Stochastic Model Checking Research Articles

Robustness Evaluation Process for Scheduling under Uncertainties

Scheduling production is an important decision issue in the manufacturing domain. With the advent of the era of Industry 4.0, the basic generation of schedules becomes no longer sufficient to face the new constraints of flexibility and agility that characterize the new architecture of production systems. In this context, schedules must take into account an increasingly disrupted environment while maintaining a good performance level. This paper contributes to the identified field of smart manufacturing scheduling by proposing a complete process for assessing the robustness of schedule solutions: i.e., its ability to resist to uncertainties. This process focuses on helping the decision maker in choosing the best scheduling strategy to be implemented. It aims at considering the impact of uncertainties on the robustness performance of predictive schedules. Moreover, it is assumed that data upcoming from connected workshops are available, such that uncertainties can be identified and modelled by stochastic variables This process is supported by stochastic timed automata for modelling these uncertainties. The proposed approach is thus based on Stochastic Discrete Event Systems models and model checking techniques defining a highly reusable and modular process. The solution process is illustrated on an academic example and its performance (generecity and scalability) are deeply evaluated using statistical analysis. The proposed application of the evaluation process is based on the technological opportunities offered by the Industry 4.0.

A three-valued model abstraction framework for PCTL* stochastic model checking

A three-valued model abstraction framework for PCTL* stochastic model checking

Complete Test of Synthesised Safety Supervisors for Robots and Autonomous Systems

Verified controller synthesis uses world models that comprise all potential behaviours of humans, robots, further equipment, and the controller to be synthesised. A world model enables quantitative risk assessment, for example, by stochastic model checking. Such a model describes a range of controller behaviours some of which -- when implemented correctly -- guarantee that the overall risk in the actual world is acceptable, provided that the stochastic assumptions have been made to the safe side. Synthesis then selects an acceptable-risk controller behaviour. However, because of crossing abstraction, formalism, and tool boundaries, verified synthesis for robots and autonomous systems has to be accompanied by rigorous testing. In general, standards and regulations for safety-critical systems require testing as a key element to obtain certification credit before entry into service. This work-in-progress paper presents an approach to the complete testing of synthesised supervisory controllers that enforce safety properties in domains such as human-robot collaboration and autonomous driving. Controller code is generated from the selected controller behaviour. The code generator, however, is hard, if not infeasible, to verify in a formal and comprehensive way. Instead, utilising testing, an abstract test reference is generated, a symbolic finite state machine with simpler semantics than code semantics. From this reference, a complete test suite is derived and applied to demonstrate the observational equivalence between the synthesised abstract test reference and the generated concrete controller code running on a control system platform.

YAP: Tool Support for Deriving Safety Controllers from Hazard Analysis and Risk Assessments

Safety controllers are system or software components responsible for handling risk in many machine applications. This tool paper describes a use case and a workflow for YAP, a research tool for risk modelling and discrete-event safety controller design. The goal of this use case is to derive a safety controller from hazard analysis and risk assessment, to define a design space for this controller, and to select a verified optimal controller instance from this design space. We represent this design space as a stochastic model and use YAP for risk modelling and generation of parts of this stochastic model. For the controller verification and selection step, we use a stochastic model checker. The approach is illustrated by an example of a collaborative robot operated in a manufacturing work cell.

A PSO-Based CEGAR Framework for Stochastic Model Checking

Counterexample-guided abstraction refinement (CEGAR) is an extremely successful methodology for combating the state-space explosion problem in model checking. State-space explosion problem is more serious in the field of stochastic model checking, and it is still a challengeable problem to apply CEGAR in stochastic model checking effectively. In this paper, we formalize the problem of applying CEGAR in stochastic model checking, and propose a novel CEGAR framework for it. In our framework, the abstract model is presented by a quotient probabilistic automaton by making a set of variables or latches invisible, which can distinguish more degrees of abstraction for each variable. The counterexample is described by a diagnostic sub-model. Validating counterexample is performed on diagnostic loop paths, and the directed explicit state-space search algorithm is used for searching diagnostic loop paths. Sample learning, particle swarm optimization algorithm (PSO) and some effective heuristics are integrated for refining abstract model guided by invalid counterexample. A prototype tool is implemented for the framework, and the feasibility and efficiency are shown by some large cases.

Rare event simulation for dynamic fault trees

Fault trees (FT) are a popular industrial method for reliability engineering, for which Monte Carlo simulation is an important technique to estimate common dependability metrics, such as the system reliability and availability. A severe drawback of Monte Carlo simulation is that the number of simulations required to obtain accurate estimations grows extremely large in the presence of rare events, i.e., events whose probability of occurrence is very low, which typically holds for failures in highly reliable systems.This paper presents a novel method for rare event simulation of dynamic fault trees with complex repairs that requires only a modest number of simulations, while retaining statistically justified confidence intervals. Our method exploits the importance sampling technique for rare event simulation, together with a compositional state space generation method for dynamic fault trees.We demonstrate our approach using three parameterized sets of case studies, showing that our method can handle fault trees that could not be evaluated with either existing analytical techniques using stochastic model checking, nor with standard simulation techniques.

A Probabilistic Assume-Guarantee Reasoning Framework Based on Genetic Algorithm

Probabilistic assume-guarantee reasoning is a theoretically feasible way to alleviate the state space explosion problem in stochastic model checking. The key to probabilistic assume-guarantee reasoning is how to generate the assumption. At present, the main way to automatically generate assumption is the L* (or symbolic L*) learning algorithm. An important limitation of it is that too many intermediate results are produced and need to be stored. To overcome this, we propose a novel assumption generation method by a genetic algorithm and present a probabilistic assume-guarantee reasoning framework for a Markov decision process (MDP). The genetic algorithm is a randomized algorithm essentially, and there are no intermediate results that need to be stored in the process of assumption generation, except the encoding of the problem domain and the training set. It can obviously reduce the space complexity of the probabilistic assume-guarantee reasoning framework. In order to improve the efficiency further, we combine the probabilistic assume-guarantee reasoning framework with interface alphabet refinement orthogonally. Moreover, we employ the diagnostic submodel as a counterexample for the guidance of augmenting training set. We implement a prototype tool for the probabilistic assume-guarantee reasoning framework and report the encouraging results.

Stochastic Model Checking for Predicting Component Failures and Service Availability

When a component fails in a critical communications service, how urgent is a repair? If we repair within 1 hour, 2 hours, or $n$ hours, how does this affect the likelihood of service failure? Can a formal model support assessing the impact, prioritisation, and scheduling of repairs in the event of component failures, and forecasting of maintenance costs? These are some of the questions posed to us by a large organisation and here we report on our experience of developing a stochastic framework based on a discrete space model and temporal logic to answer them. We define and explore both standard steady-state and transient temporal logic properties concerning the likelihood of service failure within certain time bounds, forecasting maintenance costs, and we introduce a new concept of envelopes of behaviour that quantify the effect of the status of lower level components on service availability. The resulting model is highly parameterised and user interaction for experimentation is supported by a lightweight, web-based interface.

A uniformization-based algorithm for continuous-time stochastic games model checking

Continuous-time Stochastic Game (CTSG) can be seen as a proper model to analyze probabilistic, non-deterministic, and competitive behaviors as found in Stochastic Multi-Player Game (SMG). The difference is that in an SMG the system under design is analyzed in the discrete-time setting. In comparison, in a CTSG, the system transitions occur in the continuous-time setting with exponentially distributed delays. This paper focuses on the model checking of CTSGs and presents a uniformization-based algorithm, called TPA, to approximate the time-bounded reachability probabilities with an arbitrary error bound. We concentrate on CTSGs with bounded transition rates. To illustrate the strength points of our algorithm, we have implemented it in Java, developed some large examples, and compared our results with the ones from an existing algorithm which is based on discretization. In order to express properties specifying these types of probabilities in the continuous-time setting, we adjusted the existing temporal logic, PATL. Thus, properties like the following can be stated and checked over a CTSG: “A coalition of players has a strategy to guarantee to reach the target states within time boundt∈Q⩾0with a probability equal to or greater than threshold P, regardless of the other players' behaviors.”

Counterexample Generation in Stochastic Model Checking Based on PSO Algorithm with Heuristic

Providing counterexample for the refutation of a property is an essential feature of model checking, if it is not the most important. However, generating counterexample in stochastic model checking needs a dedicated algorithm. It usually costs too much time and memory, and sometimes it cannot find the counterexample. What is worse, generating smallest counterexample in stochastic model checking has been proved to be NP-complete, and it is unlikely to be efficiently approximable. Although there are a few heuristic methods that are applied to the construction of the counterexample, it is usually difficult to determine the heuristic function which is critical for counterexample generating. In this paper, we present a particle swarm optimization (PSO)-based approach to generating counterexample for stochastic model checking. We define the diagnostic sub-graph as counterexample, and extend PSO algorithm with heuristic (HPSO) to generate counterexample. It adopts indirect path coding scheme to expand the scope of the search space, and employs heuristic operator to generate more effective path. The validity of our approach is illustrated by some case studies in a prototype tool. The experiments show that HPSO algorithm can significantly outperform the present algorithm for counterexample generation in stochastic model checking.

A Game-Based Approach for PCTL* Stochastic Model Checking with Evidence

Stochastic model checking is a recent extension and generalization of the classical model checking, which focuses on quantitatively checking the temporal property of a system model. PCTL* is one of the important quantitative property specification languages, which is strictly more expressive than either PCTL (probabilistic computation tree logic) or LTL (linear temporal logic) with probability bounds. At present, PCTL* stochastic model checking algorithm is very complicated, and cannot provide any relevant explanation of why a formula does or does not hold in a given model. For dealing with this problem, an intuitive and succinct approach for PCTL* stochastic model checking with evidence is put forward in this paper, which includes: presenting the game semantics for PCTL* in release-PNF (release-positive normal form), defining the PCTL* stochastic model checking game, using strategy solving in game to achieve the PCTL* stochastic model checking, and refining winning strategy as the evidence to certify stochastic model checking result. The soundness and the completeness of game-based PCTL* stochastic model checking are proved, and its complexity matches the known lower and upper bounds. The game-based PCTL* stochastic model checking algorithm is implemented in a visual prototype tool, and its feasibility is demonstrated by an illustrative example.

Restructuring of workflows to minimise errors via stochastic model checking: An automated evolutionary approach

This paper presents a framework for the automated restructuring of stochastic workflows to reduce the impact of faults. The framework allows for the modelling of workflows by means of a formalised subset of the BPMN workflow language. We extend this modelling formalism to describe faults and incorporate an intention preserving stochastic semantics able to model both probabilistic- and non-deterministic behaviour.Stochastic model checking techniques are employed to generate the state-space of a given workflow. Possible improvements obtained by restructuring are measured by employing the framework׳s capacity for tracking real-valued quantities associated with states and transitions of the workflow. The space of possible restructurings of a workflow is explored by means of an evolutionary algorithm, where the goals for improvement are defined in terms of optimising quantities, typically employed to model resources, associated with a workflow.The approach is fully automated and only the modelling of the production workflows, potential faults and the expression of the goals require manual input. We present the design of a software tool implementing this framework and explore the practical utility of this approach through an industrial case study in which the risk of production failures and their impact are reduced by restructuring the workflow.

Model checking single agent behaviours by fluid approximation

In this paper we investigate a potential use of fluid approximation techniques in the context of stochastic model checking of CSL formulae. We focus on properties describing the behaviour of a single agent in a (large) population of agents, exploiting a limit result known also as fast simulation. In particular, we will approximate the behaviour of a single agent with a time-inhomogeneous CTMC, which depends on the environment and on the other agents only through the solution of the fluid differential equation, and model check this process. We will prove the asymptotic correctness of our approach in terms of satisfiability of CSL formulae. We will also present a procedure to model check time-inhomogeneous CTMC against CSL formulae.

DynaDiffuse: A Dynamic Diffusion Model for Continuous Time Constrained Influence Maximization

Studying the spread of phenomena in social networks is critical but still not fully solved. Existing influence maximization models assume a static network, disregarding its evolution over time. We introduce the continuous time constrained influence maximization problem for dynamic diffusion networks, based on a novel diffusion model called DynaDiffuse. Although the problem is NP-hard, the influence spread functions are monotonic and submodular, enabling fast approximations on top of an innovative stochastic model checking approach. Experiments on real social network data show that our model finds higher quality solutions and our algorithm outperforms state-of-art alternatives.

Efficient analysis methods in synthetic biology.

This chapter describes new analysis and verification techniques for synthetic genetic circuits. In particular, it applies stochastic model checking techniques to models of genetic circuits in order to ensure that they behave correctly and are as robust as possible for a variety of different inputs and parameter settings. In addition to stochastic model checking, this chapter proposes new variants to the incremental stochastic simulation algorithm (iSSA) that are capable of presenting a researcher with a simulation trace of the typical behavior of the system. Before the development of this algorithm, discerning this information was extremely error-prone as it involved performing many simulations and attempting to wade through the massive amounts of data. This algorithm greatly aids researchers in designing genetic circuits as it efficiently shows the researcher the most likely behavior of the circuit. Both the iSSA and stochastic model checking can be used in concert to give a researcher the likelihood that the system exhibits its most typical behavior, as well as, non-typical behaviors. This methodology is applied to several genetic circuits leading to new understanding of the effects of various parameters on the behavior of these circuits.

Quantitative Verification of Trustworthy Service Flow by Stochastic Model Checking

Quantitative Verification of Trustworthy Service Flow by Stochastic Model Checking

Quantitative modelling and analysis of a Chinese smart grid: a stochastic model checking case study

Cyber-physical systems integrate information and communication technology with the physical elements of a system, mainly for monitoring and controlling purposes. The conversion of traditional power grid into a smart grid, a fundamental example of a cyber-physical system, raises a number of issues that require novel methods and applications. One of the important issues in this context is the verification of certain quantitative properties of the system. In this paper, we consider a specific Chinese smart grid implementation as a case study and address the verification problem for performance and energy consumption. We employ stochastic model checking approach and present our modelling and analysis study using PRISM model checker.

Evolutionary Optimization of Production Materials Workflow Processes

We present an evolutionary optimisation technique for stochastic production processes, which is able to find improved production materials workflow processes with respect to arbitrary combinations of numerical quantities associated with the production process. Working from a core fragment of the BPMN language, we employ an evolutionary algorithm where stochastic model checking is used as a fitness function to determine the degree of improvement of candidate processes derived from the original process through mutation and cross-over operations. We illustrate this technique using a case study where a baked goods company seeks to improve production time while simultaneously minimising the cost and use of resources.

Extending a Synthesis-Centric Model-Based Systems Engineering Framework with Stochastic Model Checking

We propose to integrate performance evaluation with supervisory control synthesis to bring higher confidence in the control design. Supervisory control theory deals with automatic synthesis of supervisory controllers that ensure safe behavior of the supervised system, based on the models of the uncontrolled system and the (safety) control requirements. For the purpose of performance evaluation, we turn to stochastic model checking of continuous-time Markov chains, which requires an extension of the model of the uncontrolled system with Markovian delays. We cast our proposal as an extension of a model-based systems engineering framework that relies on supervisor synthesis. We treat the Markovian delays syntactically, exploiting their equivalent interleaving behavior with uniquely-named uncontrollable transitions. In this way, we can employ already available synthesis tools, while preserving the stochastic behavior. To this end, we develop model transformation tools to extract the underlying Markov process from the stochastic discrete-event model of the supervised system. We illustrate the approach by modeling a pipeless plant that employs automated guided vehicles instead of fixed piping in order to ensure greater flexibility of the plant. The control problem that we solve is safe high-level movement coordination of the vehicles, ensured by the supervisory controller. We show how to seamlessly introduce stochastic behavior in the supervised system and we evaluate several performance and reliability aspects of the plant. We implement the framework by interfacing two state-of-the-art tools: Supremica for supervisory controller synthesis and MRMC for Markovian model checking. To this end, we improve previous attempts by providing support for data-based observers, which greatly improve the modeling capabilities of the framework.

Model checking for performability

This paper gives a bird's-eye view of the various ingredients that make up a modern, model-checking-based approach to performability evaluation: Markov reward models, temporal logics and continuous stochastic logic, model-checking algorithms, bisimulation and the handling of non-determinism. A short historical account as well as a large case study complete this picture. In this way, we show convincingly that the smart combination of performability evaluation with stochastic model-checking techniques, developed over the last decade, provides a powerful and unified method of performability evaluation, thereby combining the advantages of earlier approaches.