Markov regenerative processes solution and stochastic model checking

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.

This tutorial presents an overview of model checking for both discrete and continuous-time Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative properties with rewards. Example properties include the probability that a fault occurs and the expected number of faults in a given time period. We also describe the practical application of stochastic model checking with the probabilistic model checker PRISM by outlining the main features supported by PRISM and three real-world case studies: a probabilistic security protocol, dynamic power management and a biological pathway.

One of the goals of synthetic biology is to build genetic circuits to control the behavior of a cell for different application domains, such as medical, environmental, and biotech. During the design process of genetic circuits, biologists are often interested in the probability of a system to work under different conditions. Since genetic circuits are noisy and stochastic in nature, the verification process becomes very complicated. The state space of stochastic genetic circuit models is usually too large to be handled by classical model checking techniques. Therefore, the verification of genetic circuit models is usually performed by the statistical approach of model checking. In this work, we present a workflow for checking genetic circuit models using a stochastic model checker (Uppaal) and a stochastic simulator (D-VASim). We demonstrate with experimentations that the proposed workflow is not only sufficient for the model checking of genetic circuits, but can also be used to design the genetic circuits with desired timings.

A new approach to Vulnerability, Uncertainty and Probability (VUP) quantification procedure using Stochastic Petri Nets within a network of interacting satellites is presented. A Stochastic Petri Net based model is developed to quantify VUP in a network of interacting satellites. Three indicators are proposed to determine the VUP definitions in interacting network of satellites. The proposed VUP quantification scheme addresses a methodology which employs a Stochastic Petri Net for quantitative analysis of the behavior of the network. With the random variables associated with the Petri Net transitions, the dynamic behavior of the cooperating satellites in a SPN model can be mapped onto a time-continuous Markov chain with discrete state space. After generating a Markov Stochastic Petri Net model, the probability of a given condition in the network at a specified time can be computed and quantified as well as the vulnerability and uncertainty of the system using the identified indicators.

Current stochastic model checkers do not make counterexamples for property violations readily available. In this paper, we apply directed explicit state-space search to discrete and continuous-time Markov chains in order to compute counterexamples for the violation of PCTL or CSL properties. Directed explicit state-space search algorithms explore the state space on-the-fly, which makes our method very efficient and highly scalable. They can also be guided using heuristics which usually improve the performance of the method. Counterexamples provided by our method have two important properties. First, they include those traces which contribute the greatest amount of probability to the property violation. Hence, they show the most probable offending execution scenarios of the system. Second, the obtained counterexamples tend to be small. Hence, they can be effectively analyzed by a human user. Both properties make the counterexamples obtained by our method very useful for debugging purposes. We implemented our method based on the stochastic model checker PRISM and applied it to a number of case studies in order to illustrate its applicability.

Continuous-time Markov chains (CTMCs) have been largely applied with combination of high-level model specification techniques as performance evaluation and dependability, reliability analysis models for computer and communication systems. These models can be complemented by probabilistic model checking formalisms based on temporal logic to specify the guarantees on the measures of interest. We consider in this paper Continuous Stochastic Logic (CSL) which lets to express real-time probabilistic properties on CTMCs. It has been shown that the CSL operators can be checked by means of transient or steady-state analysis of the underlying CTMC. Since models are checked to see if the considered measures are guaranteed or not, bounding techniques are useful in probabilistic model checking. We propose to apply Stochastic Comparison technique to construct bounding models having a special structure which provides closed-form solutions to compute both transient and steady-state distributions. We present an algorithm to provide rapid model checking by means of these closed-form bounding distributions. Obviously, bounding distributions may not let to decide if the underlying model meets the probability thresholds or not. However in the case where the model can be checked by the proposed method, we gain significantly in time and memory complexity.

In this work, we explore the applicability of Stoch astic Petri Nets (SPNs) to multi-state failure and survivability analyses, using space sys tems as examples. Multi-state failure analyses introduce degraded states, and thus provid e more insights than the traditional binary reliability analysis into the degradation be havior of a system and its progression towards complete failure. Survivability analysis fo cuses on, among other things, the failure propagation in a system or a network following node or component failure, and it assesses for example whether the system will experience graceful degradation or catastrophic failure. The potential complexity of multi-state failure and system survivability analyses requires powerful (and flexible) stochastic modeling and simulation tools. After a brief introduction to Petri Nets, we argue that SPNs are particularly well suited to these types of analyses, and they are better at the task than the commonly used Markov Chains. We then propose a general framework for system survivability analysis, and we illustrate its applicability using space systems examples. We compare the survivability of two space architectures, a monolith spacecraft and a space-based network (which allows for distributed redundancy of certain subsystems). Monte Carlo simulations are run to generate representative results of stochastic behavior of the two architectures with r espect to on-orbit anomalies and failures. Finally, a comparison of the outputs of the two SPN models indicate, and quantify, the survivability advantage of the space-based network over the monolith spacecraft with respect to on-orbit anomalies and failures.

CSLTA is a stochastic temporal logic for continuous-time Markov chains (CTMC), that can verify the probability of following paths specified by a Deterministic Timed Automaton (DTA). A DTA expresses both logic and time constraints over a CTMC path, yielding to a very flexible way of describing performance and dependability properties. This paper explores a model checking algorithm for CSLTA based on the translation into a Deterministic and Stochastic Petri Net (DSPN). The algorithm has been implemented in a simple Model Checker prototype, that relies on existing DSPN solvers to do the actual numerical computations.

Modeling and analysis tools are essential for the design and evaluation of complex systems. This is particularly true for cellular systems, where, for instance, a variety of handoff, channel allocation, and data-transmission algorithms have been proposed. The capabilities of Petri nets (PNs) are used as a novel approach in the analysis of handoff, dynamic channel allocation (DCA), and cellular digital packet data resource management problems. The generalized stochastic PN (GSPN) models are obtained and analyzed as continuous-time Markov chains (MCs) derived from the reachability graphs. Solution of the MC results in performance indicators, which show the impacts of different algorithms on the system behavior.

This study focuses on the stochastic modelling and analysis of a serial production network consisting of two manufacturing stations operating under a make-to-stock inventory policy. The outcome is a single type of product and every manufacturing station includes a machine and an output buffer. Both machines are gradually deteriorating during their operation. Deterioration results in a reduced production rate. Continuous-time Markov chain was used to model all the possible states the network transits over time due to the occurrence of certain events, such as client arrival, deterioration failure, production or repair completion. The structure of the Markov chain was thoroughly studied providing useful information, supporting the effort of numerical solving to determine the steady-state probabilities enabling the calculation of useful performance metrics like equipment availability, down time, idle time, utilisation and average inventory. Through a series of numerical experiments, the behaviour of the serial production network was examined while alternating its parameters. Interesting conclusions emerged regarding the factors affecting the operation of such production systems subjected to gradual deterioration.

Software rejuvenation is a proactive maintenance technique that counteracts software aging by restarting a system, making selection of rejuvenation times critical to improve reliability without incurring excessive downtime costs. Various stochastic models of Software Aging and Rejuvenation (SAR) have been developed, mostly having an underlying stochastic process in the class of Continuous Time Markov Chains (CTMCs), Semi-Markov Processes (SMPs), and Markov Regenerative Processes (MRGPs) under the enabling restriction, requiring that at most one general (GEN), i.e., non-Exponential, timer be enabled in each state. We present a SAR model with an underlying MRGP under the bounded regeneration restriction, allowing for multiple GEN timers to be concurrently enabled in each state. This expressivity gain not only supports more accurate fitting of duration distributions from observed statistics, but also enables the definition of mixed rejuvenation strategies combining time-based and inspection-based policies, where the time to the next inspection or rejuvenation depends on the outcomes of diagnostic tests. Experimental results show that replacing GEN timers with Exponential timers with the same mean (to satisfy the enabling restriction) yields inaccurate rejuvenation policies, and that mixed rejuvenation outperforms time-based rejuvenation in maximizing reliability, though at the cost of an acceptable decrease in availability.

Non-functional requirements like performance and reliability play a prominent role in distributed and dynamic systems. To measure and predict such properties using stochastic formal methods is crucial. At the same time, graph transformation systems are a suitable formalism to formally model distributed and dynamic systems. Already, to address these two issues, Stochastic Graph Transformation Systems (SGTS) have been introduced to model dynamic distributed systems. But most of the researches so far are concentrated on SGTS as a modeling means without considering the need for suitable analysis tools. In this paper, we present an approach to verify this kind of graph transformation systems using PRISM (a stochastic model checker). We translate the SGTS to the input language of PRISM and then PRISM performs the model checking and returns the results back to the designers.

Higher-order model checking - the model checking of trees generated by higher-order recursion schemes (HORS) - is a natural generalisation of finite-state and pushdown model checking. Recent work has shown that it can serve as a basis for software model checking for functional languages such as ML and Haskell. In this paper, we introduce higher-order recursion schemes with cases (HORSC), which extend HORS with a definition-by-cases construct (to express program branching based on data) and non-determinism (to express abstractions of behaviours). This paper is a study of the universal HORSC model checking problem for deterministic trivial automata : does the automaton accept every tree in the tree language generated by the given HORSC? We first characterise the model checking problem by an intersection type system extended with a carefully restricted form of union types. We then present an algorithm for deciding the model checking problem, which is based on the notion of traversals induced by the fully abstract game semantics of these schemes, but presented as a goal-directed construction of derivations in the intersection and union type system. We view HORSC model checking as a suitable backend engine for an approach to verifying functional programs. We have implemented the algorithm in a tool called TravMC , and demonstrated its effectiveness on a test suite of programs, including abstract models of functional programs obtained via an abstraction-refinement procedure from pattern-matching recursion schemes.

ORIS provides a graphical interface to draw Petri nets, analysis engines for different classes of underlying stochastic process, and visualization of reward-based metrics. It also includes a Java API for model definition and analysis, which can be used to carry out parametric performance studies. ORIS implements methods for steady-state and transient analysis of Semi-Markov Processes (SMPs), Markov Regenerative Processes (MRPs), Generalized Semi-Markov Processes (GSMPs), and Continuous-Time Markov Chains (CTMCs).

This paper describes a portfolio-based approach for model checking, i.e., an approach in which several model checking engines are orchestrated to reach the best possible performance on a broad and real set of designs. Model checking algorithms are evaluated through experiments, and experimental data inspire package tuning, as well as new algorithmic features and methodologies. This approach, albeit similar to several industrial and academic experiences, and already applied in other domains, is somehow new to the model checking field. Its contributions lie in the description of how we: (1) characterize and classify benchmarks in a dynamic way, throughout experimental runs, (2) relate model checking problems to algorithms and engines, (3) introduce a dynamic tuning of sub-engines, exploiting an on-the-fly performance analysis, (4) record results of different approaches, and sort out heuristics to target different classes of problems. We provide a detailed description of the experiments performed in preparation of the Model Checking Competition 2010, where PdTRAV, our academic verification tool, won the UNSAT division, while ranking second in the OVERALL category.