Model Checker PRISM Research Articles

A Markov Game Theory-Based Energy Balance Routing Algorithm

Energy balance routing is of great importance in wireless sensor networks(WSNs).As a response to this issue,in the paper,a Markov Game Model for WSNs is proposed.Based on the basic characteristic of energy balance routing and node cooperation,a Markov Game TheoryBased Energy Balance Routing(MGTEBR)Algorithm is designed for decreasing the whole energy consumption and maximizing the network lifetime.First,a binary payoff function of energy and reputation is defined,and the transition probability of node forwarding state is given.Based on the payoff function,the equilibrium coefficient between energy and reputation values—Nash equilibrium is computed.Probabilistic model checker PRISM is adopted for simulation.The results show that there exists Nash equilibrium in our algorithm,and the cooperation between the nodes can be promoted,the maximum life can be obtained.

Verification and Optimal Control of Context-Sensitive Probabilistic Boolean Networks Using Model Checking and Polynomial Optimization

One of the significant topics in systems biology is to develop control theory of gene regulatory networks (GRNs). In typical control of GRNs, expression of some genes is inhibited (activated) by manipulating external stimuli and expression of other genes. It is expected to apply control theory of GRNs to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of GRNs, and gene expression is expressed by a binary value (ON or OFF). In particular, a context-sensitive probabilistic Boolean network (CS-PBN), which is one of the extended models of BNs, is used. For CS-PBNs, the verification problem and the optimal control problem are considered. For the verification problem, a solution method using the probabilistic model checker PRISM is proposed. For the optimal control problem, a solution method using polynomial optimization is proposed. Finally, a numerical example on the WNT5A network, which is related to melanoma, is presented. The proposed methods provide us useful tools in control theory of GRNs.

A property-based abstraction framework for SysML activity diagrams

SysML activity diagrams are OMG/INCOSE standards used for modeling, analyzing and specifying probabilistic systems. Since they are considered as a de facto systems’ modeling language, it is of a major importance to verify these diagrams. Moreover, it is even more important to reduce the cost of their verification process. In this paper, we propose a probabilistic abstraction framework to efficiently verify SysML activity diagrams. It is based on reducing the diagram complexity with respect to a system requirement. For verification, we use our verification approach that relies on PRISM model checker. To ensure the correctness of our proposed approach, we prove its soundness. This is achieved by finding the adequate pre-order relation between the semantics of the abstract and the concrete diagrams. This relation is shown to preserve the satisfaction of systems requirements. To this end, a calculus to capture the underlying semantics of SysML activity diagrams is proposed. Finally, the effectiveness of our approach is demonstrated on two real systems.

Unified Functional Safety Assessment of Industrial Automation Systems

The IEC 61499 standard enables the model-based design of complex industrial automation systems, in which a model of the controlled physical processes called a plant, is codeveloped with the controller. However, the existing design flow does not address functional safety issues, which include limiting risk to acceptable levels. Standards like IEC 61508 provide safety guidelines for measuring and managing risk to acceptable ranges using quantitative or probabilistic methods for hardware, and qualitative or systematic analysis techniques for software. Such analyses are inadequate in situations where safety depends on both hardware and software. This paper proposes a unifying model-based approach for the quantitative and qualitative analysis of IEC 61499 designs. The approach combines Markov analysis and model checking to estimate quantified risk and is more expressive than traditional analyses like reliability block diagrams. At design level, unified safety requirements are captured using safety blocks, which is an extension of the IEC 61499 basic blocks. The PRISM model checker is used to analyze the system, based on a sound conversion of IEC 61499 designs into PRISM models. A tool-chain enabling the proposed approach shows encouraging benchmarking results confirming the feasibility of unified analysis.

Precise Quantitative Analysis of Probabilistic Business Process Model and Notation Workflows

We present a framework for modeling and analysis of real-world business workflows. We present a formalized core subset of the business process modeling and notation (BPMN) and then proceed to extend this language with probabilistic nondeterministic branching and general-purpose reward annotations. We present an algorithm for the translation of such models into Markov decision processes (MDP) expressed in the syntax of the PRISM model checker. This enables precise quantitative analysis of business processes for the following properties: transient and steady-state probabilities, the timing, occurrence and ordering of events, reward-based properties, and best- and worst- case scenarios. We develop a simple example of medical workflow and demonstrate the utility of this analysis in accurate provisioning of drug stocks. Finally, we suggest a path to building upon these techniques to cover the entire BPMN language, allow for more complex annotations and ultimately to automatically synthesize workflows by composing predefined subprocesses, in order to achieve a configuration that is optimal for parameters of interest.

Formal Approach for DVS-Based Power Management for Multiple Server System in Presence of Server Failure and Repair

The paper presents a DVS-based power management policy for multiprocessor systems. The aim is to optimize power consumption by keeping the job loss probability as a system-wide constraint. Optimal values for service rate are computed using an ideal setting where speed can change continuously. As real processors have discrete speed levels, we switch between two nearby speeds to achieve the optimal rate. We develop a formal model of such a system using the probabilistic model checker PRISM and prove properties satisfied by the system. We demonstrated the applicability of the policy on multiple servers and under both kinds of deadlines: DBS and DES. For a constraint value of 25%, the DBS model achieved power savings of 29.46% in theoretical, 8.75% in actual, and 7.23% in leakage power. The DES model achieved power savings of 30% in theoretical, 11.9% in actual, and 8.7% in leakage power. For robustness, a repair facility was used which can have repairmen varying from one to the total number of servers.

Modelling IEEE 802.11 CSMA/CA RTS/CTS with stochastic bigraphs with sharing

Abstract Stochastic bigraphical reactive systems (SBRS) is a recent formalism for modelling systems that evolve in time and space. However, the underlying spatial model is based on sets of trees and thus cannot represent spatial locations that are shared among several entities in a simple or intuitive way. We adopt an extension of the formalism, SBRS with sharing , in which the topology is modelled by a directed acyclic graph structure. We give an overview of SBRS with sharing, we extend it with rule priorities, and then use it to develop a model of the 802.11 CSMA/CA RTS/CTS protocol with exponential backoff, for an arbitrary network topology with possibly overlapping signals. The model uses sharing to model overlapping connectedness areas, instantaneous prioritised rules for deterministic computations, and stochastic rules with exponential reaction rates to model constant and uniformly distributed timeouts and constant transmission times. Equivalence classes of model states modulo instantaneous reactions yield states in a CTMC that can be analysed using the model checker PRISM. We illustrate the model on a simple example wireless network with three overlapping signals and we present some example quantitative properties.

Symbolic approach to verification and control of deterministic/probabilistic Boolean networks

A Boolean network (BN) is well known as one of the models of biological networks such as gene regulatory networks, and has been extensively studied. In this study, for a BN, the verification/control problems are discussed. First, a probabilistic model including both synchronous and asynchronous Boolean dynamics is derived. This model can be generalised as a probabilistic BN. Next, a solution method of the verification/control problems is proposed, based on a probabilistic model checker PRISM. Finally, the PRISM-based method is applied to an apoptosis network and a WNT5A network. The proposed approach provides us an easy and convenient tool for analysis and control of biological networks.

Constructive model-based analysis for safety assessment

The aerospace industry still uses fault trees to perform reliability analysis. This is because fault-tree modeling and analysis (FTA) seems easier to practical engineers when compared with Markov models, even though FTA provides a weaker form of analysis. In this paper, we propose an automatic strategy for generating Markov-based models and corresponding analysis formulations, according to ARP 4761, directly from Simulink diagrams annotated with failure information. The generated Markov-based models are expressed in the formal language PRISM, and the analysis is carried out by the PRISM model checker. The strategy is compositional and based on a comprehensive set of translation rules from Simulink to PRISM. We briefly address soundness and completeness of the rules and, to illustrate the application of the strategy, we apply it to a classical avionics case study: an actuator control system.

Probabilistic verification of Herman’s self-stabilisation algorithm

Abstract Herman’s self-stabilisation algorithm provides a simple randomised solution to the problem of recovering from faults in an N -process token ring. However, a precise analysis of the algorithm’s maximum execution time proves to be surprisingly difficult. McIver and Morgan have conjectured that the worst-case behaviour results from a ring configuration of three evenly spaced tokens, giving an expected time of approximately 0.15 N 2 . However, the tightest upper bound proved to date is 0.64 N 2 . We apply probabilistic verification techniques, using the probabilistic model checker PRISM, to analyse the conjecture, showing it to be correct for all sizes of the ring that can be exhaustively analysed. We furthermore demonstrate that the worst-case execution time of the algorithm can be reduced by using a biased coin.

Tuning Temporal Features within the Stochastic π-Calculus

The stochastic π-calculus is a formalism that has been used for modeling complex dynamical systems where the stochasticity and the delay of transitions are important features, such as in the case of biochemical reactions. Commonly, durations of transitions within stochastic π-calculus models follow an exponential law. The underlying dynamics of such models are expressed in terms of continuous-time Markov chains, which can then be efficiently simulated and model-checked. However, the exponential law comes with a huge variance, making it difficult to model systems with accurate temporal constraints. In this paper, a technique for tuning temporal features within the stochastic π-calculus is presented. This method relies on the introduction of a stochasticity absorption factor by replacing the exponential distribution with the Erlang distribution, which is a sum of exponential random variables. This paper presents a construction of the stochasticity absorption factor in the classical stochastic π-calculus with exponential rates. Tools for manipulating the stochasticity absorption factor and its link with timed intervals for firing transitions are also presented. Finally, the model-checking of such designed models is tackled by supporting the stochasticity absorption factor in a translation from the stochastic π-calculus to the probabilistic model checker PRISM.

Modeling the reliability of a group membership protocol for dual-scheduled time division multiple access networks

We present reliability models for a group membership protocol designed for TDMA networks such as FlexRay, a protocol that is likely to become the de facto standard for next generation automotive networks. The models are based on discrete-time Markov chains and consider a comprehensive set of fault scenarios. Furthermore, they are parametric allowing for a sensitivity analysis. The results, obtained by a numeric solution of the models using the PRISM model-checker, show that they are computationally practical for realistic configurations and that the GMP can achieve reliability levels in the range required for safety critical applications.

A Study of the PDGF Signaling Pathway with PRISM

In this paper, we apply the probabilistic model checker PRISM to the analysis of a biological system -- the Platelet-Derived Growth Factor (PDGF) signaling pathway, demonstrating in detail how this pathway can be analyzed in PRISM. We show that quantitative verification can yield a better understanding of the PDGF signaling pathway.

Steady state property verification of very large systems

Model checking of probabilistic models can be done either by numerical analysis or by simulation and statistical methods. In this paper, we compare the efficiency and the scalability of these approaches when they are applied to the verification of steady state properties of very large models. We provide an experimental comparison study between the statistical model checking using perfect sampling, the numerical method implemented in model checker PRISM and the statistical model checking implemented in model checker MRMC for the verification of CSL steady state properties. We show that the statistical approach using perfect sampling is generally more efficient than the two other approaches and it allows us to consider very large models and to verify rare event properties efficiently.

A Model and Analysis of the AKAP Scaffold

We study the biochemical processes involved in scaffold-mediated crosstalk between the cAMP and the Raf-1/MEK/ERK pathways. We model the system by a continuous time Markov chain with levels and analyse properties using Continuous Stochastic Logic and the symbolic probabilistic model checker PRISM. We consider two kinds of properties of the model, causal events and pulsating behaviour, and, in order to formulate these properties, we enrich the model with trend formulas. The system is currently under wet-lab investigation and our approach was developed in collaboration with the experimentalists.

Parallel probabilistic model checking on general purpose graphics processors

We present algorithms for parallel probabilistic model checking on general purpose graphic processing units (GPGPUs). Our improvements target the numerical components of the traditional sequential algorithms. In particular, we capitalize on the fact that in most of them operations like matrix–vector multiplication and solving systems of linear equations are the main complexity bottlenecks. Since linear algebraic operations can be implemented very efficiently on GPGPUs, the new parallel algorithms show considerable runtime improvements compared to their counterparts on standard architectures. We implemented our parallel algorithms on top of the probabilistic model checker PRISM. The prototype implementation was evaluated on several case studies in which we observed significant speedup over the standard CPU implementation of the tool.

Probabilistic verification and evaluation of Backoff procedure of the WSN ECo-MAC protocol

Communication protocols and techniques are often evaluated using simulation techniques. However, the use of formal modeling and analysis techniques for verification and evaluation in particular for Wireless Sensor Networks (WSN) becomes a necessity. In this paper we present a formal analysis of the backoff procedure integrated in the medium access control protocol named ECo-MAC designed for WSN. We describe this backoff procedure in terms of discrete time Markov chains (DTMCs) and evaluated using the well known probabilistic model checker PRISM. After checking the different invariants of the proposed model, we study the effect of contention window length (in number of time contention unit) on the acceptable number of simultaneous senders in a neighborhood of a given receiver. The obtained quantitative results confirm those provided by the simulation using OPNET tool and justify the validity of the adopted value for the time contention unit TCU.

Quantitative Analysis of System Based on Extended UML State Diagrams and Probabilistic Model Checking

If probabilistic model checking is applied in software architecture, function validation and quantitative analysis for Markov process based real-time model can be automatically performed in model refinement, which will improve software quality. In this paper, the exact definitions and mapping rules between UML state diagrams and probabilistic Kripke structure semantics are proposed, as well as the general translation algorithm of formal semantics. An asynchronous parallel composited DTMC system is illustrated, the key non-function properties of system are described by PCTL, which is automatically validated and analyzed by PRISM model checker. The key system properties are also manually deduced and proved, and compared with the experiment results. The mapping rules we proposed are bi-direction, so it can be used in both forward and reverse software engineering.

Directed Explicit State-Space Search in the Generation of Counterexamples for Stochastic Model Checking

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.

Integrated Simulation and Model-Checking for the Analysis of Biochemical Systems

Model-checking can provide valuable insight into the behaviour of biochemical systems, answering quantitative queries which are more difficult to answer using stochastic simulation alone. However, model-checking is a computationally intensive technique which can become infeasible if the system under consideration is too large. Moreover, the finite nature of the state representation used means that a priori bounds must be set for the numbers of molecules of each species to be observed in the system. In this paper we present an approach which addresses these problems by using stochastic simulation and the PRISM model checker in tandem. The stochastic simulation identifies reasonable bounds for molecular populations in the context of the considered experiment. These bounds are used to parameterise the PRISM model and limit its state space. A simulation pre-run identifies interesting time intervals on which model-checking should focus, if this information is not available from experimental data.