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

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

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

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

A formal approach to adaptive software: continuous assurance of non-functional requirements

Abstract Modern software systems are increasingly requested to be adaptive to changes in the environment in which they are embedded. Moreover, adaptation often needs to be performed automatically, through self-managed reactions enacted by the application at run time. Off-line, human-driven changes should be requested only if self-adaptation cannot be achieved successfully. To support this kind of autonomic behavior, software systems must be empowered by a rich run-time support that can monitor the relevant phenomena of the surrounding environment to detect changes, analyze the data collected to understand the possible consequences of changes, reason about the ability of the application to continue to provide the required service, and finally react if an adaptation is needed. This paper focuses on non-functional requirements, which constitute an essential component of the quality that modern software systems need to exhibit. Although the proposed approach is quite general, it is mainly exemplified in the paper in the context of service-oriented systems, where the quality of service (QoS) is regulated by contractual obligations between the application provider and its clients. We analyze the case where an application, exported as a service, is built as a composition of other services. Non-functional requirements—such as reliability and performance—heavily depend on the environment in which the application is embedded. Thus changes in the environment may ultimately adversely affect QoS satisfaction. We illustrate an approach and support tools that enable a holistic view of the design and run-time management of adaptive software systems. The approach is based on formal (probabilistic) models that are used at design time to reason about dependability of the application in quantitative terms. Models continue to exist at run time to enable continuous verification and detection of changes that require adaptation.</jats:p

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

Syntax-driven program verification of matching logic properties

We describe a novel approach to program verification and its application to verification of C programs, where properties are expressed in matching logic. The general approach is syntax-directed: semantic rules, expressed according to Knuths attribute grammars, specify how verification conditions can be computed. Evaluation is performed by interplaying attribute computation and propagation through the syntax tree with invocation of a solver of logic formulae. The benefit of a general syntax-driven approach is that it provides a reusable reference scheme for implementing verifiers for different languages. We show that the instantiation of a general approach to a specific language does not penalize the efficiency of the resulting verifier. This is done by comparing our C verifier for matching logic with an existing tool for the same programming language and logic. A further key advantage of the syntax-directed approach is that it can be the starting point for an incremental verifier -- which is our long-term research target

Compositional Solution Space Quantification for Probabilistic Software Analysis

Probabilistic software analysis aims at quantifying how likely a target event is to occur during program execution. Current approaches rely on symbolic execution to identify the conditions to reach the target event and try to quantify the fraction of the input domain satisfying these conditions. Precise quantification is usually limited to linear constraints, while only approximate solutions can be provided in general through statistical approaches. However, statistical approaches may fail to converge to an acceptable accuracy within a reasonable time. We present a compositional statistical approach for the efficient quantification of solution spaces for arbitrarily complex constraints over bounded floating-point domains. The approach leverages interval constraint propagation to improve the accuracy of the estimation by focusing the sampling on the regions of the input domain containing the sought solutions. Preliminary experiments show significant improvement on previous approaches both in results accuracy and analysis time

An iterative decision-making scheme for Markov decision processes and its application to self-adaptive systems

Software is often governed by and thus adapts to phenomena that occur at runtime. Unlike traditional decision problems, where a decision-making model is determined for reasoning, the adaptation logic of such software is concerned with empirical data and is subject to practical constraints. We present an Iterative Decision-Making Scheme (IDMS) that infers both point and interval estimates for the undetermined transition probabilities in a Markov Decision Process (MDP) based on sampled data, and iteratively computes a confidently optimal scheduler from a given finite subset of schedulers. The most important feature of IDMS is the flexibility for adjusting the criterion of confident optimality and the sample size within the iteration, leading to a tradeoff between accuracy, data usage and computational overhead. We apply IDMS to an existing self-adaptation framework Rainbow and conduct a case study using a Rainbow system to demonstrate the flexibility of IDMS