [1], [3]. In this short paper, we describe the prototype model checker $E \vdash M C^2$ for discrete and continuous-time Markov chains, where properties are expressed in appropriate extensions of CTL.We illustrate the general benefits of this approach and discuss the structure of the tool

Formal analysis techniques for gossiping protocols

We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them

A Markov Chain Model Checker

Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [17,6] and the continuous time setting [4,8]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen Twente Markov Chain Checker $(E \vdash MC^2$), where properties are expressed in appropriate extensions of CTL. We illustrate the general bene ts of this approach and discuss the structure of the tool. Furthermore we report on first successful applications of the tool to non-trivial examples, highlighting lessons learned during development and application of $(E \vdash MC^2$)

First and second order semi-Markov chains for wind speed modeling

The increasing interest in renewable energy, particularly in wind, has given rise to the necessity of accurate models for the generation of good synthetic wind speed data. Markov chains are often used with this purpose but better models are needed to reproduce the statistical properties of wind speed data. We downloaded a database, freely available from the web, in which are included wind speed data taken from L.S.I. -Lastem station (Italy) and sampled every 10 minutes. With the aim of reproducing the statistical properties of this data we propose the use of three semi-Markov models. We generate synthetic time series for wind speed by means of Monte Carlo simulations. The time lagged autocorrelation is then used to compare statistical properties of the proposed models with those of real data and also with a synthetic time series generated though a simple Markov chain.Comment: accepted for publication on Physica