Probabilistic Symbolic Model Research Articles

Utilizing Continuous Time Markov Chain for analyzing video-on-demand streaming in multimedia systems

In multimedia systems, Tree and Mesh-based topologies are the popular ways to organize the peers in an overlay and provide video streaming services. Unlike Content Delivery Networks (CDN), providing streaming services through a Peer-to-Peer (P2P) overlay poses the challenge of unpredictable churn for both provider and consumer peers. The dynamically arriving and departing peers, with Video Cassette Recorder (VCR) actions like jump, pause, forward, rewind, etc., controlled by end users, makes it challenging to reason about such systems. Though techniques like prototype test beds, simulation, etc., are successful to some extent in analyzing the behavior of such complex systems before the actual deployment, they either require lots of effort to set up or fail to capture the finer anomalies. Therefore, there is a need to have a formal framework that can specify the system at the desired abstraction level and capture the stochastic behavior exhibited by the actors of such systems. This paper addresses this issue and provides a platform for analyzing the behavior of real-time Video-on-Demand (VoD) streaming behavior with VCR actions over P2P overlays. To capture the stochastic behavior of actors, the Continuous Time Markov Chain (CTMC) is used to design a model of both the tree and mesh-based systems. This CTMC model is written in the Probabilistic Symbolic Model Checker (PRISM) language, which assists in containing the state space explosion and specifies the QoUX properties using Continuous Stochastic Logic (CSL). The proposed methodology uses the scenarios described in various simulation-based studies and industry standards of VoD systems available in the proposed formal model and finds a striking resemblance in the results. Eventually, given a joining-delay threshold of 170 ms, a P2P-Tree-based architecture resulted in an optimal tree height of 4-5 levels; after that, the startup delay of playback gets affected. Similarly, for a given startup delay threshold of 700 ms after departure and seek-jump actions, the maximum P2P-Tree height should be 5. We have also compared the performance properties of P2P tree and mesh-based VoD streaming systems with industry standards of centralized VoD systems. It is observed that the performance of P2P-tree and P2P-mesh-based VoD streaming systems also meet the industry standards. The results we got from the proposed formal framework are conclusive and establish the applicability of the approach.

Probabilistic model checking of cancer metabolism

Cancer cell metabolism is often deregulated as a result of adaption to meeting energy and biosynthesis demands of rapid growth or direct mutation of key metabolic enzymes. Better understanding of such deregulation can provide new insights on targetable vulnerabilities, but is complicated by the difficulty in probing cell metabolism at different levels of resolution and under different experimental conditions. We construct computational models of glucose and glutamine metabolism with focus on the effect of IDH1/2-mutations in cancer using a combination of experimental metabolic flux data and patient-derived gene expression data. Our models demonstrate the potential of computational exploration to reveal biologic behavior: they show that an exogenously-mutated IDH1 experimental model utilizes glutamine as an alternative carbon source for lactate production under hypoxia, but does not fully-recapitulate the patient phenotype under normoxia. We also demonstrate the utility of using gene expression data as a proxy for relative differences in metabolic activity. We use the approach of probabilistic model checking and the freely-available Probabilistic Symbolic Model Checker to construct and reason about model behavior.

Probabilistic Modeling of Histogram Based Fuzzy Image Enhancement Algorithm

Probabilistic model checking is frequently used to examine stochastic behavior. Model-checking is important for examining before extensive simulations, in differing fields, including computer communications, networks, security, and biology. In this work performance of histogram-based fuzzy image enhancement (HFIE Algorithm). The fuzzy contrast enhancement algorithm based on histograms is used to improve low contrast colored photographs. K is the contrast intensification parameter calculated from the histogram. The RGB image is transformed into HSV to preserve the chromatic information in the original image. To improve the image, only the V component is stretched using the M and K parameters. HFIE Algorithm is analyzed by developing its Discrete-time Markov Chain (DTMC) model in the Probabilistic Symbolic Model Checker (PRISM). First, a labeled transition diagram showing the functionality of HFIE Algorithm is constructed, then the HFIE Algorithm model using the PRISM tool is developed. The expected time to convert RGB image to HSV, probability of achieving enhanced RGB image, and expected SNR are measured with the help of properties.

Probabilistic modelling of deception-based security framework using markov decision process

Existing studies using deception are ad-hoc attempts and few theoretical models have been designed to plan and integrate deception. We theorise that a pre-planning stage should be a fundamental part to obtain information about the attackers’ behaviours and the attack process by analysing known attacks. This will help plan and take defence actions by actively interacting with the attackers and predicting their actions using a probabilistic approach. This paper proposes a framework that provides a theoretical understanding to plan and integrate deception systematically and strategically. We also present probabilistic modelling to predict attack actions by formalising a real case of attacks captured on simulated Internet of Things devices as an Markov Decision Process (MDP) and verifying related properties using Probabilistic Symbolic Model Checker (PRISM). MDP’s properties verification results reveal that the associated cost for defence actions can be decreased by successfully predicting attackers’ probable actions. Moreover, we identify several quantification metrics (e.g. cost, reward, trust, incentive and penalty) to evaluate the performance of actions performed by attackers and defenders.

Quantitative survivability analysis using probability model checking: A study of cluster-based vehicle networks with dual cluster heads

As an important part of future 5G wireless networks, a vehicular network demands safety, reliability and connectivity. In this context, networking survivability is usually considered an important metric to evaluate network performance. In this paper, we propose a survivability model for vehicle communication networking based on dual cluster heads, wherein a backup cluster head (CH) will be activated if the primary CH fails, thereby effectively enhancing the network lifetime. Additionally, we introduce a software rejuvenation strategy for the prime CH to further improve the survivability of the entire network. Using the Probabilistic Symbolic Model Checker (PRISM), we verify and discuss the proposed survivability model via numerical simulations. The results show that network survivability can be effectively improved by introducing an additional CH and further enhanced by adopting the software rejuvenation technique.

A Probabilistic Extension of UML-B

This paper extends the graphical and formal language of UML-B to provide the ability to model probabilities. Discrete probabilities, interval probabilities, and stochastic delays are added to the UML-B's state-machine syntax, and their corresponding semantics are defined in Event-B. In addition, as a secondary contribution, UML-B (probabilistic) state-machine models are defined as MDP (Markov Decision Process) models in order to provide a means of quantitative verification in PRISM (Probabilistic Symbolic Model Checker). As an important feature of the proposed method, it does not change the Event-B syntax or semantics. To evaluate this work, as a case study, the Zeroconf protocol will be modeled in the extended UML-B using the Rodin tool, and its Event-B counterpart is converted to a PRISM model. The results of evaluations indicate that this study's additions provide the capability of modeling and verification of probabilistic and stochastic systems.

Formal Analysis of an Energy-aware Collision Resolution Protocol for Wireless Sensor Networks

This paper provides a comprehensive and rigorous study of a novel collision resolution algorithm for wireless sensor networks: 2CS-WSN. It is specifically designed to be used during the contention phase of IEEE 802.15.4. This algorithm has been modelled in terms of discrete time Markov chains (DTMCs) and, using the probabilistic symbolic model checker PRISM, correctness properties and different operation modes of the algorithm have been studied. Moreover, different model abstractions have been used in order to identify any inconsistencies or ambiguities, and to prove interesting properties for non-trivial, practical and relevant scenarios. Finally, since the biggest source of energy waste is the collision, this paper conducts a wide study of energy saving in this algorithm.

Probabilistic Model Checking: One Step Forward in Wireless Sensor Networks Simulation

A novel collision resolution algorithm for wireless sensor networks is formally analysed via probabilistic model checking. The algorithm called 2CS-WSN is specifically designed to be used during the contention phase of IEEE 802.15.4. Discrete time Markov chains (DTMCs) have been proposed as modelling formalism and the well-known probabilistic symbolic model checker PRISM is used to check some correctness properties and different operating modes and, furthermore, to collect some performance measures. Thus, all the benefits of formal verification and simulation are gathered. These correctness properties as well as practical and relevant scenarios for the real world have agreed with the algorithm designers.

Security analysis of socio-technical physical systems

Recent initiatives that evaluate the security of physical systems with objects as assets and people as agents – here called socio-technical physical systems – have limitations: their agent behavior is too simple, they just estimate feasibility and not the likelihood of attacks, or they do estimate likelihood but on explicitly provided attacks only. We propose a model that can detect and quantify attacks. It has a rich set of agent actions with associated probability and cost. We also propose a threat model, an intruder that can misbehave and that competes with honest agents. The intruder’s actions have an associated cost and are constrained to be realistic. We map our model to a probabilistic symbolic model checker and we express templates of security properties in the Probabilistic Computation Tree Logic, thus supporting automatic analysis of security properties. A use case shows the effectiveness of our approach.

Quantitative and qualitative analysis of SysML activity diagrams

Model-driven engineering refers to a range of approaches that uses models throughout systems and software development life cycle. Towards sustaining such a successful approach in practice, we present a model-based verification framework that supports the quantitative and qualitative analysis of SysML activity diagrams. To this end, we propose an algorithm that maps SysML activity diagrams into Markov decision processes expressed using the language of the probabilistic symbolic model checker PRISM. Furthermore, we elaborate on the correctness of our translation algorithm by proving its soundness with respect to a SysML activity diagrams operational semantics that we also present in this work. The generated models can be verified against a set of properties expressed in the probabilistic computation tree logic. To automate our approach, we developed a prototype tool that interfaces a modeling environment and the probabilistic model checker. We also show how to leverage adversary generation to provide the developer with a useful counterexample/witness as a feedback on the verified properties. Finally, the established theoretical foundations are complemented with an illustrative case study that demonstrates the usability and benefit of such a framework.

A formal verification framework for SysML activity diagrams

SysML activity diagrams are OMG/INCOSE standard diagrams used for modeling and specifying probabilistic systems. They support systems composition by call behavior and send/receive artifacts. For verification, the existing approaches dedicated to these diagrams are limited to a restricted set of artifacts. In this paper, we propose a formal verification framework for these diagrams that supports the most important artifacts. It is based on mapping a composition of SysML activity diagrams to the input language of the probabilistic symbolic model checker called “PRISM”. To prove the soundness of our mapping approach, we capture the underlying semantics of both the SysML activity diagrams and their generated PRISM code. We found that the probabilistic equivalence relation between both semantics preserve the satisfaction of the system requirements. Finally, we demonstrate the effectiveness of our approach by presenting real case studies.

Modelling and symmetry reduction of a target-tracking protocol using wireless sensor networks

To achieve precise modelling of real-time systems stochastic behaviours are considered which lead towards probabilistic modelling. Probabilistic modelling has been successfully employed in wide array of application domains including, for example, randomised distributed algorithms, communication, security and power management protocols. This study is an improvement over our previous work, which was based on the probabilistic analysis of a cluster-based fault tolerant target-tracking protocol (FTTT) using only grid-based sensor nodes arrangement. Probabilistic modelling is chosen for the analysis of FTTT protocol to facilitate benefits of symmetry reduction in conjunction with modelling. It is believed that for the first time correctness of the simplified version of a target-tracking protocol is verified by developing its continuous-time Markov chain (CTMC) model using symbolic modelling language. The proposed probabilistic model of a target-tracking wireless sensor networks will help to analyse the phases of FTTT protocol on a limited scale with finite utilisation of time. There are three main contributions of this study; first consideration of synchronised events between the modules, second, random placement of sensor nodes is taken into account in addition to grid-based sensor node arrangement, third one is the reduction in state space size through symmetry reduction technique, which also facilitates to analyse a larger size network. Symmetry reduction on Probabilistic Symbolic Model (PRISM) checker models is performed by PRISM-symm and the generic representatives in PRISM (GRIP) tool. Modelling of FTTT protocol is proved better with the usage of PRISM-symm after comparing the results of PRISM model, PRISM-symm and GRIP.

Modeling A Multi-Compartments Biological System with Membrane Computing

Problem statement: Most of the biological systems have been hierarchical in structure with processes interacting between different compartments. Membrane computing formalism has provided modeling capabilities in representing the structure of biological systems. Approach: This study was carried to investigate the modeling of a multi-compartment biological system by using membrane computing formalism. The hormone-induced calcium oscillations in liver cells which was modeled with ordinary differential equation was used as a case study. The membrane computing model of this case study was verified and validated by using simulation strategy of Gillespie algorithm and the method of model checking using probabilistic symbolic model checker. The results of membrane computing model were compared to the ordinary differential equation model. Results: The simulation and model checking of membrane computing model of the biological case study showed that the properties of the multi-compartments biological system could be preserved with the membrane computing model. Membrane computing model could also accommodate the structure and processes of the multi-compartments biological system which were absent in the ordinary differential equation model. Conclusion: Membrane computing model provides a better approach in representing a multi-compartment system and able to sustain the basic properties of the system. However appropriate value of parameters to represent the rules of the processes of the membrane computing model to manage the stochastic behavior should be formulated to meet the performance of the biological system.

Model Checking the Biological Model of Membrane Computing with Probabilistic Symbolic Model Checker by Using Two Biological Systems

Problem statement: Membrane computing formalism has provided better modeling capabilities for biological systems in comparison to conventional mathematical models. Model checking could be used to reason about the biological system in detail and with precision by verifying formally whether membrane computing model meets the properties of the system. Approach: This study was carried to investigate the preservation of properties of two biological systems that had been modeled and simulated in membrane computing by a method of model checking using PRISM. The two biological systems were prey-predator population and signal processing in the legend-receptor networks of protein TGF-β. Results: The model checking of membrane computing model of the biological systems with five different properties showed that the properties of the biological systems could be preserved in the membrane computing model. Conclusion: Membrane computing model not only provides a better approach in representing and simulating a biological system but also able to sustain the basic properties of the system.

Probabilistic symbolic model checking with PRISM: a hybrid approach

In this paper we present efficient symbolic techniques for probabilistic model checking. These have been implemented in PRISM, a tool for the analysis of probabilistic models such as discrete-time Markov chains, continuous-time Markov chains and Markov decision processes using specifications in the probabilistic temporal logics PCTL and CSL. Motivated by the success of model checkers such as SMV which use BDDs (binary decision diagrams), we have developed an implementation of PCTL and CSL model checking based on MTBDDs (multi-terminal BDDs) and BDDs. Existing work in this direction has been hindered by the generally poor performance of MTBDD-based numerical computation, which is often substantially slower than explicit methods using sparse matrices. The focus of this paper is a novel hybrid technique which combines aspects of symbolic and explicit approaches to overcome these performance problems. For typical examples, we achieve a dramatic improvement over the purely symbolic approach. In addition, thanks to the compact model representation using MTBDDs, we can verify systems an order of magnitude larger than with sparse matrices, while almost matching or even beating them for speed.