Modelling, reduction and analysis of Markov automata (extended version)

Markov automata (MA) constitute an expressive continuous-time compositional modelling formalism. They appear as semantic backbones for engineering frameworks including dynamic fault trees, Generalised Stochastic Petri Nets, and AADL. Their expressive power has thus far precluded them from effective analysis by probabilistic (and statistical) model checkers, stochastic game solvers, or analysis tools for Petri net-like formalisms. This paper presents the foundations and underlying algorithms for efficient MA modelling, reduction using static analysis, and most importantly, quantitative analysis. We also discuss implementation pragmatics of supporting tools and present several case studies demonstrating feasibility and usability of MA in practice

Analysis of Timed and Long-Run Objectives for Markov Automata

Markov automata (MAs) extend labelled transition systems with random delays and probabilistic branching. Action-labelled transitions are instantaneous and yield a distribution over states, whereas timed transitions impose a random delay governed by an exponential distribution. MAs are thus a nondeterministic variation of continuous-time Markov chains. MAs are compositional and are used to provide a semantics for engineering frameworks such as (dynamic) fault trees, (generalised) stochastic Petri nets, and the Architecture Analysis & Design Language (AADL). This paper considers the quantitative analysis of MAs. We consider three objectives: expected time, long-run average, and timed (interval) reachability. Expected time objectives focus on determining the minimal (or maximal) expected time to reach a set of states. Long-run objectives determine the fraction of time to be in a set of states when considering an infinite time horizon. Timed reachability objectives are about computing the probability to reach a set of states within a given time interval. This paper presents the foundations and details of the algorithms and their correctness proofs. We report on several case studies conducted using a prototypical tool implementation of the algorithms, driven by the MAPA modelling language for efficiently generating MAs.Comment: arXiv admin note: substantial text overlap with arXiv:1305.705

Coupling of Active Motion and Advection Shapes Intracellular Cargo Transport

Intracellular cargo transport can arise from passive diffusion, active motor-driven transport along cytoskeletal filament networks, and passive advection by fluid flows entrained by such motor/cargo motion. Active and advective transport are thus intrinsically coupled as related, yet different representations of the same underlying network structure. A reaction-advection-diffusion system is used here to show that this coupling affects the transport and localization of a passive tracer in a confined geometry. For sufficiently low diffusion, cargo localization to a target zone is optimized either by low reaction kinetics and decoupling of bound and unbound states, or by a mostly disordered cytoskeletal network with only weak directional bias. These generic results may help to rationalize subtle features of cytoskeletal networks, for example as observed for microtubules in fly oocytes.Comment: revtex, 5 pages, 5 figures, to appear in PRL (http://prl.aps.org/

Asymmetric Optical Radiation Pressure Effects on Liquid Interfaces Under Intense Illumination

Deformations of horizontal liquid interfaces by optical radiation pressure are generally expected to display similar behaviors whatever the direction of propagation of the exciting laser beam is. In the present experiment we find this expectation to be borne out, as long as the cw laser illumination is moderate in strength. However, as a striking contrast in the case of high field strengths, we find that either a large stable tether can be formed, or else that a break-up of the interface can occur, depending on whether the laser beam is upward or downward directed. Physically, the reason for this asymmetry can be traced to whether total reflection can occur or not. We also present two simple theoretical models, one based on geometrical optics, the other on wave optics, that are able to illustrate the essence of the effect. In the case leading to interface disruption our experimental results are compared with those obtained by Zhang and Chang for water droplets under intense laser pulses [Opt. Lett. \textbf{13}, 916 (1988)]. A key point in our experimental investigations is to work with a near-critical liquid/liquid interface. The surface tension becomes therefore significantly reduced, which thus enhances the magnitude of the stationary deformations induced.Comment: 25 pages text, plus 6 figures. Discussion expanded. Submitted to JOSA

Time dependent analysis with dynamic counter measure trees

The success of a security attack crucially depends on time: the more time available to the attacker, the higher the probability of a successful attack. Formalisms such as Reliability block diagrams, Reliability graphs and Attack Countermeasure trees provide quantitative information about attack scenarios, but they are provably insufficient to model dependent actions which involve costs, skills, and time. In this presentation, we extend the Attack Countermeasure trees with a notion of time; inspired by the fact that there is a strong correlation between the amount of resources in which the attacker invests (in this case time) and probability that an attacker succeeds. This allows for an effective selection of countermeasures and rank them according to their resource consumption in terms of costs/skills of installing them and effectiveness in preventing an attack

Fault maintenance trees: reliability centered maintenance via statistical model checking

The current trend in infrastructural asset management is towards risk-based (a.k.a. reliability centered) maintenance, promising better performance at lower cost. By maintaining crucial components more intensively than less important ones, dependability increases while costs decrease.\ud \ud This requires good insight into the effect of maintenance on the dependability and associated costs. To gain these insights, we propose a novel framework that integrates fault tree analysis with maintenance. We support a wide range of maintenance procedures and dependability measures, including the system reliability, availability, mean time to failure, as well as the maintenance and failure costs over time, split into different cost components.\ud \ud Technically, our framework is realized via statistical model checking, a state-of-the-art tool for flexible modelling and simulation. Our compositional approach is flexible and extendible. We deploy our framework to two cases from industrial practice: insulated joints, and train compressors

Extending Markov Automata with State and Action Rewards

This presentation introduces the Markov Reward Automaton (MRA), an extension of the Markov automaton that allows the modelling of systems incorporating rewards in addition to nondeterminism, discrete probabilistic choice and continuous stochastic timing. Our models support both rewards that are acquired instantaneously when taking certain transitions (action rewards) and rewards that are based on the duration that certain conditions hold (state rewards). In addition to introducing the MRA model, we extend the process-algebraic language MAPA to easily specify MRAs. Also, we provide algorithms for computing the expected reward until reaching one of a certain set of goal states, as well as the long-run average reward. We extended the MAMA tool chain (consisting of the tools SCOOP and IMCA) to implement the reward extension of MAPA and these algorithms