Using the probabilistic evaluation tool for the analytical solution of large Markov models

Stochastic Petri net-based Markov modeling is a potentially very powerful and generic approach for evaluating the performance and dependability of many different systems, such as computer systems, communication networks, manufacturing systems, etc. As a consequence of their general applicability, SPN-based Markov models form the basic solution approach for several software packages that have been developed for the analytic solution of performance and dependability models. In these tools, stochastic Petri nets are used to conveniently specify complicated models, after which an automatic mapping can be carried out to an underlying Markov reward model. Subsequently, this Markov reward model is solved by specialized solution algorithms, appropriately selected for the measure of interest. One of the major aspects that hampers the use of SPN-based Markov models for the analytic solution of performance and dependability results is the size of the state space. Although typically models of up to a few hundred thousand states can conveniently be solved on modern-day work-stations, often even larger models are required to represent all the desired detail of the system. Our tool PET (probabilistic evaluation tool) circumvents problems of large state spaces when the desired performance and dependability measure are transient measures. It does so by an approach named probabilistic evaluatio

Transient analysis of some rewarded Markov models using randomization with quasistationarity detection

Rewarded homogeneous continuous-time Markov chain (CTMC) models can be used to analyze performance, dependability and performability attributes of computer and telecommunication systems. In this paper, we consider rewarded CTMC models with a reward structure including reward rates associated with states and two measures summarizing the behavior in time of the resulting reward rate random variable: the expected transient reward rate at time t and the expected averaged reward rate in the time interval [0, t]. Computation of those measures can be performed using the randomization method, which is numerically stable and has good error control. However, for large stiff models, the method is very expensive. Exploiting the existence of a quasistationary distribution in the subset of transient states of discrete-time Markov chains with a certain structure, we develop a new variant of the (standard) randomization method, randomization with quasistationarity detection, covering finite CTMC models with state space S\cup {f_1, f_2, ..., f_A}, A\geq 1, where all states in S are transient and reachable among them and the states f_i are absorbing. The method has the same good properties as the standard randomization method and can be much more efficient. We also compare the performance of the method with that of regenerative randomization.Postprint (published version

Performance Analysis of a Consensus Algorithm Combining Stochastic Activity Networks and Measurements

A. Coccoli, P. Urban, A. Bondavalli, and A. Schiper. Performance analysis of a consensus algorithm combining Stochastic Activity Networks and measurements. In Proc. Int'l Conf. on Dependable Systems and Networks (DSN), pages 551-560, Washington, DC, USA, June 2002. Protocols which solve agreement problems are essential building blocks for fault tolerant distributed applications. While many protocols have been published, little has been done to analyze their performance. This paper represents a starting point for such studies, by focusing on the consensus problem, a problem related to most other agreement problems. The paper analyzes the latency of a consensus algorithm designed for the asynchronous model with failure detectors, by combining experiments on a cluster of PCs and simulation using Stochastic Activity Networks. We evaluated the latency in runs (1) with no failures nor failure suspicions, (2) with failures but no wrong suspicions and (3) with no failures but with (wrong) failure suspicions. We validated the adequacy and the usability of the Stochastic Activity Network model by comparing experimental results with those obtained from the model. This has led us to identify limitations of the model and the measurements, and suggests new directions for evaluating the performance of agreement protocols. Keywords: quantitative analysis, distributed consensus, failure detectors, Stochastic Activity Networks, measurement

Algorithms for Performance, Dependability, and Performability Evaluation using Stochastic Activity Networks

Modeling tools and technologies are important for aerospace development. At the University of Illinois, we have worked on advancing the state of the art in modeling by Markov reward models in two important areas: reducing the memory necessary to numerically solve systems represented as stochastic activity networks and other stochastic Petri net extensions while still obtaining solutions in a reasonable amount of time, and finding numerically stable and memory-efficient methods to solve for the reward accumulated during a finite mission time. A long standing problem when modeling with high level formalisms such as stochastic activity networks is the so-called state space explosion, where the number of states increases exponentially with size of the high level model. Thus, the corresponding Markov model becomes prohibitively large and solution is constrained by the the size of primary memory. To reduce the memory necessary to numerically solve complex systems, we propose new methods that can tolerate such large state spaces that do not require any special structure in the model (as many other techniques do). First, we develop methods that generate row and columns of the state transition-rate-matrix on-the-fly, eliminating the need to explicitly store the matrix at all. Next, we introduce a new iterative solution method, called modified adaptive Gauss-Seidel, that exhibits locality in its use of data from the state transition-rate-matrix, permitting us to cache portions of the matrix and hence reduce the solution time. Finally, we develop a new memory and computationally efficient technique for Gauss-Seidel based solvers that avoids the need for generating rows of A in order to solve Ax = b. This is a significant performance improvement for on-the-fly methods as well as other recent solution techniques based on Kronecker operators. Taken together, these new results show that one can solve very large models without any special structure

Methodologies synthesis

This deliverable deals with the modelling and analysis of interdependencies between critical infrastructures, focussing attention on two interdependent infrastructures studied in the context of CRUTIAL: the electric power infrastructure and the information infrastructures supporting management, control and maintenance functionality. The main objectives are: 1) investigate the main challenges to be addressed for the analysis and modelling of interdependencies, 2) review the modelling methodologies and tools that can be used to address these challenges and support the evaluation of the impact of interdependencies on the dependability and resilience of the service delivered to the users, and 3) present the preliminary directions investigated so far by the CRUTIAL consortium for describing and modelling interdependencies

Caractérisation de la sûreté de fonctionnement des systèmes d'exploitation en présence de pilotes défaillants

Les pilotes de périphériques composent désormais une part essentielle des systèmes d’exploitation. Plusieurs études montrent qu’ils sont fréquemment à l’origine des dysfonctionnements des systèmes opératoires. Dans ce mémoire, nous présentons une méthode pour l’évaluation de la robustesse des noyaux face aux comportements anormaux des pilotes de périphériques. Pour cela, après avoir analysé et précisé les caractéristiques des échanges entre les pilotes et le noyau (DPI - Driver Programming Interface), nous proposons une technique originale d’injection de fautes basée sur la corruption des paramètres des fonctions manipulées au niveau de cette interface. Nous définissons différentes approches pour l’analyse et l’interprétation des résultats observés pour obtenir des mesures objectives de sûreté de fonctionnement. Ces mesures permettent la prise en compte de différents points de vue afin de répondre aux besoins réels de l’utilisateur. Enfin, nous illustrons et validons l’applicabilité de cette méthode par sa mise en oeuvre dans le cadre d’un environnement expérimental sous Linux. La méthode proposée contribue à la caractérisation de la sûreté de fonctionnement des noyaux vis-à-vis des défaillances des pilotes du système. L’impact des résultats est double : a) permettre au développeur de tels logiciels d’identifier les faiblesses potentielles affectant la sûreté de fonctionnement du système, b) aider un intégrateur dans le choix du composant le mieux adapté à ses besoins

Fiabilité opérationnelle des avoins (Approche basée sur les modèles et cas d'étude)

Lors de la conception des avions, il est courant que les constructeurs évaluent la sûreté de fonctionnement en utilisant des modèles stochastiques, mais l'évaluation de la fiabilité opérationnelle à l aide de modèles en ligne, pendant la réalisation des missions, reste rarement effectuée. Souvent, l'évaluation stochastique concerne la sécurité des avions. Cette thèse porte sur la modélisation de la fiabilité opérationnelle des avions, pour aider à la planification des activités de maintenance et des missions, ainsi qu à la bonne réalisation de ces dernières. Nous avons développé une approche de modélisation, basée sur un méta-modèle qui sert de base i) de structuration des informations nécessaires à l évaluation de la fiabilité opérationnelle d un avion et ii) pour la construction de modèles stochastiques pouvant être mis à jour dynamiquement. La mise à jour concerne l'état courant des systèmes avion, un profil de mission et les moyens de maintenance disponibles dans les diverses escales incluses dans le profil de la mission. L'objectif est de permettre l'évaluation de la fiabilité opérationnelle en ligne. Deux cas d études, basés sur des sous-systèmes avion, sont considérés à titre d'illustration. Nous présentons des exemples de résultats qui montrent le rôle important de l évaluation de la fiabilité opérationnelle pendant une mission d avionDependability assessment, by system manufacturer, during aircraft design, based on stochastic modeling, is of common practice, but model based operational dependability assessment online, during missions' achievement, is seldom done. Usually, the stochastic assessment addresses aircraft safety.This thesis addresses aircraft operational dependability modeling to support mission and maintenance planning, as well as the achievement of the missions. We develop a modeling approach, based on a meta-model that is used as a basis i) to structure the information needed to assess aircraft operational reliability and ii) to build a stochastic model that can be updated dynamically. The update concerns the current state of the aircraft system, a mission profile and the maintenance facilities available at the flight stop locations involved in the mission. The aim is to enable operational reliability assessment online. Two case studies, based on aircraft subsystems, are considered for illustration. We present examples of evaluation results that show the valuable role of operational dependability assessment during aircraft missionTOULOUSE-INSA-Bib. electronique (315559905) / SudocSudocFranceF

Resilience-Building Technologies: State of Knowledge -- ReSIST NoE Deliverable D12

This document is the first product of work package WP2, "Resilience-building and -scaling technologies", in the programme of jointly executed research (JER) of the ReSIST Network of Excellenc