23,330 research outputs found
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
A Tutorial on Advanced Dynamic Monte Carlo Methods for Systems with Discrete State Spaces
Advanced algorithms are necessary to obtain faster-than-real-time dynamic
simulations in a number of different physical problems that are characterized
by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms
that preserve the dynamics of the model are described. These include the
-fold way algorithm, the Monte Carlo with Absorbing Markov Chains (MCAMC)
algorithm, and the Projective Dynamics (PD) algorithm. To demonstrate the use
of these algorithms, they are applied to some simplified models of dynamic
physical systems. The models studied include a model for ion motion through a
pore such as a biological ion channel and the metastable decay of the
ferromagnetic Ising model. Non-trivial parallelization issues for these dynamic
algorithms, which are in the class of parallel discrete event simulations, are
discussed. Efforts are made to keep the article at an elementary level by
concentrating on a simple model in each case that illustrates the use of the
advanced dynamic Monte Carlo algorithm.Comment: 53 pages, 17 figure
Estimating the Probability of a Rare Event Over a Finite Time Horizon
We study an approximation for the zero-variance change of measure to estimate the probability of a rare event in a continuous-time Markov chain. The rare event occurs when the chain reaches a given set of states before some fixed time limit. The jump rates of the chain are expressed as functions of a rarity parameter in a way that the probability of the rare event goes to zero when the rarity parameter goes to zero, and the behavior of our estimators is studied in this asymptotic regime. After giving a general expression for the zero-variance change of measure in this situation, we develop an approximation of it via a power series and show that this approximation provides a bounded relative error when the rarity parameter goes to zero. We illustrate the performance of our approximation on small numerical examples of highly reliableMarkovian systems. We compare it to a previously proposed heuristic that combines forcing with balanced failure biaising. We also exhibit the exact zero-variance change of measure for these examples and compare it with these two approximations
Accurate Reaction-Diffusion Operator Splitting on Tetrahedral Meshes for Parallel Stochastic Molecular Simulations
Spatial stochastic molecular simulations in biology are limited by the
intense computation required to track molecules in space either in a discrete
time or discrete space framework, meaning that the serial limit has already
been reached in sub-cellular models. This calls for parallel simulations that
can take advantage of the power of modern supercomputers; however exact methods
are known to be inherently serial. We introduce an operator splitting
implementation for irregular grids with a novel method to improve accuracy, and
demonstrate potential for scalable parallel simulations in an initial MPI
version. We foresee that this groundwork will enable larger scale, whole-cell
stochastic simulations in the near future.Comment: 33 pages, 10 figure
Update statistics in conservative parallel discrete event simulations of asynchronous systems
We model the performance of an ideal closed chain of L processing elements
that work in parallel in an asynchronous manner. Their state updates follow a
generic conservative algorithm. The conservative update rule determines the
growth of a virtual time surface. The physics of this growth is reflected in
the utilization (the fraction of working processors) and in the interface
width. We show that it is possible to nake an explicit connection between the
utilization and the macroscopic structure of the virtual time interface. We
exploit this connection to derive the theoretical probability distribution of
updates in the system within an approximate model. It follows that the
theoretical lower bound for the computational speed-up is s=(L+1)/4 for L>3.
Our approach uses simple statistics to count distinct surface configuration
classes consistent with the model growth rule. It enables one to compute
analytically microscopic properties of an interface, which are unavailable by
continuum methods.Comment: 15 pages, 12 figure
Fluid Model Checking of Timed Properties
We address the problem of verifying timed properties of Markovian models of
large populations of interacting agents, modelled as finite state automata. In
particular, we focus on time-bounded properties of (random) individual agents
specified by Deterministic Timed Automata (DTA) endowed with a single clock.
Exploiting ideas from fluid approximation, we estimate the satisfaction
probability of the DTA properties by reducing it to the computation of the
transient probability of a subclass of Time-Inhomogeneous Markov Renewal
Processes with exponentially and deterministically-timed transitions, and a
small state space. For this subclass of models, we show how to derive a set of
Delay Differential Equations (DDE), whose numerical solution provides a fast
and accurate estimate of the satisfaction probability. In the paper, we also
prove the asymptotic convergence of the approach, and exemplify the method on a
simple epidemic spreading model. Finally, we also show how to construct a
system of DDEs to efficiently approximate the average number of agents that
satisfy the DTA specification
Simulation of networks of spiking neurons: A review of tools and strategies
We review different aspects of the simulation of spiking neural networks. We
start by reviewing the different types of simulation strategies and algorithms
that are currently implemented. We next review the precision of those
simulation strategies, in particular in cases where plasticity depends on the
exact timing of the spikes. We overview different simulators and simulation
environments presently available (restricted to those freely available, open
source and documented). For each simulation tool, its advantages and pitfalls
are reviewed, with an aim to allow the reader to identify which simulator is
appropriate for a given task. Finally, we provide a series of benchmark
simulations of different types of networks of spiking neurons, including
Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based
or conductance-based synapses, using clock-driven or event-driven integration
strategies. The same set of models are implemented on the different simulators,
and the codes are made available. The ultimate goal of this review is to
provide a resource to facilitate identifying the appropriate integration
strategy and simulation tool to use for a given modeling problem related to
spiking neural networks.Comment: 49 pages, 24 figures, 1 table; review article, Journal of
Computational Neuroscience, in press (2007
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