List of requirements on formalisms and selection of appropriate tools

This deliverable reports on the activities for the set-up of the modelling environments for the evaluation activities of WP5. To this objective, it reports on the identified modelling peculiarities of the electric power infrastructure and the information infrastructures and of their interdependencies, recalls the tools that have been considered and concentrates on the tools that are, and will be, used in the project: DrawNET, DEEM and EPSys which have been developed before and during the project by the partners, and M\uf6bius and PRISM, developed respectively at the University of Illinois at Urbana Champaign and at the University of Birmingham (and recently at the University of Oxford)

A template-based methodology for the specification and automated composition of performability models

Dependability and performance analysis of modern systems is facing great challenges: their scale is growing, they are becoming massively distributed, interconnected, and evolving. Such complexity makes model-based assessment a difficult and time-consuming task. For the evaluation of large systems, reusable submodels are typically adopted as an effective way to address the complexity and to improve the maintainability of models. When using state-based models, a common approach is to define libraries of generic submodels, and then compose concrete instances by state sharing, following predefined “patterns” that depend on the class of systems being modeled. However, such composition patterns are rarely formalized, or not even documented at all. In this paper, we address this problem using a model-driven approach, which combines a language to specify reusable submodels and composition patterns, and an automated composition algorithm. Clearly defining libraries of reusable submodels, together with patterns for their composition, allows complex models to be automatically assembled, based on a high-level description of the scenario to be evaluated. This paper provides a solution to this problem focusing on: formally defining the concept of model templates, defining a specification language for model templates, defining an automated instantiation and composition algorithm, and applying the approach to a case study of a large-scale distributed system69129330

Extending the Logic IM-SPDL with Impulse and State Rewards

This report presents the logic SDRL (Stochastic Dynamic Reward Logic), an extension of the stochastic logic IM-SPDL, which supports the specication of complex performance and dependability requirements. SDRL extends IM-SPDL with the possibility to express impulse- and state reward measures.\ud The logic is interpreted over extended action-based Markov reward model (EMRM), i.e. transition systems containing both immediate and Markovian transitions, where additionally the states and transitions can be enriched with rewards.\ud We define ne the syntax and semantics of the new logic and show that SDRL provides powerful means to specify path-based properties with timing and reward-based restrictions.\ud In general, paths can be characterised by regular expressions, also called programs, where the executability of a program may depend on the validity of test formulae. For the model checking of SDRL time- and reward-bounded path formulae, a deterministic program automaton is constructed from the requirement. Afterwards the product transition\ud system between this automaton and the EMRM is built and subsequently transformed into a continuous time Markov reward model (MRM) on which numerical\ud analysis is performed.\u

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

Stochastic Activity Networks Templates: Supporting Variability in Performability Models

Model-based evaluation is extensively used to estimate performance and reliability of dependable systems. Traditionally, those systems were small and self-contained, and the main challenge for model-based evaluation has been the efficiency of the solution process. Recently, the problem of specifying and maintaining complex models has increasingly gained attention, as modern systems are characterized by many components and complex interactions. Components share similarities, but also exhibit variations in their behavior due to different configurations or roles in the system. From the modeling perspective, variations lead to replicating and altering a small set of base models multiple times. Variability is taken into account only informally, by defining a sample model and explaining its possible variations. In this paper we address the problem of including variability in performability models, focusing on Stochastic Activity Networks (SANs). We introduce the formal definition of Stochastic Activity Networks Templates (SAN-T), a formalism based on SANs with the addition of variability aspects. Differently from other approaches, parameters can also affect the structure of the model, like the number of cases of activities. We apply the SAN-T formalism to the modeling of the backbone network of an environmental monitoring infrastructure. In particular, we show how existing SAN models from the literature can be generalized using the newly introduced formalism

Computing performability measures in Markov chains by means of matrix functions

We discuss the efficient computation of performance, reliability, and availability measures for Markov chains; these metrics, and the ones obtained by combining them, are often called performability measures. We show that this computational problem can be recasted as the evaluation of a bilinear forms induced by appropriate matrix functions, and thus solved by leveraging the fast methods available for this task. We provide a comprehensive analysis of the theory required to translate the problem from the language of Markov chains to the one of matrix functions. The advantages of this new formulation are discussed, and it is shown that this setting allows to easily study the sensitivities of the measures with respect to the model parameters. Numerical experiments confirm the effectiveness of our approach; the tests we have run show that we can outperform the solvers available in state of the art commercial packages on a representative set of large scale examples

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

Discrete-time rewards model-checked

This paper presents a model-checking approach for analyzing discrete-time Markov reward models. For this purpose, the temporal logic probabilistic CTL is extended with reward constraints. This allows to formulate complex measures – involving expected as well as accumulated rewards – in a precise and succinct way. Algorithms to efficiently analyze such formulae are introduced. The approach is illustrated by model-checking a probabilistic cost model of the IPv4 zeroconf protocol for distributed address assignment in ad-hoc networks