20,510 research outputs found
Using the probabilistic evaluation tool for the analytical solution of large Markov models
Stochastic Petri net-based Markov modeling is a potentially very powerful and generic approach for evaluating the performance and dependability of many different systems, such as computer systems, communication networks, manufacturing systems, etc. As a consequence of their general applicability, SPN-based Markov models form the basic solution approach for several software packages that have been developed for the analytic solution of performance and dependability models. In these tools, stochastic Petri nets are used to conveniently specify complicated models, after which an automatic mapping can be carried out to an underlying Markov reward model. Subsequently, this Markov reward model is solved by specialized solution algorithms, appropriately selected for the measure of interest. One of the major aspects that hampers the use of SPN-based Markov models for the analytic solution of performance and dependability results is the size of the state space. Although typically models of up to a few hundred thousand states can conveniently be solved on modern-day work-stations, often even larger models are required to represent all the desired detail of the system. Our tool PET (probabilistic evaluation tool) circumvents problems of large state spaces when the desired performance and dependability measure are transient measures. It does so by an approach named probabilistic evaluatio
Evaluating the reliability of NAND multiplexing with PRISM
Probabilistic-model checking is a formal verification technique for analyzing the reliability and performance of systems exhibiting stochastic behavior. In this paper, we demonstrate the applicability of this approach and, in particular, the probabilistic-model-checking tool PRISM to the evaluation of reliability and redundancy of defect-tolerant systems in the field of computer-aided design. We illustrate the technique with an example due to von Neumann, namely NAND multiplexing. We show how, having constructed a model of a defect-tolerant system incorporating probabilistic assumptions about its defects, it is straightforward to compute a range of reliability measures and investigate how they are affected by slight variations in the behavior of the system. This allows a designer to evaluate, for example, the tradeoff between redundancy and reliability in the design. We also highlight errors in analytically computed reliability bounds, recently published for the same case study
Evaluating the reliability of NAND multiplexing with PRISM
Probabilistic-model checking is a formal verification technique for analyzing the reliability and performance of systems exhibiting stochastic behavior. In this paper, we demonstrate the applicability of this approach and, in particular, the probabilistic-model-checking tool PRISM to the evaluation of reliability and redundancy of defect-tolerant systems in the field of computer-aided design. We illustrate the technique with an example due to von Neumann, namely NAND multiplexing. We show how, having constructed a model of a defect-tolerant system incorporating probabilistic assumptions about its defects, it is straightforward to compute a range of reliability measures and investigate how they are affected by slight variations in the behavior of the system. This allows a designer to evaluate, for example, the tradeoff between redundancy and reliability in the design. We also highlight errors in analytically computed reliability bounds, recently published for the same case study
Practical applications of probabilistic model checking to communication protocols
Probabilistic model checking is a formal verification technique for the analysis of systems that exhibit stochastic behaviour. It has been successfully employed in an extremely wide array of application domains including, for example, communication and multimedia protocols, security and power management. In this chapter we focus on the applicability of these techniques to the analysis of communication protocols. An analysis of the performance of such systems must successfully incorporate several crucial aspects, including concurrency between multiple components, real-time constraints and randomisation. Probabilistic model checking, in particular using probabilistic timed automata, is well suited to such an analysis. We provide an overview of this area, with emphasis on an industrially relevant case study: the IEEE 802.3 (CSMA/CD) protocol. We also discuss two contrasting approaches to the implementation of probabilistic model checking, namely those based on numerical computation and those based on discrete-event simulation. Using results from the two tools PRISM and APMC, we summarise the advantages, disadvantages and trade-offs associated with these techniques
An Analytical Solution for Probabilistic Guarantees of Reservation Based Soft Real-Time Systems
We show a methodology for the computation of the probability of deadline miss
for a periodic real-time task scheduled by a resource reservation algorithm. We
propose a modelling technique for the system that reduces the computation of
such a probability to that of the steady state probability of an infinite state
Discrete Time Markov Chain with a periodic structure. This structure is
exploited to develop an efficient numeric solution where different
accuracy/computation time trade-offs can be obtained by operating on the
granularity of the model. More importantly we offer a closed form conservative
bound for the probability of a deadline miss. Our experiments reveal that the
bound remains reasonably close to the experimental probability in one real-time
application of practical interest. When this bound is used for the optimisation
of the overall Quality of Service for a set of tasks sharing the CPU, it
produces a good sub-optimal solution in a small amount of time.Comment: IEEE Transactions on Parallel and Distributed Systems, Volume:27,
Issue: 3, March 201
Construction and Verification of Performance and Reliability Models
Over the last two decades formal methods have been extended towards performance and reliability evaluation. This paper tries to provide a rather intuitive explanation of the basic concepts and features in this area.
Instead of striving for mathematical rigour, the intention is to give an illustrative introduction to the basics of stochastic models, to stochastic modelling using process algebra, and to model checking as a technique to analyse stochastic models
Probabilistic Numerics and Uncertainty in Computations
We deliver a call to arms for probabilistic numerical methods: algorithms for
numerical tasks, including linear algebra, integration, optimization and
solving differential equations, that return uncertainties in their
calculations. Such uncertainties, arising from the loss of precision induced by
numerical calculation with limited time or hardware, are important for much
contemporary science and industry. Within applications such as climate science
and astrophysics, the need to make decisions on the basis of computations with
large and complex data has led to a renewed focus on the management of
numerical uncertainty. We describe how several seminal classic numerical
methods can be interpreted naturally as probabilistic inference. We then show
that the probabilistic view suggests new algorithms that can flexibly be
adapted to suit application specifics, while delivering improved empirical
performance. We provide concrete illustrations of the benefits of probabilistic
numeric algorithms on real scientific problems from astrometry and astronomical
imaging, while highlighting open problems with these new algorithms. Finally,
we describe how probabilistic numerical methods provide a coherent framework
for identifying the uncertainty in calculations performed with a combination of
numerical algorithms (e.g. both numerical optimisers and differential equation
solvers), potentially allowing the diagnosis (and control) of error sources in
computations.Comment: Author Generated Postprint. 17 pages, 4 Figures, 1 Tabl
Transient Reward Approximation for Continuous-Time Markov Chains
We are interested in the analysis of very large continuous-time Markov chains
(CTMCs) with many distinct rates. Such models arise naturally in the context of
reliability analysis, e.g., of computer network performability analysis, of
power grids, of computer virus vulnerability, and in the study of crowd
dynamics. We use abstraction techniques together with novel algorithms for the
computation of bounds on the expected final and accumulated rewards in
continuous-time Markov decision processes (CTMDPs). These ingredients are
combined in a partly symbolic and partly explicit (symblicit) analysis
approach. In particular, we circumvent the use of multi-terminal decision
diagrams, because the latter do not work well if facing a large number of
different rates. We demonstrate the practical applicability and efficiency of
the approach on two case studies.Comment: Accepted for publication in IEEE Transactions on Reliabilit
Parametric Inference for Biological Sequence Analysis
One of the major successes in computational biology has been the unification,
using the graphical model formalism, of a multitude of algorithms for
annotating and comparing biological sequences. Graphical models that have been
applied towards these problems include hidden Markov models for annotation,
tree models for phylogenetics, and pair hidden Markov models for alignment. A
single algorithm, the sum-product algorithm, solves many of the inference
problems associated with different statistical models. This paper introduces
the \emph{polytope propagation algorithm} for computing the Newton polytope of
an observation from a graphical model. This algorithm is a geometric version of
the sum-product algorithm and is used to analyze the parametric behavior of
maximum a posteriori inference calculations for graphical models.Comment: 15 pages, 4 figures. See also companion paper "Tropical Geometry of
Statistical Models" (q-bio.QM/0311009
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