40,402 research outputs found
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
Probabilistic models to describe the dynamics of migrating microbial communities
In all but the most sterile environments bacteria will reside in fluid being transported through conduits and some of these will attach and grow as biofilms on the conduit walls. The concentration and diversity of bacteria in the fluid at the point of delivery will be a mix of those when it entered the conduit and those that have become entrained into the flow due to seeding from biofilms. Examples include fluids through conduits such as drinking water pipe networks, endotracheal tubes, catheters and ventilation systems. Here we present two probabilistic models to describe changes in the composition of bulk fluid microbial communities as they are transported through a conduit whilst exposed to biofilm communities. The first (discrete) model simulates absolute numbers of individual cells, whereas the other (continuous) model simulates the relative abundance of taxa in the bulk fluid. The discrete model is founded on a birth-death process whereby the community changes one individual at a time and the numbers of cells in the system can vary. The continuous model is a stochastic differential equation derived from the discrete model and can also accommodate changes in the carrying capacity of the bulk fluid. These models provide a novel Lagrangian framework to investigate and predict the dynamics of migrating microbial communities. In this paper we compare the two models, discuss their merits, possible applications and present simulation results in the context of drinking water distribution systems. Our results provide novel insight into the effects of stochastic dynamics on the composition of non-stationary microbial communities that are exposed to biofilms and provides a new avenue for modelling microbial dynamics in systems where fluids are being transported
Injecting Abstract Interpretations into Linear Cost Models
We present a semantics based framework for analysing the quantitative
behaviour of programs with regard to resource usage. We start from an
operational semantics equipped with costs. The dioid structure of the set of
costs allows for defining the quantitative semantics as a linear operator. We
then present an abstraction technique inspired from abstract interpretation in
order to effectively compute global cost information from the program.
Abstraction has to take two distinct notions of order into account: the order
on costs and the order on states. We show that our abstraction technique
provides a correct approximation of the concrete cost computations
Value Iteration for Long-run Average Reward in Markov Decision Processes
Markov decision processes (MDPs) are standard models for probabilistic
systems with non-deterministic behaviours. Long-run average rewards provide a
mathematically elegant formalism for expressing long term performance. Value
iteration (VI) is one of the simplest and most efficient algorithmic approaches
to MDPs with other properties, such as reachability objectives. Unfortunately,
a naive extension of VI does not work for MDPs with long-run average rewards,
as there is no known stopping criterion. In this work our contributions are
threefold. (1) We refute a conjecture related to stopping criteria for MDPs
with long-run average rewards. (2) We present two practical algorithms for MDPs
with long-run average rewards based on VI. First, we show that a combination of
applying VI locally for each maximal end-component (MEC) and VI for
reachability objectives can provide approximation guarantees. Second, extending
the above approach with a simulation-guided on-demand variant of VI, we present
an anytime algorithm that is able to deal with very large models. (3) Finally,
we present experimental results showing that our methods significantly
outperform the standard approaches on several benchmarks
Zero-Reachability in Probabilistic Multi-Counter Automata
We study the qualitative and quantitative zero-reachability problem in
probabilistic multi-counter systems. We identify the undecidable variants of
the problems, and then we concentrate on the remaining two cases. In the first
case, when we are interested in the probability of all runs that visit zero in
some counter, we show that the qualitative zero-reachability is decidable in
time which is polynomial in the size of a given pMC and doubly exponential in
the number of counters. Further, we show that the probability of all
zero-reaching runs can be effectively approximated up to an arbitrarily small
given error epsilon > 0 in time which is polynomial in log(epsilon),
exponential in the size of a given pMC, and doubly exponential in the number of
counters. In the second case, we are interested in the probability of all runs
that visit zero in some counter different from the last counter. Here we show
that the qualitative zero-reachability is decidable and SquareRootSum-hard, and
the probability of all zero-reaching runs can be effectively approximated up to
an arbitrarily small given error epsilon > 0 (these result applies to pMC
satisfying a suitable technical condition that can be verified in polynomial
time). The proof techniques invented in the second case allow to construct
counterexamples for some classical results about ergodicity in stochastic Petri
nets.Comment: 20 page
Network-aware Evaluation Environment for Reputation Systems
Parties of reputation systems rate each other and use ratings to compute reputation scores that drive their interactions. When deciding which reputation model to deploy in a network environment, it is important to find the
most suitable model and to determine its right initial configuration. This calls for an engineering approach for describing, implementing and evaluating reputation
systems while taking into account specific aspects of both the reputation systems and the networked environment where they will run. We present a software tool (NEVER) for network-aware evaluation of reputation systems and their rapid prototyping through experiments performed according to user-specified parameters. To demonstrate effectiveness of NEVER, we analyse reputation models based on the beta distribution and the maximum likelihood estimation
An efficient and versatile approach to trust and reputation using hierarchical Bayesian modelling
In many dynamic open systems, autonomous agents must interact with one another to achieve their goals. Such agents may be self-interested and, when trusted to perform an action, may betray that trust by not performing the action as required. Due to the scale and dynamism of these systems, agents will often need to interact with other agents with which they have little or no past experience. Each agent must therefore be capable of assessing and identifying reliable interaction partners, even if it has no personal experience with them. To this end, we present HABIT, a Hierarchical And Bayesian Inferred Trust model for assessing how much an agent should trust its peers based on direct and third party information. This model is robust in environments in which third party information is malicious, noisy, or otherwise inaccurate. Although existing approaches claim to achieve this, most rely on heuristics with little theoretical foundation. In contrast, HABIT is based exclusively on principled statistical techniques: it can cope with multiple discrete or continuous aspects of trustee behaviour; it does not restrict agents to using a single shared representation of behaviour; it can improve assessment by using any observed correlation between the behaviour of similar trustees or information sources; and it provides a pragmatic solution to the whitewasher problem (in which unreliable agents assume a new identity to avoid bad reputation). In this paper, we describe the theoretical aspects of HABIT, and present experimental results that demonstrate its ability to predict agent behaviour in both a simulated environment, and one based on data from a real-world webserver domain. In particular, these experiments show that HABIT can predict trustee performance based on multiple representations of behaviour, and is up to twice as accurate as BLADE, an existing state-of-the-art trust model that is both statistically principled and has been previously shown to outperform a number of other probabilistic trust models
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