Guoxin Su

Asymptotic Bounds for Quantitative Verification of Perturbed Probabilistic Systems

The majority of existing probabilistic model checking case studies are based on well understood theoretical models and distributions. However, real-life probabilistic systems usually involve distribution parameters whose values are obtained by empirical measurements and thus are subject to small perturbations. In this paper, we consider perturbation analysis of reachability in the parametric models of these systems (i.e., parametric Markov chains) equipped with the norm of absolute distance. Our main contribution is a method to compute the asymptotic bounds in the form of condition numbers for constrained reachability probabilities against perturbations of the distribution parameters of the system. The adequacy of the method is demonstrated through experiments with the Zeroconf protocol and the hopping frog problem.

Reliability of Run-Time Quality-of-Service evaluation using parametric model checking

Run-time Quality-of-Service (QoS) assurance is crucial for business-critical systems. Complex behavioral performance metrics (PMs) are useful but often difficult to monitor or measure. Probabilistic model checking, especially paramet- ric model checking, can support the computation of aggre- gate functions for a broad range of those PMs. In practice, those PMs may be defined with parameters determined by run-time data. In this paper, we address the reliability of QoS evaluation using parametric model checking. Due to the imprecision with the instantiation of parameters, an evaluation outcome may mislead the judgment about requirement violations. Based on a general assumption of run-time data distribution, we present a novel framework that contains light-weight statistical inference methods to analyze the re- liability of a parametric model checking output with respect to an intuitive criterion. We also present case studies in which we test the stability and accuracy of our inference methods and describe an application of our framework to a cloud server management problem.

Towards complex activity recognition using a Bayesian network-based probabilistic generative framework

A Bayesian network-based probabilistic generative framework is presented to address diversity and uncertainty in complex activity recognition.The framework introduces the Chinese restaurant process to explicitly characterize the unique configurations of a complex activity.An enhanced model is presented to characterize more temporal relational variabilities than the previous models over our framework.Our models significantly outperform the state-of-the-arts on three benchmark datasets with different challenges.Our approach is robust against the incomplete or incorrect observations of primitive events. Complex activity recognition is challenging since a complex activity can be performed in different ways, with each having its own configuration of primitive events and their temporal dependencies. To address such temporal relational variabilities in complex activity recognition, we propose a Bayesian network-based probabilistic generative framework that employs Allens interval relation network to represent local temporal dependencies in a generative way. By employing the Chinese restaurant process and introducing relation generation constraints, our framework can characterize these unique internal configurations of a particular complex activity as a joint distribution. Three concrete models are implemented based on our framework. Specifically, in this paper we improve two of our previous models and provide an enhanced model to handle temporal relational variabilities in complex activities more efficiently. Empirical evaluations on three benchmark datasets demonstrate the competitiveness of our framework. In particular, it is shown that our models are rather robust against errors caused by the low-level predictions from raw signals.

Perturbation analysis of stochastic systems with empirical distribution parameters

Probabilistic model checking is a quantitative verification technology for computer systems and has been the focus of intense research for over a decade. While in many circumstances of probabilistic model checking it is reasonable to anticipate a possible discrepancy between a stochastic model and a real-world system it represents, the state-of-the-art provides little account for the effects of this discrepancy on verification results. To address this problem, we present a perturbation approach in which quantities such as transition probabilities in the stochastic model are allowed to be perturbed from their measured values. We present a rigorous mathematical characterization for variations that can occur to verification results in the presence of model perturbations. The formal treatment is based on the analysis of a parametric variant of discrete-time Markov chains, called parametric Markov chains (PMCs), which are equipped with a metric to measure their perturbed vector variables. We employ an asymptotic method from perturbation theory to compute two forms of perturbation bounds, namely condition numbers and quadratic bounds, for automata-based verification of PMCs. We also evaluate our approach with case studies on variant models for three widely studied systems, the Zeroconf protocol, the Leader Election Protocol and the NAND Multiplexer.

Perturbation Analysis in Verification of Discrete-Time Markov Chains

Perturbation analysis in probabilistic verification addresses the robustness and sensitivity problem for verification of stochastic models against qualitative and quantitative properties. We identify two types of perturbation bounds, namely non-asymptotic bounds and asymptotic bounds. Non-asymptotic bounds are exact, pointwise bounds that quantify the upper and lower bounds of the verification result subject to a given perturbation of the model, whereas asymptotic bounds are closed-form bounds that approximate non-asymptotic bounds by assuming that the given perturbation is sufficiently small. We perform perturbation analysis in the setting of Discrete-time Markov Chains. We consider three basic matrix norms to capture the perturbation distance, and focus on the computational aspect. Our main contributions include algorithms and tight complexity bounds for calculating both non-asymptotic bounds and asymptotic bounds with respect to the three perturbation distances.

Nested Reachability Approximation for Discrete-Time Markov Chains with Univariate Parameters

As models of real-world stochastic systems usually contain inaccurate information, probabilistic model checking for models with open or undetermined parameters has recently aroused research attention. In this paper, we study a kind of parametric variant of Discrete-time Markov Chains with uncertain transition probabilities, namely Parametric Markov Chains (PMCs), and probabilistic reachability properties with nested PCTL probabilistic operators. Such properties for a PMC with a univariate parameter define univariate real functions, called reachability functions, that map the parameter to reachability probabilities. An interesting application of these functions is sensitivity and robustness analysis of probabilistic model checking. However, a pitfall of computing the closed-form expression of a reachability function is the possible dynamism of its constraint set and target set. We pursue interval approximations for reachability functions with high accuracy. In particular, for reachability functions involving only single-nested probabilistic operators, we provide an efficient algorithm to compute their approximations. We demonstrate the applicability of our approach with a case study on a NAND multiplexing unit.

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.

Asymptotic Perturbation Bounds for Probabilistic Model Checking with Empirically Determined Probability Parameters

Probabilistic model checking is a verification technique that has been the focus of intensive research for over a decade. One important issue with probabilistic model checking, which is crucial for its practical significance but is overlooked by the state-of-the-art largely, is the potential discrepancy between a stochastic model and the real-world system it represents when the model is built from statistical data. In the worst case, a tiny but nontrivial change to some model quantities might lead to misleading or even invalid verification results. To address this issue, in this paper, we present a mathematical characterization of the consequences of model perturbations on the verification distance. The formal model that we adopt is a parametric variant of discrete-time Markov chains equipped with a vector norm to measure the perturbation. Our main technical contributions include a closed-form formulation of asymptotic perturbation bounds, and computational methods for two arguably most useful forms of those bounds, namely linear bounds and quadratic bounds. We focus on verification of reachability properties but also address automata-based verification of omega-regular properties. We present the results of a selection of case studies that demonstrate that asymptotic perturbation bounds can accurately estimate maximum variations of verification results induced by model perturbations.

An ADL-approach to specifying and analyzing centralized-mode architectural connection

A rigorous paradigm coordinating components is important in the design stage of large-scale software engineering. In this paper we propose a new Architecture Description Language, called ACDL, to represent the centralizedmode architectural connection in which all components are linked by a single connector. Following one usual approach to architectural description, in which component types and components are distinguished, and connectors integrate behaviors of components by specifying their coordination protocols, ACDL describes connectors in such a way that connectors are insensitive to the numbers of attached same-type components. Based on ACDL, we develop analytic techniques to facilitate the system checking of temporal properties of an architecture. In particular, our method shows to what extent one can add, delete and replace components without making the whole system lose desired temporal properties, and improves the system checking in several ways, for example enhancing the use of previous checking results to deal with new checking problems.

ProEva: runtime proactive performance evaluation based on continuous-time markov chains

Software systems, especially service-based software systems, need to guarantee runtime performance. If their performance is degraded, some reconfiguration countermeasures should be taken. However, there is usually some latency before the countermeasures take effect. It is thus important not only to monitor the current system status passively but also to predict its future performance proactively. Continuous-time Markov chains (CTMCs) are suitable models to analyze time-bounded performance metrics (e.g., how likely a performance degradation may occur within some future period). One challenge to harness CTMCs is the measurement of model parameters (i.e., transition rates) in CTMCs at runtime. As these parameters may be updated by the system or environment frequently, it is difficult for the model builder to provide precise parameter values. In this paper, we present a framework called ProEva, which extends the conventional technique of time-bounded CTMC model checking by admitting imprecise, interval-valued estimates for transition rates. The core method of ProEva computes asymptotic expressions and bounds for the imprecise model checking output. We also present an evaluation of accuracy and computational overhead for ProEva.