Discrete-time dynamic modeling for software and services composition as an extension of the Markov chain approach

Discrete Time Markov Chains (DTMCs) and Continuous Time Markov Chains (CTMCs) are often used to model various types of phenomena, such as, for example, the behavior of software products. In that case, Markov chains are widely used to describe possible time-varying behavior of “self-adaptive” software systems, where the transition from one state to another represents alternative choices at the software code level, taken according to a certain probability distribution. From a control-theoretical standpoint, some of these probabilities can be interpreted as control signals and others can just be observed. However, the translation between a DTMC or CTMC model and a corresponding first principle model, that can be used to design a control system is not immediate. This paper investigates a possible solution for translating a CTMC model into a dynamic system, with focus on the control of computing systems components. Notice that DTMC models can be translated as well, providing additional information

A compositional method for reliability analysis of workflows affected by multiple failure modes

We focus on reliability analysis for systems designed as workflow based compositions of components. Components are characterized by their failure profiles, which take into account possible multiple failure modes. A compositional calculus is provided to evaluate the failure profile of a composite system, given failure profiles of the components. The calculus is described as a syntax-driven procedure that synthesizes a workflows failure profile. The method is viewed as a design-time aid that can help software engineers reason about systems reliability in the early stage of development. A simple case study is presented to illustrate the proposed approach

On the probabilistic symbolic analysis of programs

Recently we have proposed symbolic execution techniques for the probabilistic analysis of programs. These techniques seek to quan- tify the probability of a program to satisfy a property of interest under a relevant usage profile. We describe recent advances in prob- abilistic symbolic analysis including handling of complex floating- point constraints and nondeterminism, and the use of statistical techniques for increased scalability

Iterative test suites refinement for elastic computing systems

Elastic computing systems can dynamically scale to continuously and cost-effectively provide their required Quality of Service in face of time-varying workloads, and they are usually implemented in the cloud. Despite their wide-spread adoption by industry, a formal definition of elasticity and suitable procedures for its assessment and verification are still missing. Both academia and industry are trying to adapt established testing procedures for functional and non-functional properties, with limited effectiveness with respect to elasticity. In this paper we propose a new methodology to automatically generate test-suites for testing the elastic properties of systems. Elasticity, plasticity, and oscillations are first formalized through a convenient behavioral abstraction of the elastic system and then used to drive an iterative test suite refinement process. The outcomes of our approach are a test suite tailored to the violation of elasticity properties and a human-readable abstraction of the system behavior to further support diagnosis and fix

Lightweight adaptive filtering for efficient learning and updating of probabilistic models

Adaptive software systems are designed to cope with unpredictable and evolving usage behaviors and environmental conditions. For these systems reasoning mechanisms are needed to drive evolution, which are usually based on models capturing relevant aspects of the running software. The continuous update of these models in evolving environments requires efficient learning procedures, having low overhead and being robust to changes. Most of the available approaches achieve one of these goals at the price of the other. In this paper we propose a lightweight adaptive filter to accurately learn time-varying transition probabilities of discrete time Markov models, which provides robustness to noise and fast adaptation to changes with a very low overhead. A formal stability, unbiasedness and consistency assessment of the learning approach is provided, as well as an experimental comparison with state-of-the-art alternatives

Supporting self-adaptation via quantitative verification and sensitivity analysis at run time

Modern software-intensive systems often interact with an environment whose behavior changes over time, often unpredictably. The occurrence of changes may jeopardize their ability to meet the desired requirements. It is therefore desirable to design software in a way that it can self-adapt to the occurrence of changes with limited, or even without, human intervention. Self-adaptation can be achieved by bringing software models and model checking to run time, to support perpetual automatic reasoning about changes. Once a change is detected, the system itself can predict if requirements violations may occur and enable appropriate counter-actions. However, existing mainstream model checking techniques and tools were not conceived for run-time usage; hence they hardly meet the constraints imposed by on-the-fly analysis in terms of execution time and memory usage. This paper addresses this issue and focuses on perpetual satisfaction of non-functional requirements, such as reliability or energy consumption. Its main contribution is the description of a mathematical framework for run-time efficient probabilistic model checking. Our approach statically generates a set of verification conditions that can be efficiently evaluated at run time as soon as changes occur. The proposed approach also supports sensitivity analysis, which enables reasoning about the effects of changes and can drive effective adaptation strategies

Run-time efficient probabilistic model checking

Since the inception of discontinuous Galerkin (DG) methods for elliptic problems, there has existed a question of whether DG methods can be made more computationally efficient than continuous Galerkin (CG) methods. Fewer degrees of freedom, approximation properties for elliptic problems together with the number of optimization techniques, such as static condensation, available within CG framework made it challenging for DG methods to be competitive until recently. However, with the introduction of a static-condensation-amenable DG method—the hybridizable discontinuous Galerkin (HDG) method—it has become possible to perform a realistic comparison of CG and HDG methods when applied to elliptic problems. In this work, we extend upon an earlier 2D comparative study, providing numerical results and discussion of the CG and HDG method performance in three dimensions. The comparison categories covered include steady-state elliptic and time-dependent parabolic problems, various element types and serial and parallel performance. The postprocessing technique, which allows for superconvergence in the HDG case, is also discussed. Depending on the direct linear system solver used and the type of the problem (steady-state vs. time-dependent) in question the HDG method either outperforms or demonstrates a comparable performance when compared with the CG method. The HDG method however falls behind performance-wise when the iterative solver is used, which indicates the need for an effective preconditioning strategy for the method

Model-counting approaches for nonlinear numerical constraints

Model counting is of central importance in quantitative rea- soning about systems. Examples include computing the probability that a system successfully accomplishes its task without errors, and measuring the number of bits leaked by a system to an adversary in Shannon entropy. Most previous work in those areas demonstrated their analysis on pro- grams with linear constraints, in which cases model counting is polynomial time. Model counting for nonlinear constraints is notoriously hard, and thus programs with nonlinear constraints are not well-studied. This paper surveys state-of-the-art techniques and tools for model counting with respect to SMT constraints, modulo the bitvector theory, since this theory is decidable, and it can express nonlinear constraints that arise from the analysis of computer programs. We integrate these techniques within the Symbolic Pathfinder platform and evaluate them on difficult nonlinear constraints generated from the analysis of cryptographic functions